Abstract

By selectively blocking specific laser beams, we investigate coexisting seven distinguishable dressed odd-order multi-wave mixing (MWM) signals in a K-type five-level atomic system. We demonstrate that the enhancement and suppression of dressed four-wave mixing (FWM) signal can be directly detected by scanning the dressing field instead of the probe field. We also study the temporal and spatial interference between two FWM signals. Surprisingly, the pure-suppression of six-wave mixing signal has been shifted far away from resonance by atomic velocity component. Moreover, the interactions among six MWM signals have been studied.

©2012 Optical Society of America

1. Introduction

Recently a lot of attention has been concentrated on the four-wave mixing (FWM) [15] and six-wave-mixing (SWM) [6-8] under atomic coherence. And electromagnetically induced transparency (EIT) [9, 10] is an beneficial tool to investigate these multi-wave mixing (MWM) processes since the weak generated signals can be allowed to transmit through the resonant atomic medium with little absorption. It also plays an important role in lasing without inversion [11], quantum communications [12], slow light [13], photon controlling and information storage [1416]. Furthermore, the enhancement and suppression of FWM also attracted the attention of many researchers, which has been experimentally studied and the generated FWM signals can be selectively enhanced and suppressed [17]. Besides, the doubly-dressed states in cold atoms were observed, in which triple-photon absorption spectrum exhibits a constructive interference between transition paths of two closely spaced, doubly-dressed-states [18, 19]. In addition, the generated FWM and SWM signals can be made to coexist and interfere with each other not only in the frequency domain but also spatially, using phase control [20].

In this paper, we show seven coexisting distinguishable multi-wave mixing signals (including three FWM and four SWM signals) by selectively blocking different laser beams in a K-type five-level atomic system. Also by blocking several certain laser beams respectively, the interactions among six MWM signals have been studied. In addition, when scanning the frequency detuning of external-dressing, self-dressing and probe fields respectively in the dressed FWM process, we first analyze the corresponding relationship and differentia between the experimental results of different scanning methods, and demonstrate that scanning the dressing field can be used as a technique to directly observe the dressing effects of FWM process. Also, we first observe the enhancement and suppression of SWM signal at large detuning, due to the atomic velocity component and optical pumping effect. Moreover, we demonstrate the temporal and spatial interferences between two FWM signals.

2. Basic theory and experimental scheme

The experiments are performed in a five-level atomic system as shown in Fig. 1(a) where the five energy levels are 5S1/2(F=3)(|0), 5P3/2(|1), 5D5/2(|2), 5S1/2(F=2)(|3) and 5D3/2(|4) in 85Rb. The resonant frequencies are Ω1, Ω2, Ω3 and Ω4 for transitions|0 to |1, |1 to |2,|1 to |3 and |1 to |4 respectively. The lower transition |0 to |1 is driven and probed by a weak laser beam E1, and the two strong coupling beams E2 and E2 connect with the transition |1 to |2. Two pumping beams E3 and E3 are applied to drive the transition |1 to |3 and two additional strong coupling beams E4 and E4 drive the transition |1 to |4. In the experimental setup, the two coupling beams E2 (frequency ω2, wave vector k2, Rabi frequency G2 and frequency detuning Δ2, where Δi=Ωiωi) and E2 (ω2, k2, G2 and Δ2) with vertical polarization (wavelength 775.978nm) are from the same external cavity diode laser (ECDL) . The other two vertically polarized coupling beams E4 (ω4, k4, G4 and Δ4) and E4 (ω4, k4, G4 and Δ4) are from a tapered-amplifier diode laser with the same wavelength 776.157nm. Two pumping beams E3(ω3, k3, G3 and Δ3) and E3 (ω3, k3, G3 and Δ3) with equal power are split from a LD beam and have polarizations vertical with each other via a polarization beam splitter. The probe beam E1 (ω1, k1, G1 and Δ1) is generated by a ECDL (Toptica DL100L) with horizontally polarization. These laser beams are spatially designed in a square-box pattern as shown in Fig. 1(b), in which the laser beams E2, E2, E3, E3, E4 and E4 propagate through the Rubidium vapor cell (50mm long) with a temperature of 60 °C in the same direction with small angles (about 0.3°) between one another, and the probe beam E1 propagates in the opposite direction with a small angle from the other beams.

 

Fig. 1 (a) The diagram of the K-type five-level atomic system. (b) Spatial beam geometry used in the experiment. (c) The diagram of the ladder-type three-level atomic subsystem when the fieldsE3, E3, E4 and E4 are blocked and E1, E2 and E2 are turned on. (d) The diagram of the Y-type four-level atomic subsystem when the fields E3 and E3 are blocked and other beams are turned on. (e) The diagram of the K-type five-level atomic system when the fields E2 and E4 are blocked only.

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In such beam geometric configuration, the two-photon Doppler-free conditions will be satisfied for the two ladder-type subsystems both |0|1|2 and |0|1|4, thus two EIT windows appear. When all the seven laser beams (E1, E2, E2, E3, E3, E4, E4) are turned on, three FWM processes EF2 (satisfying the phase-matching condition kF2=k1+k2-k2), EF4 (satisfying kF4=k1+k4-k4) and EF3 (satisfying kF3=k1-k3+k3), and four SWM processes ES2 (satisfying kS2=k1-k3+k3+k2-k2), ES2 (satisfying kS2=k1-k3+k3+k2-k2), ES4 (satisfying kS4=k1-k3+k3+k4-k4) and ES4 (satisfying kS4=k1-k3+k3+k4-k4) can occur simultaneously. The propagation direction of all the generated signals with horizontal polarization is determined by the phase-matching conditions, so all the signals propagate along the same direction deviated from probe beam at an angle θ, as shown in Fig. 1(a). The wave-mixing signals are detected by an avalanche photodiode detector, and the probe beam transmission is simultaneously detected by a silicon photodiode.

Generally, the expression of the density-matrix element related to the MWM signals can be obtained by solving the density-matrix equations. For the simple FWM process of EF2, via the perturbation chain ρ00(0)ω1ρ10(1)ω2ρ20(2)ω2ρ10(3) we can obtain the third-order density element ρF2(3)=GF2/(d12d2), the amplitude of which determines the intensity of the simple FWM process, where GF2=iG1G2(G2)*exp(ikF2r), d1=Γ10+iΔ1, d2=Γ20+i(Δ1+Δ2), and Γij is the transverse relaxation rate between states |i and |j. Similarly, for the simple FWM process of EF4, we can obtain ρF4(3)=GF4/(d12d4) via ρ00(0)ω1ρ10(1)ω4ρ40(2)ω4ρ10(3), where GF4=iG1G4(G4)*exp(ikF4r), d4=Γ40+i(Δ1+Δ4). And for the simple FWM process of EF3, we can obtain ρF3(3)=GF3/(d12d4) via ρ00(0)ω1ρ10(1)ω3ρ30(2)ω3ρ10(3), where GF3=iG1G3(G3)*exp(ikF3r), d3=Γ30+i(Δ1Δ3). Additionally, via perturbation chain ρ00(0)ω1ρ10(1)ω3ρ30(2)ω3ρ10(3)ω2ρ20(4)ω2ρ10(5) we can obtain ρS2(5)=GS2/(d13d2d3) for the simple SWM process ofES2, where GS2=iG1G2G2*G3*G3exp(ikS2r) (or ρS2(5)=GS2/(d13d2d3) for ES2, where GS2=iG1G2G2*G3*G3exp(ikS2r)). And via ρ00(0)ω1ρ10(1)ω3ρ30(2)ω3ρ10(3)ω4ρ40(4)ω4ρ10(5) we obtain ρS4(5)=GS4/(d13d4d3) for the simple SWM process of ES4, where GS4=iG1G4G4*G3*G3exp(ikS4r) (or ρS4(5)=GS4/(d13d4d3) for ES4, where GS4=iG1G4G4*G3*G3exp(ikS4r)). Further, the dressing effect on these MWM signals and the interaction among them will be researched in the following section.

In the experiments, these multi-wave mixing signals are researched by selectively blocking different laser beams. When the beams E3, E3, E4 and E4 are blocked and E1,E2 and E2 are turned on (as shown in Fig. 1(c)), only the EF2 signal with self-dressing effect could be generated in the ladder-type three-level subsystem |0|1|2. When the beams E3 and E3 are blocked and other beams on (Fig. 1(d)), two FWM signals EF2 and EF4 will coexist in the Y-type four-level subsystem, both of them would be perturbed by self-dressing effect and external-dressing effect, and spatiotemporal coherent interference and interaction between them could be observed. When the beams E2 and E4 are blocked only (Fig. 1(e)), two SWM signals ES2 and ES4 will coexist and interact with each other.

3. Dressed odd-order multi-wave mixing

By individually adjusting the frequency detunings Δ2 and Δ4, these generated wave-mixing signals can be separated in spectra for the identification, or be overlapped for investigating the interplay among them. Firstly, by detuning the frequency of the participating laser beams and blocking one or two participating laser beams, we can successfully separate two EIT windows and these MWM signals can be identified. Figures 2(a) -2(e) present the measured signals versus the probe detuning Δ1 with different laser beams blocked, in which the lower curves are the measured MWM signals while the corresponding probe transmission signals versus Δ1 are shown in the upper curves. Figure 2(a) depicts the case when all the participating laser beams are turned on, and Figs. 2(b), 2(c), 2(d) and 2(e) show the measured signals when the laser beams or beam combinations E2, E2, E4&E4 and E3&E3 are blocked, respectively. In the upper curves, the left EIT window is created by E4(E4) at Δ1=140MHz satisfying Δ1+Δ4=0 and the right one is created by E2(E2) at Δ1=150MHz satisfying Δ1+Δ2=0. The generated FWM and SWM signals except for EF3 all fall into these two separate EIT windows, so the linear absorptions of the generated signals are greatly suppressed. Specifically, the MWM signals related to E4(E4) (i.e. EF4, ES4 and ES4) fall into the |0|1|4 EIT window while the MWM signals related to E2(E2) (i.e. EF2, ES2 and ES2) fall into the |0|1|2 EIT window. The FWM signal EF3 can be obtained in Figs. 2(a)-(d), and it appears as a Doppler broadened background signal because the Doppler-free condition cannot be satisfied in the FWM process generating EF3 with opposite propagation direction between E1 and E3(E3). By comparing Fig. 2(a) with Fig. 2(d), we find the interaction between MWM signals related to E4(E4) and those related to E2(E2) does not exist when the two EIT widows are separated from each other, since the intensity of the MWM signals related to E2(E2) behaves identical in both curves.

 

Fig. 2 The probe transmission (the upper curves) and measured MWM signals (the bottom curves) with different ways of blocking laser beams. The left peaks show the EIT window and MWM signals related to E4(E4) and the right peaks are related to E2(E2). (a) Measured total MWM signals with all beams turned on. (b) Measured MWM signals related to E4(E4) and SWM signal ES2, with E2 blocked. (c) Measured MWM signals related to E4(E4) and SWM signal ES2, with E2 blocked. (d) Measured MWM signals related to E2(E2) with E4and E4 blocked. (e) Measured FWM signal EF2 and EF4 withE3 and E3 blocked. The experimental parameters are Δ2=150MHz, Δ4=140MHz, Δ3=0MHz, and the powers of all laser beams are 5.3mW (E1), 40.9mW (E2), 5mW (E2), 44mW (E3 and E3), 21mW (E4 and E4).

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Moreover, the interaction between FWM and SWM processes in the same EIT window of E2(E2) can be observed, by comparing the total MWM signal related to E2(E2) (Fig. 2(a)) with the sum of FWM signal EF2 (Fig. 2(e)), SWM signals ES2 (Fig. 2(b)) and ES2 (Fig. 2(c)) in amplitude. We can find that the MWM signal is suppressed by 40%, which shows the interaction and competition between FWM and SWM when they coexist. This phenomenon could be explained by the dressing effect of E3(E3) on FWM signal EF2. The dressed FWM process can be described by ρ00(0)ω1ρ(G3±)0(1)ω2ρ20(2)ω2ρ(G3±)0(3), we can obtain ρF2(3)=GF2/[d2(d1+|G3b|2/d3)2], where G3b=G3+G3. And the density-matrix element related to the SWM processes can be obtained as ρS2(5)=GS2/(d13d2d3) and ρS2(5)=GS2/(d13d2d3) (for simplicity, the self-dressing effects on EF2, ES2 and ES2 are not considered here). Since these MWM processes exist at the same time in the experiment, and the signals are copropagating in the same direction, the total detected MWM signal (Fig. 2(a)) will be proportional to the mod square of ρM, where ρM=ρS2(5)+ρS2(5)+ρF2(3).

Next, we investigate the singly-dressed FWM process in the ladder-type three-level subsystem |0|1|2 (shown as Fig. 1(c)) when only the laser beams E1, E2 and E2 are turned on. In this three-level subsystem, only the wave-mixing signal EF2 is generated, with self-dressing effect of E2(E2). According to the perturbation chain of the self-dressed FWM process ρ00(0)ω1ρ(G2±)0(1)ω2ρ20(2)ω2ρ(G2±)0(3), we obtain ρF2(3)=GF2/[d2(d1+|G2b|2/d2)2] for this singly-dressed FWM process, where G2b=G2+G2.

The spectra of the singly-dressed FWM process are shown in Fig. 3 . Figures 3(a1) and (a2) respectively present the intensities of the probe transmission (Fig. 3(a1)) and EF2 (Fig. 3(a2)) versus Δ2 at discrete Δ1 values. Figure 3(a3) and (a4) respectively depict the intensities of probe transmission (Fig. 3(a3)) and EF2 (Fig. 3(a4)) versus Δ1 at discrete Δ2 values, and the Doppler Broadening of the probe transmission signal in Fig. 3(a3) has been subtracted. Figures 3(b1), (b3), (b4) and (b5) are the theoretical calculations corresponding to Figs. 3(a1)-(a4), and Fig. 3(b2) represents the theoretical enhancement and suppression of EF2, which respectively depicted as the peak and dip on each baseline of the curves, by the self-dressing effect. Notice the experimentally obtained EF2 signal when scanning Δ2 (Fig. 3(a2)) includes two components: the pure FWM signal when not considering dressing effect, and the modification (enhancement and suppression) of the FWM process which is theoretically shown in Fig. 3(b2). Figure 3(c) shows the singly-dressed energy level diagrams corresponding to the curves at discrete frequency detunings in Fig. 3(a).

 

Fig. 3 (a) The measured intensity of (a1) the probe transmission and (a2) the singly-dressed FWM signal EF2 versus Δ2 at discrete probe detunings Δ1=80,20,0,20and80MHz, and the measured intensity of (a3) the probe transmission and (a4) the singly-dressed FWM signal EF2 versus Δ1 at discrete dressing detunings Δ2=80,20,0,20and80MHz. (b1), (b3), (b4), (b5) are theoretical calculations corresponding to (a1)-(a4). (b2) is the theoretical calculations of enhancement and suppression of singly-dressed EF2. (c) The dressed energy level diagrams corresponding to (a). Powers of participating laser beams are 4mW (E1), 34.5mW (E2), 8.7mW (E2).The detuning range is 200MHz when scanning Δ1, 60MHz when scanning Δ2.

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When scanning Δ2, the FWM signal shows the evolution from pure-enhancement (Δ1=80MHz), to first enhancement and next suppression (Δ1=20MHz), to pure-suppression (Δ1=0), to first suppression and next enhancement (Δ1=20MHz), to pure-enhancement (Δ1=80MHz), as shown in Fig. 3(b2). And the corresponding probe transmission shows the evolution from pure-EIA, to first EIA and next EIT, to pure-EIT, to first EIT and next EIA, finally to pure-EIA (electromagnetically induced absorption) in series as shown in Fig. 3(a1). The height of each baseline of the curves represents the probe transmission without dressing effect of E2(E2) versus probe detuning Δ1, while the peak and dip on each baseline represent EIT and EIA respectively. We can see that every enhancement and suppression correspond to EIA and EIT respectively, and the curves show symmetric behavior.

In order to understand the phenomena mentioned above, we resort to the singly-dressed energy level diagrams in Fig. 3(c). With the self-dressing effect of E2(E2), the energy level |1 will be split into two dressed states |G2±, as shown in Figs. 3(c1)-3(c5). When Δ2 is scanned at Δ1=0, on the one hand, EIT is obtained in Fig. 3(a1) at the point Δ2=0 where the suppression condition Δ1+Δ2=0 is satisfied. On the other hand, a pure-suppression of EF2 is gotten in Fig. 3(b2) because the probe field E1 could not resonate with either of the two dressed energy levels |G2±, as shown in Fig. 3(c3). In the region with Δ1<0, when Δ2 is scanned, the probe transmission shows EIA firstly and EIT afterwards in Fig. 3(a1) at Δ1=20MHz. Correspondingly, EF2 is first enhanced when the EIA is gotten and next suppressed when the EIT is obtained, shown in Fig. 3(b2) at Δ1=20MHz. The reason for the first EIA and the corresponding enhancement of EF2 is that the probe field E1 resonates with the dressed state |G2+ at first, thus the enhancement condition Δ1+(Δ2+Δ22+4|G2b|2)/2=0 is satisfied. While the reason for the next EIT and the corresponding suppression of EF2 is that two-photon resonance occurs so as to satisfy the suppression condition Δ1+Δ2=0 (see Fig. 3(c2)). When Δ1 changes to be positive, the curves at Δ1=20MHz show symmetric evolution behavior with the curves at Δ1=20MHz, i.e., EIT as well as a suppression of EF2 are obtained due to the two-photon resonance which matched the suppression condition Δ1+Δ2=0 firstly; and then EIA as well as an enhancement of EF2 are obtained when E1 is in resonance with |G2 satisfying the enhancement condition Δ1+(Δ2Δ22+4|G2b|2)/2=0, as depicted in Fig. 3(c4). When Δ1 is far away from resonance point (Δ1=±80MHz), the pure-EIA as well as the pure-enhancement of EF2 are obtained because the probe field can only resonate with one of the two dressed states |G2± (as shown in Figs. 3(c1) and 3(c5)).

On the other hand, when Δ2 is set at discrete values orderly from positive to negative and Δ1 is scanned, the probe transmission shows an EIT window on each curve in Fig. 3(a3) satisfying Δ1+Δ2=0. Also, the FWM signal EF2 presents double peaks (Fig. 3(a4)), due to Autler-Townes (AT) splitting. The two peaks are obtained when E1 resonates with |G4+ and |G4, respectively. The theoretical calculations (Fig. 3(b)) are in good agreement with the experimental results (Fig. 3(a)).

Moreover, when we compare the results of these two kinds of scanning method (i.e. scanning Δ2 at discrete Δ1 values, and scanning Δ1 at discrete Δ2 values), an interesting corresponding relationship between them could be discovered, as expressed with the dash lines in Fig. 3(a) and 3(b). Referring to the dressed energy level diagrams in Figs. 3(c), one can easily find out that the curves in the same column which are connected by dash lines correspond to the same dressed energy level diagram in Fig. 3(c), although these curves are obtained by scanning different fields. In other words, the positions of enhancement points and suppression points of FWM signal in the probe frequency detuning (Δ1) domain correspond with the positions in the dressing frequency detuning (Δ2) domain, satisfying same enhancement/suppression conditions. Take the curves obtained when scanning Δ2 at Δ1=20MHz in Figs. 3(b1)-3(b2), and curves obtained when scanning Δ1 at Δ2=20MHz in Figs. 3(b4)-3(b5) for example. These four curves, although gotten by scanning different field, correspond to the same energy state depicted in Fig. 3(c2) and reveal some common features. When E1 resonates with the dressed state |G2+, a dip of probe transmission (EIA) is gotten both in Fig. 3(b1) and 3(b4), and a peak (enhancement point) of EF2 appears correspondingly both in Fig. 3(b2) and 3(b5), as the left dash line expresses; when two-photon resonance occurs at the point Δ1+Δ2=0, a peak (EIT) is gotten both in Fig. 3(b1) and 3(b4), and a dip (suppression point) of EF2 appears correspondingly both in Fig. 3(b2) and 3(b5), as the right dash line expresses. Additionally, we notice that when scanning the probe detuning, two enhancement points (i.e. the two peaks of AT splitting) and one suppression point could be obtained, while when scanning the dressing detuning, only one enhancement point and one suppression point could be gotten at most. The reason is that the two splitting states |G2± could not move across the original position of |1 and therefore only one of them can resonate with E1 when scanning the dressing detuning.

Furthermore, the spectra of the doubly-dressed FWM process of EF2 in the Y-type four-level subsystem are investigated as shown in Fig. 4 , with the laser beams E3, E3 and E4 blocked and E1, E2, E2 and E4 turned on. Since E4 is turned on, the FWM signal EF2 is dressed by E4 (external-dressing effect) as well as E2(E2) (self-dressing effect). According to the perturbation chain of the doubly-dressed FWM process: ρ00(0)ω1ρ(G2±G4±)0(1)ω2ρ20(2)ω2ρ(G2±G4±)0(3), we can obtain ρF2(3)=GF2/[(d1+|G2b|2/d2+|G4|2/d4)2d2] for the doubly-dressed FWM process.

 

Fig. 4 (a) The measured intensity of (a1) the probe transmission and (a2) the doubly-dressed FWM signal EF2 versus Δ2 at discrete probe detunings Δ1=80,40,20,10,0,10,20,40and80MHz, and the measured intensity of (a3) the probe transmission and (a4) the doubly-dressed FWM signal EF2 versus Δ1 at discrete self-dressing detunings Δ2=80,40,20,10,0,10,20,40and80MHz (Δ4 is fixed at Δ4=0). (b1), (b3), (b4), (b5) are theoretical calculations corresponding to (a1)-(a4). (b2) is the theoretical calculations of enhancement and suppression of doubly-dressed EF2. (c) The energy level diagrams corresponding to (a). (d) The measured intensity of (d1) the probe transmission and (d2) the doubly-dressed FWM signal EF2 versus Δ4 at discrete probe detunings Δ1=80,40,20,10,0,10,20,40and80MHz, and the measured intensity of (d3) the probe transmission and (d4) the doubly-dressed FWM signal EF2 versus Δ1at discrete external-dressing detunings Δ4=80,40,20,10,0,10,20,40and80MHz (Δ2 is fixed at Δ2=0). (e1)-(e4) Theoretical calculations corresponding to (d1)-(d4). (f) The energy level diagrams corresponding to (d). Powers of participating laser beams are 4.6mW (E1), 33mW (E2), 8.4mW (E2), 39mW (E4).

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Firstly, the probe transmission and FWM signal EF2 versus probe detuning Δ1 and self-dressing detuning Δ2 are investigated (Figs. 4(a)-4(c)). Figures 4(a1) and 4(a2) present the intensities of the probe transmission (Fig. 4(a1)) and EF2 (Fig. 4(a2)), respectively, versus Δ2 at discrete Δ1 values. Figures 4(a3) and (a4) depict the intensities of probe transmission (Fig. 4(a3)) and EF2 (Fig. 4(a4)) versusΔ1, respectively, at discrete Δ2 values (with fixed Δ4 at Δ4=0). Notice the Doppler Broadening of the probe transmission signal in Fig. 3(a3) has been subtracted. Figures 4(b1), 4(b3), 4(b4) and 4(b5) are the theoretical calculations corresponding to Fig. 4(a1)-(a4), while Fig. 4(b2) represents the theoretical enhancement and suppression of EF2, respectively expressed by the peak and dip on each baseline of the curves. Figure 4(c) show the doubly-dressed energy level diagrams corresponding to the curves at discrete detuning values in Fig. 4(a).

When Δ1 is set at discrete values orderly from negative to positive and Δ2 is scanned, the experimentally obtained EF2 signal is shown in Fig. 4(a2), including two components: the pure FWM signal when not considering dressing effect, and the modification (enhancement and suppression) of the FWM process which is theoretically shown in Fig. 4(b2). The profile of all the baselines in Fig. 4(b2) reveals AT splitting of E4, and the transition of enhancement and suppression in each curve is induced by the interaction between E2(E2) and E4, showing the evolution from pure-enhancement (Δ1=80MHz), to first enhancement and next suppression (Δ1=40MHz), to pure-suppression (Δ1=20MHz), to first suppression and next enhancement (Δ1=10MHz), to pure-suppression (Δ1=0), to first enhancement and next suppression (Δ1=10MHz), to pure-suppression (Δ1=20MHz), to first suppression and next enhancement (Δ1=40MHz), finally to pure-enhancement (Δ1=80MHz). Correspondingly, the probe transmission shows the evolution from pure-EIA, to first EIA and next EIT, to pure-EIT, to first EIT and next EIA, to pure-EIT, to first EIA and next EIT, to pure-EIT, to first EIT and next EIA, finally to pure-EIA in series as shown in Fig. 4(a1). The height of the baseline of each curve represents the probe transmission without dressing field E2(E2) versus probe detuning Δ1. The profile of these baselines reveals an EIT window induced by external-dressing field E4 at Δ1=Δ4. While the peak and dip on each baseline of the curves represent EIT and EIA induced by self-dressing fields E2 and E2. We can see that every enhancement and suppression correspond to EIA and EIT respectively, which is similar to the singly-dressing case observed in Fig. 3.

Such variations in the probe transmission and the transition of enhancement and suppression of EF2 are caused by the interaction of the dressing fields E2(E2) and E4. Because of the doubly-dressing effect, the energy level |1 is totally split into three dressed states (shown in Fig. 4(c)). Firstly under the external-dressing effect of E4, the energy level |1 will be broken into two primarily dressed states |G4±. Then in the region with Δ1<0, when Δ2 is scanned around |G4+, two secondarily dressed states |G4+G2± could be created from |G4+ by the self-dressing effect of E2(E2), as shown in Figs. 4(c1)-4(c4). Symmetrically, in the region with Δ1>0, when Δ2 is scanned around |G4, two secondarily dressed states |G4G2± could be created from |G4, as shown in Figs. 4(c6)-(c9). Since the phenomena and analysis method are similar with those in the singly-dressing case, here we only give the enhancement and suppression conditions as Δ1+(Δ2±Δ22+4|G2b|2)/2+G4=0 and Δ1+Δ2=0 for Δ1<0, where Δ2=Δ2G4 represents the detuning of E2(E2) from |G4+, and Δ1+(Δ2±Δ22+4|G2b|2)/2G4=0 and Δ1+Δ2=0 for Δ1>0, where Δ2=Δ2+G4 represents the detuning of E2(E2) from |G4. When the enhancement condition is satisfied, the probe field E1 resonates with one of the secondarily dressed states, leading to an EIA of probe transmission and enhancement of EF2. When the suppression condition is satisfied, two-photon resonance occurs, leading to an EIT and suppression of EF2. Especially, we notice the enhancement and suppression of EF2 in Fig. 4(b2) show symmetric behavior with three symmetric centers at Δ1=0,20,and20MHz, all of which are pure-suppression. The pure-suppression at Δ1=0MHz is induced by primary dressing effect of E4, while pure-suppressions at Δ1=±20MHz are caused by the secondary dressing effect of E2(E2).

On the other hand, when Δ2 is set at discrete values orderly from positive to negative and Δ1 is scanned, the intensity of probe transmission shows double EIT windows on each curve in Fig. 4(a3), which are EIT windows |0|1|2 (appearing at Δ1=Δ2) and |0|1|4 (appearing at Δ1=Δ4), respectively. As Δ4 is fixed at Δ4=0 and Δ2 is set at discrete values from positive to negative, the EIT window |0|1|4 is fixed at Δ1=Δ4=0 and the EIT window |0|1|2 moves from negative to positive. Especially, when Δ2 is set at Δ2=0, the two EIT windows overlap as shown in Fig. 4(a3), and a double-peak FWM signal is obtained because both E2(E2) and E4 dress the energy level |1 simultaneously into two dressed states |+ and |, as shown in Fig. 4(a4). When Δ2 is set at Δ20, in the process of scanning Δ1, the FWM signal EF2 presents three peaks, corresponding to the three dressed state respectively. Firstly, E4 dresses |1 into two primarily dressed state |G4+ and |G4, corresponding to primary AT splitting. Then when the frequency of E2 and E2 is tuned so as to move the |0|1|2 EIT window into the left FWM peak (Δ2>0), secondary AT splitting occurs and the left peak splits into two peaks, respectively corresponding to secondarily dressed states |G4+G2+ and |G4+G2. Symmetrically, in the region with Δ2<0, the three peaks corresponding to |G4+, |G4G2+ and |G4G2 respectively. The theoretical calculations (Fig. 4(b)) are in good agreement with the experimental results (Fig. 4(a)).

When comparing the results of these two kinds of scanning method (i.e. scanning Δ2 at discrete Δ1 values, and scanning Δ1 at discrete Δ2 values), the corresponding relationship could also be discovered, as expressed with the dash lines in Figs. 4(a) and 4(b). By referring to the energy level diagrams in Figs. 4(c), one can easily find out that positions of enhancement points and suppression points of FWM signal in the probe frequency detuning (Δ1) domain correspond with the positions in the self-dressing frequency detuning (Δ2) domain, satisfying same enhancement/suppression conditions. Take the curves at Δ1=40MHz in Figs. 4(b1)-(b2) and the curves at Δ2=40MHz in Figs. 4(b4)-4(b5) for example. These four curves, although gotten by scanning different fields, correspond to the same energy state depicted in Fig. 4(c2) and reveal some common features. When E1 resonates with the dressed state |G4+G2+, a dip of probe transmission (EIA) is gotten both in Fig. 4(b1) and 4(b4), and a peak (enhancement point) of EF2 signal appears both in Fig. 4(b2) and 4(b5), as the left dash line expresses; when two-photon resonance (Δ1+Δ2=0) occurs, a peak (EIT) is gotten both in Fig. 4(b1) and 4(b4), and a dip (suppression point) appears both in Fig. 4(b2) and (b5), as the right dash line expresses. Especially, the position of the pure-suppression at Δ1=0 in Fig. 4(b2) corresponds to the center of primary AT splitting at Δ2=0 in Fig. 4(b5); and the positions of the pure-suppression at Δ1=±20MHz in Fig. 4(b2) correspond to the center of secondary AT splitting at Δ2=±20MHz in Fig. 4(b5). We also notice that when Δ1 scanned, three enhancement points and two suppression points could be obtained, while when scanning Δ2 only one enhancement point and one suppression point could be gotten at most.

Next, we investigate the probe transmission and the enhancement and suppression of EF2 versus the probe detuning Δ1 and external-dressing detuning Δ4 (Figs. 4(d)-4(e)). Figures 4(d1) and 4(d2) respectively present the intensities of the probe transmission (Fig. 4(d1)) and the enhancement and suppression of EF2 (Fig. 4(d2)) versus Δ4 at discrete Δ1 values. While Fig. 4(d3) and (d4) depict the intensities of probe transmission (Fig. 4(d3)) and EF2 (Fig. 4(d4)) versus Δ1 at discrete Δ4 values (with fixed Δ2 at Δ2=0). Figures 4(e1)-4(e4) are the theoretical calculations corresponding to Figs. 4(d1)-4(d4). Figure 4(f) shows the doubly-dressed energy level diagrams corresponding to the curves at discrete detuning values in Fig. 4(d). Similar to the above discussion of Figs. 4(a)-(c), the signal EF2 is dressed by both E2(E2) and E4. Firstly, under the self-dressing effect of E2(E2), the state |1 will be broken into two primarily dressed states |G2±. Then in the region with Δ1<0, when Δ4 is scanned around |G2+, two secondarily dressed states |G2+G4± could be created from |G2+ by the external-dressing field E4, as shown in Fig. 4(f1)-4(f4). Symmetrically, in the region with Δ1>0, when Δ4 is scanned around |G2, two secondarily dressed states |G2G4± could be created from |G2, as shown in Fig. 4(f6)-4(f9). Here we only give the enhancement and suppression conditions as Δ1+(Δ4±Δ42+4|G4|2)/2+G2=0 and Δ1+Δ4=0 for Δ1<0, where Δ4=Δ4G2 represents the detuning of E4 from |G2+, and Δ1+(Δ4±Δ42+4|G4|2)/2G2=0 and Δ1+Δ4=0 for Δ1>0, where Δ4=Δ4+G2 represents the detuning of E4 from |G2. Unlike scanning self-dressing detuning (Fig. 4(a2)), by scanning the external-dressing detuning the enhancement and suppression of EF2 could be detected directly, excluding the pure FWM component (Fig. 4(d2)). We can see that the enhancement and suppression of EF2 in Fig. 4(d2) shows similar evolution with that in Fig. 4(b2). The profile of all the baselines, which has two peaks, reveals AT splitting of E2(E2), and the transition of enhancement and suppression in each curve is induced by the interaction between E2(E2) and E4 with three symmetric centers at Δ1=0,20,and20MHz, all of which are pure-suppression. The pure-suppression at Δ1=0MHz is induced by primary dressing effect of E2(E2), while pure-suppressions at Δ1=±20MHz are caused by the secondary dressing effect of E4. On the other hand, when Δ1 is scanned, the FWM signal EF2 in Fig. 4(d4) also presents three peaks, corresponding to the three dressed state respectively. Moreover, the corresponding relationship between scanning probe detuning and scanning external-dressing detuning is similar with above, as expressed by the dash lines in Fig. 4(d) and 4(e). It is obvious that the theoretical calculations (Fig. 4(e)) are in good agreement with the experimental results (Fig. 4(d)).

Comparing with the singly-dressed FWM process in Fig. 3, we notice the doubly-dressed FWM process, although derives from the former, shows more complexities since one more dressing field is considered. When scanning probe detuning, doubly-dressed FWM signal shows three peaks resulting from two orders of AT splitting (Fig. 4(a4) and 4(d4)); whereas singly-dressed FWM signal shows only two peaks resulting from of AT splitting of self-dressing effect (Fig. 3(a4)). When scanning the dressing detuning, only one symmetric center appears in singly-dressing case (Fig. 3(b2)), whereas three symmetric centers appear in doubly-dressing case respectively at Δ1=0,20,and20MHz (Fig. 4(b2) and 4(e2)), all of which reveals pure-suppression. The symmetric center at Δ1=0 is caused by the primary dressing effect, while the two symmetric centers at Δ1=±20MHz are due to the secondary dressing effect.

Synthetically, based on the analysis above, we find the methods of scanning the probe detuning (Fig. 3(a3)-3(a4), Fig. 4(a3)-4(a4), Fig. 4(d3)-4(d4)), scanning self-dressing detuning (Fig. 3(a1)-3(a2), Fig. 4(a1)-4(a2)) and scanning external-dressing detuning (Fig. 4(d1)-4(d2)) individually show some different features and advantages on research the FWM process. When scanning the probe detuning, the obtained FWM signal includes two components: the pure FWM signal when not considering dressing effects, and the modification (revealing AT splitting) of the FWM process. When scanning self-dressing detuning, the obtained signal also includes two components: the pure FWM signal and the modification (revealing the transition between enhancement and suppression) of the FWM process. While by scanning external-dressing detuning, the enhancement and suppression could be detected directly, excluding the pure FWM component. On the other hand, by scanning the probe detuning, all enhancement points and suppression points could be observed corresponding to the peaks and dips of AT splitting. In singly-dressing case, there are two enhancement points and one suppression point (Fig. 3(a3)-3(a4)), and in doubly-dressing case, three enhancement points and two suppression points (Fig. 4(a3)-4(a4)), etc. In contrast, by scanning dressing detuning, at most one enhancement point and one suppression point could be gotten in the spectra. Furthermore, the positions of the enhancement and suppression points when scanning dressing detuning match with the positions of corresponding points when scanning probe detuning, as the dash lines express in Fig. 3 and Fig. 4.

After that, we demonstrate a new type of phase-controlled, spatiotemporal coherent interference between two FWM processes (EF2 and EF4) in a four-level, Y-type subsystem when the laser beams E3 and E3 are turned off (shown as Fig. 1(d)). With a specially designed spatial configuration for the laser beams with phase matching and an appropriate optical delay introduced in one of the coupling laser beams, we can have a controllable phase difference between the two FWM processes in the subsystem. When this relative phase is varied, temporal and spatial interferences can be observed. The interference in the time domain is in the femtosecond time scale, corresponding to the optical transition frequency excited by the delayed laser beam. In the experiment, the beam E2 is delayed by an amount τ using a computer-controlled stage. The CCD and an avalanche photodiode (APD) are set on the propagation path of the two FWM signals to measure them. By changing the frequency detuning Δ4, the |0|1|4 EIT window can be shifted toward the |0|1|2 EIT window. When the two EIT windows overlap with each other, temporal and spatial interferences of two FWM signal EF2 and EF4 can be observed, as shown in Fig. 5 .

 

Fig. 5 The spatiotemporal interferograms of EF2 and EF4 in the Y-type atomic subsystem. (a) A three-dimensional spatiotemporal interferogram of the total FWM signal intensity I(τ,r) versus time delay τ of beam E2 and transverse position r. (b) The temporal interference with a much longer time delay of beam E2. (c) Measured beat signal intensity I(τ,r) versus time delay τ together with the theoretically simulated result (solid curve).

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The coexisting EF1 and EF2 signals give the total detected intensity as:I(τ,r)|χF2(3)|2+|χF4(3)|2+2|χF2(3)||χF4(3)|cos(φ2φ4+φ), where χF2(3)=Nμ12ε0G1ρF2(3)×μ222G2G2* =iμ12μ22N/{ε03(d1+G22/d2+G42/d4)2d2}=|χF2(3)|exp(iφ2), χF4(3)=Nμ12ε0G1ρF4(3)×μ422G4G4* =iμ12μ42N/{ε03(d1+G22/d2+G42/d4)2d4}=|χF4(3)|exp(iφ4), and φ=Δkrω2τ with the frequency of spatial interference Δk=kF2kF4=(k2k2)(k4k4). μ1,μ2, and μ4 are the dipole moments of the transitions |0|1, |1|2, and |1|4, respectively. From the expression of I(τ,r), we can see that the total signal has an ultrafast time oscillation with a period of 2π/ω2 and spatial interference with a period of 2π/Δk, which forms a spatiotemporal interferogram. Fig. 5(a) shows a three-dimensional interferogram pattern, and Fig. 5(b) shows the temporal interference with a much longer time delay in beam E2 while Fig. 5(c) shows its projections on time. Figure 5(c) depicts a typical temporal interferogram with the temporal oscillation period of 2π/ω2=2.6fs corresponding to the |1 to |2 transition frequency of Ω2=2.4fs1 in R85b.This gives a technique for precision measurement of atomic transition frequency in optical wavelength range. The solid curve in Fig. 5(c) is the theoretical calculation from the full density-matrix equations. It is easy to see that the theoretical results fit well with the experimentally measured results.

Now, we concentrate on the SWM process when Δ3 is at large detuning, with E2 and E4 blocked (shown as Fig. 1(e)). When take the atomic velocity component and the dressing effect of E3(E3) into consideration, the enhancement and suppression of the SWM signal would be shifted far away from resonance, as shown in Fig. 6 .

 

Fig. 6 (a1) The probe transmission signal and (a2) the SWM signal with the enhancement and suppression effect versus Δ2 for different Δ1 with the laser beams E2 and E4 blocked when Δ3 is at large detuning. (b) The doubly-dressed state diagram of the SWM signal. Powers of participating laser beams are 3mW (E1), 4.6mW (E2), 44mW (E3 and E3), 65mW (E4).

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When considering Doppler effect the atom moving towards the probe laser beam with velocity v, the frequency of E1 is changed to ω1+ω1v/c, and the frequencies of E2, E3 and E4 are changed to ω2ω2v/c, ω3-ω3v/c, ω4ω4v/c under our experimental geometry configuration, therefore their detunings are changed to Δ1ω1v/c, Δ2+ω2v/c, Δ3+ω3v/c, Δ4+ω4v/c. Noticing that in such beam geometric configuration, the two-photon Doppler-free condition will not be satisfied for the Λ-type three-level subsystem |0|1|3, the atomic velocity component ω3v/c will behaves dominant. The density-matrix element of SWM signal ES4 can be obtained as ρS4(5)=GS4/[d1d3d4(d1+|G4|2/d4+|G3b|2/d3)2] via the self-dressed perturbation chain ρ00(0)ω1ρ(G4±G3±)0(1)ω3ρ30(2)ω3ρ(G4±G3±)0(3)ω4ρ40(4)ω4ρ10(5), where d1=d1iω1v/c+γ1, d3=d3iω3v/ciω1v/c+γ1γ3, d4=d4+iω4v/ciω1v/c+γ1+γ4, and γ1, γ3, γ4 are the half linewidth of laser beams E1, E3, E4 respectively. When the SWM signal ES4 is externally dressed by E2 (defined as ES4D), the solved expression is ρS4(5)=GS4/[d3d4(d1+|G2|2/d2)(d1+|G2|2/d2+|G4|2/d4+|G3b|2/d3)2] via the dressed perturbation chain: ρ00(0)ω1ρ(G4±G3±G2±)0(1)ω3ρ30(2)ω3ρ(G4±G3±G2±)0(3)ω4ρ40(4)ω4ρ(G2±)0(5), where d2=d2+iω2v/ciω1v/c+γ1+γ2 and γ2 are the half linewidth of laser beam E2. Similarly, the density-matrix element of SWM signalES2 can be obtained as ρS2(5)=GS2/[d1d2d3(d1+|G2|2/d2+|G3b|2/d3)2] via the self-dressed perturbation chain: ρ00(0)ω1ρ(G2±G3±)0(1)ω3ρ30(2)ω3ρ(G2±G3±)0(3)ω2ρ20(4)ω2ρ10(5). When the SWM signal ES2 is externally dressed by E4 (defined as ES2D), the solved expression is ρS2(5)=GS2/[d2d3(d1+|G4|2/d4)(d1+|G2|2/d2+|G4|2/d4+|G3b|2/d3)2] via the dressed perturbation chain: ρ00(0)ω1ρ(G2±G3±G4±)0(1)ω3ρ30(2)ω3ρ(G2±G3±G4±)0(3)ω2ρ20(4)ω2ρ(G4±)0(5). From the expressions of ES4D and ES2D signals, one can see that the two SWM processes are closely connected by mutual dressing effect.

In Fig. 6(a), we present the probe transmission (Fig. 6(a1)) and the measured SWM signal (Fig. 6(a2)) by scanning Δ2 at different designated Δ1 values, with G2<<G4. In Fig. 6(a1), The profile of each baseline represents the probe transmission without dressing field E2 versus probe detuning Δ1, which reveals an EIT window (80MHz<Δ1<80MHz) induced by E4, and the peak on each baseline is the EIT induced by E2. In Fig. 6(a2), the profile of each baseline represents the intensity variation of the triple-peak SWM signal ES4 versus Δ1. The peak and dip on each baseline include the dressed SWM signal ES2D and the enhancement and suppression of ES4 induced by E2. Considering G2<<G4, we can deduce the signal of ES2D is quite small. Therefore, the peak and dip on each baseline mainly represent the enhancement and suppression of SWM signal ES4 induced by E2.

One can see that the curves in Fig. 6(a2) shows pure-suppression at Δ1=0MHz and Δ1=250MHz. This two pure-suppressions can be explained by the triple-dressing effect of E2, E3(E3) and E4. The enhancement and suppression of the SWM is caused by the triply-dressing fields. Firstly, due to the self-dressing effect of E4, the state |1 would be split into two dressed states |G4±. Next, the dressing field E3(E3) split the state |G4+ into |G4+G3±. Finally, when Δ2 is scanned, E2 will further split |G4+G3± into two dressed states |G4+G3+G2± or |G4+G3G2±; or split |G4 into two dressed states |G4G2±, as shown in Fig. 6(b). When two-photon resonance occurs at the original states |G4+G3+ (Fig. 6(b2)), |G4+G3 (Fig. 6(b3)) or |G4 (Fig. 6(b4)), the pure-suppressions of SWM can be obtained. When Doppler effect being considered, the dominant atomic velocity component ω3v/c moving the |G4+G3+ state far away from the resonance, the pure-suppression on the left induced by triply-dressing effect will be shifted to large detuning. In the experiment, only two pure-suppressions can be obtained, of which the left one is caused by two-photon resonance at original |G4+G3+ state, and the right one is related to the original |G4+G3 state. This inconsistence is because when the frequency of E3(E3) is at large detuning (Δ3>>0), the enhancement and suppression of SWM signal is no more symmetrical. Specifically, due to the optical pumping effect corresponding to the transition from |3 to |1 by E3 and E3, the suppression will be intensified with Δ1<0 (especially when Δ1+Δ3=0) as shown in Fig. 6(b); but with Δ1>0, the inexistence of such effect makes the suppression caused by the two photon resonance at original |G4 state unobtainable.

In this way, we first demonstrate that the enhancement and suppression signal can be observed out of the EIT window (-80MHz<Δ1<+80MHz) through the Doppler frequency shift led by atomic velocity component and optical pumping. From the figures one can see that even Δ1 is at large detuning (Fig. 6(b1) and 6(b5)), the enhancement and suppression of SWM will still exists in the region with Δ1<0.

Finally, the interaction of the six wave-mixing signals is studied. When all seven laser beams are turned on, two FWM signals (EF2 and EF4) and four SWM signals (ES2, ES2, ES4 and ES4) can be generated simultaneously and interact with each other (considering the FWM signal EF3 is so weak that it could be negligible). When the |0|1|4 EIT window and the |0|1|2 EIT window are tuned separated, the interaction of MWM processes related to the same EIT window has been displayed in Fig. 2, by scanning probe detuning under different blocking conditions. Here, we overlap the two EIT windows experimentally, therefore the interaction between these two groups of wave-mixing signals (those related to E2(E2) and those related to E4(E4)) will be studied, by scanning the dressing field detuning Δ2 at discrete probe detuning Δ1 values (as shown in Fig. 7 ).

 

Fig. 7 (a) Measured total MWM signal versus Δ2 at discrete Δ1 when all seven laser beams on. (b) Measured FWM signals versus Δ2 at discrete Δ1. (b1) Signal obtained with the laser beams E3 and E3 blocked and others on. (b2) The enhancement and suppression of the FWM signal EF4 when the laser beams E3, E3 and E2 are blocked. (b3) The FWM signal when the laser beams E3, E3 and E4 are blocked. (c) Measured SWM signals versus Δ2 at discrete Δ1. (c1) Signal obtained with laser beams E2, E4 blocked and others on. (c3) Signal obtained with the laser beams E2, E4 and E4 blocked. (c2) The sum of ES4DES4 and ES2DES2. Powers of all laser beams are 3.7mW (E1), 55mW (E2), 5.3mW (E2), 44mW (E3 and E3), 85mW (E4), 8.6mW (E4).

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Generally, due to the mutual dressings of the two ladder subsystems, we can obtain the density elements ρF2(3)=GF2/[d2(d1+|G4b|2/d4)2] (where G4b=G4+G4) for the external-dressed FWM process of EF2, ρS2(5)=GS2/[d3d2(d1+|G4b|2/d4)3] (or ρS2(5)=GS2/[d3d2(d1+|G4b|2/d4)3]) for the external-dressed SWM process of ES2 (or ES2); and ρF4(3)=GF4/[d4(d1+|G2b|2/d2)2] for the external-dressed FWM process EF4, ρS4(5)=GS4/[d3d4(d1+|G2b|2/d2)3] (or ρS4(5)=GS4/[d3d4(d1+|G2b|2/d2)3]) for the external-dressed SWM process of ES4 (or ES4), when not considering the self-dressing effects. The total detected MWM signal (Fig. 7(a)) will be proportional to the mod square of ρM, where ρM=(ρS2(5)+ρS2(5)+ρF2(3))+(ρS4(5)+ρS4(5)+ρF4(3)).

The measured total MWM signal when all the laser beams are turned on is depicted in Fig. 7(a). The global profile of the baselines of each curve, which mainly includes the self-dressed EF4, ES4 and ES4 signals, exhibits AT splitting induced by E4(E4). The peak on each profile is mainly composed of the doubly-dressed EF2, ES2, ES2 signals and the enhancement and suppression of EF4, ES4 and ES4 induced by E2(E2). To understand the interaction of these six generated signals deeply, we divide it into two parts: the interaction of FWM signals EF2 and EF4 (shown as Fig. 7(b)), and the interaction of SWM signals ES2, ES2 and ES4, ES4. Since ES2 and ES2 share similar characteristics (so do ES4 and ES4), the interaction between ES2, ES2 and ES4, ES4 can be studied by only investigating the interaction between ES2 and ES4 (shown as Fig. 7(c)) [21]. Therefore, by blocking different laser beams and scanning Δ2 at discrete Δ1 values, the interaction of these six wave-mixing signals can be observed directly, separated into the interplay between two FWM signals, two SWM signals and the interplay between FWM and SWM signals.

First we investigate the interplay between the two FWM signals EF2 and EF4 in the Y-type subsystem (Fig. 1(d)) by blocking the laser beams E3 and E3. The interplay between these two FWM signals will occur when we overlap the two separated EIT windows, as shown in Fig. 7(b). Figure 7(b1) shows the measured FWM signal versus Δ2 at discrete Δ1 values, which including the information of both EF2 and EF4, with mutual dressings. In Fig. 7(b1), the global profile of baselines of all the curves represents the intensity variation of EF4 at designated probe detuning values, and the peak and dip on each baseline include two components: the doubly-dressed EF2 signal and the enhancement and suppression of EF4 induced by E2(E2). These two components could be individually detected by additionally blocking E2 or E4, as shown in Fig. 7(b2) and 7(b3) separately. When blocking E2, the information related to EF4 could be extracted since EF2 is turned off (Fig. 7(b2)). The global profile of all the baselines in Fig. 7(b2) reveals AT splitting of EF4, and the peak and dip of each curve represent the enhancement and suppression of EF4 induced by E2, which show similar evolution to the curves in Fig. 4(d2). On the other hand, when turning on E2 and blocking E4, the doubly-dressed EF2 signal could be obtained in Fig. 7(b3), which is similar to Fig. 4(a2). It is quite obvious that the measured total FWM signal (Fig. 7(b1)) is approximate to the sum of the enhancement and suppression of EF4 which mainly behaves dips (Fig. 7(b2)), and the dressed FWM signal EF2, which mainly behave peaks (Fig. 7(b3)).

Next we investigate the interplay between two SWM signals ES2 and ES4 in Fig. 7(c) [21], with E2 and E4 blocked (shown as Fig. 1(e)). When all the five laser beams (E1, E2, E4, E3 and E3) are turned on, two external-dressed SWM signals ES2D and ES4D will form simultaneously, as shown in Fig. 7(c1). The global baseline variation profile shows the intensity variation of the SWM signal ES4 revealing AT splitting. The peak and dip on each baseline include the SWM signal ES2D and ES4DES4 which represents the enhancement and suppression of ES4 caused by E2. When the beam E4 is also blocked, only the measured SWM signal ES2 remains, as shown in Fig. 7(c3). By subtracting the SWM signal ES2 (Fig. 7(c3)) and the height of each baseline from the total signal (Fig. 7(c1)), the sum of the signals ES4DES4 and ES2DES2 revealing the pure dressing effect can be obtained, as shown in Fig. 7(c2). Here, ES2DES2 expresses the enhancement or suppression of the ES2 caused by the E4. On the one hand, we can see from the curve (c2) that when two-photon resonance occurs at Δ1=20MHz and Δ1=25MHz, the depth of the dip is approximately maximum, meaning that the suppression is most significant. On the other hand, when E1 resonates with |G4+G2+ and |G4G2, the generated SWM signals are enhanced as shown by the small peaks.

When the FWM signals and SWM signals coexist in Fig. 7(a) with all seven beams on, the interaction of these generated wave-mixing signals can be obtained. Theoretically, the intensity of the measured total MWM signal in Fig. 7(a) can be described as sum of the FWM signal intensity (Fig. 7(b1)), the SWM signal intensity (Fig. 7(c1)) and the intensity of the SWM signals relate to ES2 and ES4 which is similar to Fig. 7(c1). From the experimental result, one can see that the generated signal with all laser beams tuned on in (a) is approximate to the sum of the FWM intensity in (b1) and the SWM intensity in (c1), but behaves FWM dominant. Because the SWM signals are too weak to be distinguished when compared with the FWM. We also notice that when the FWM signals and SWM signals coexist and interplay with each other, the enhancement and suppression effect of FWM will be weakened by the interaction of six MWM signal.

4. Conclusion

In summary, we distinguish seven coexisting multi-wave mixing signals in a K-type five-level atomic system by selectively blocking different laser beams. And the interactions among these MWM signals have been studied by investigating the interaction between two FWM signals, between two SWM signals, and the interaction between FWM and SWM signals. We also report our experimental results on the dressed FWM process by scanning the frequency detuning of the probe field, the self-dressing field and the external-dressing field respectively, proving the corresponding relationship between different scanning methods. Especially, by scanning external-dressing detuning, the enhancements and suppressions of FWM can be detected directly. In addition, we successfully demonstrate the temporal interference between two FWM signals with a femtosecond time scale. Moreover, when Δ3 is far away from resonance, we first observe the enhancement and suppression of SWM signal at large detuning, which is moved out of the EIT window through the Doppler frequency shift led by atomic velocity component.

Acknowledgments

This work was supported by 973 Program (2012CB921804), NSFC (10974151, 61078002, 61078020, 11104214, 61108017, 11104216), NCET (08-0431), RFDP (20110201110006, 20110201120005, 20100201120031).

References and links

1. P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, “Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium,” Opt. Lett. 20(9), 982–984 (1995). [CrossRef]   [PubMed]  

2. Y. Q. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms,” Opt. Lett. 21(14), 1064–1066 (1996). [CrossRef]   [PubMed]  

3. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999). [CrossRef]  

4. D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93(18), 183601 (2004). [CrossRef]   [PubMed]  

5. H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70(6), 061804 (2004). [CrossRef]  

6. Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006). [CrossRef]   [PubMed]  

7. H. Ma and C. B. de Araujo, “Interference between third- and fifth-order polarizations in semiconductor doped glasses,” Phys. Rev. Lett. 71(22), 3649–3652 (1993). [CrossRef]   [PubMed]  

8. D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, “Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes,” J. Chem. Phys. 108(10), 3897–3902 (1998). [CrossRef]  

9. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997). [CrossRef]  

10. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005). [CrossRef]  

11. A. Imamoğlu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14(24), 1344–1346 (1989). [CrossRef]   [PubMed]  

12. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001). [CrossRef]   [PubMed]  

13. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999). [CrossRef]  

14. M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001). [CrossRef]   [PubMed]  

15. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001). [CrossRef]   [PubMed]  

16. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001). [CrossRef]   [PubMed]  

17. C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009). [CrossRef]  

18. M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001). [CrossRef]  

19. M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999). [CrossRef]  

20. B. Anderson, Y. P. Zhang, U. Khadka, and M. Xiao, “Spatial interference between four- and six-wave mixing signals,” Opt. Lett. 33(18), 2029–2031 (2008). [CrossRef]   [PubMed]  

21. Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011). [CrossRef]  

References

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  1. P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, “Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium,” Opt. Lett. 20(9), 982–984 (1995).
    [Crossref] [PubMed]
  2. Y. Q. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms,” Opt. Lett. 21(14), 1064–1066 (1996).
    [Crossref] [PubMed]
  3. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999).
    [Crossref]
  4. D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93(18), 183601 (2004).
    [Crossref] [PubMed]
  5. H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70(6), 061804 (2004).
    [Crossref]
  6. Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006).
    [Crossref] [PubMed]
  7. H. Ma and C. B. de Araujo, “Interference between third- and fifth-order polarizations in semiconductor doped glasses,” Phys. Rev. Lett. 71(22), 3649–3652 (1993).
    [Crossref] [PubMed]
  8. D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, “Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes,” J. Chem. Phys. 108(10), 3897–3902 (1998).
    [Crossref]
  9. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997).
    [Crossref]
  10. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
    [Crossref]
  11. A. Imamoğlu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14(24), 1344–1346 (1989).
    [Crossref] [PubMed]
  12. L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
    [Crossref] [PubMed]
  13. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
    [Crossref]
  14. M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001).
    [Crossref] [PubMed]
  15. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
    [Crossref] [PubMed]
  16. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001).
    [Crossref] [PubMed]
  17. C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009).
    [Crossref]
  18. M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001).
    [Crossref]
  19. M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999).
    [Crossref]
  20. B. Anderson, Y. P. Zhang, U. Khadka, and M. Xiao, “Spatial interference between four- and six-wave mixing signals,” Opt. Lett. 33(18), 2029–2031 (2008).
    [Crossref] [PubMed]
  21. Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011).
    [Crossref]

2011 (1)

Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011).
[Crossref]

2009 (1)

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009).
[Crossref]

2008 (1)

2006 (1)

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006).
[Crossref] [PubMed]

2005 (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[Crossref]

2004 (2)

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93(18), 183601 (2004).
[Crossref] [PubMed]

H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70(6), 061804 (2004).
[Crossref]

2001 (5)

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001).
[Crossref]

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001).
[Crossref] [PubMed]

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[Crossref] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001).
[Crossref] [PubMed]

1999 (3)

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999).
[Crossref]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999).
[Crossref]

1998 (1)

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, “Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes,” J. Chem. Phys. 108(10), 3897–3902 (1998).
[Crossref]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997).
[Crossref]

1996 (1)

1995 (1)

1993 (1)

H. Ma and C. B. de Araujo, “Interference between third- and fifth-order polarizations in semiconductor doped glasses,” Phys. Rev. Lett. 71(22), 3649–3652 (1993).
[Crossref] [PubMed]

1989 (1)

Albrecht, A. C.

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, “Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes,” J. Chem. Phys. 108(10), 3897–3902 (1998).
[Crossref]

Anderson, B.

Balic, V.

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93(18), 183601 (2004).
[Crossref] [PubMed]

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[Crossref] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

Braje, D. A.

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93(18), 183601 (2004).
[Crossref] [PubMed]

Chen, H.

Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011).
[Crossref]

Cirac, J. I.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

Cronin-Golomb, M.

de Araujo, C. B.

H. Ma and C. B. de Araujo, “Interference between third- and fifth-order polarizations in semiconductor doped glasses,” Phys. Rev. Lett. 71(22), 3649–3652 (1993).
[Crossref] [PubMed]

Donoghue, J.

Duan, L.-M.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[Crossref] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001).
[Crossref] [PubMed]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[Crossref]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999).
[Crossref]

Fry, E. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999).
[Crossref]

Fu, G. S.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006).
[Crossref] [PubMed]

Fu, P. M.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006).
[Crossref] [PubMed]

Fu, Y.

Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011).
[Crossref]

Goda, S.

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93(18), 183601 (2004).
[Crossref] [PubMed]

Harris, S. E.

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93(18), 183601 (2004).
[Crossref] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997).
[Crossref]

A. Imamoğlu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14(24), 1344–1346 (1989).
[Crossref] [PubMed]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[Crossref] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

Hemmer, P. R.

Hernandez, G.

H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70(6), 061804 (2004).
[Crossref]

Hollberg, L.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999).
[Crossref]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[Crossref]

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001).
[Crossref] [PubMed]

A. Imamoğlu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14(24), 1344–1346 (1989).
[Crossref] [PubMed]

Jiang, Q.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006).
[Crossref] [PubMed]

Kang, H.

H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70(6), 061804 (2004).
[Crossref]

Kash, M. M.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999).
[Crossref]

Katz, D. P.

Khadka, U.

Kirkwood, J. C.

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, “Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes,” J. Chem. Phys. 108(10), 3897–3902 (1998).
[Crossref]

Kumar, P.

Li, C. B.

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009).
[Crossref]

Li, Y. Q.

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[Crossref] [PubMed]

Liu, X.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006).
[Crossref] [PubMed]

Lukin, M. D.

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001).
[Crossref] [PubMed]

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001).
[Crossref] [PubMed]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999).
[Crossref]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999).
[Crossref]

Ma, H.

H. Ma and C. B. de Araujo, “Interference between third- and fifth-order polarizations in semiconductor doped glasses,” Phys. Rev. Lett. 71(22), 3649–3652 (1993).
[Crossref] [PubMed]

Mair, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001).
[Crossref] [PubMed]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[Crossref]

Nie, Z. Q.

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009).
[Crossref]

Phillips, D. F.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001).
[Crossref] [PubMed]

Rickey, E. G.

M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001).
[Crossref]

Rostovtsev, Y.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999).
[Crossref]

Sautenkov, V. A.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999).
[Crossref]

Scully, M. O.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999).
[Crossref]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999).
[Crossref]

Shahriar, M. S.

Song, J. P.

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009).
[Crossref]

Sun, J.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006).
[Crossref] [PubMed]

Ulness, D. J.

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, “Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes,” J. Chem. Phys. 108(10), 3897–3902 (1998).
[Crossref]

Walsworth, R. L.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001).
[Crossref] [PubMed]

Wang, Z.

Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011).
[Crossref]

Welch, G. R.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999).
[Crossref]

Wu, L. A.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006).
[Crossref] [PubMed]

Wu, Z.

Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011).
[Crossref]

Xiao, M.

Yan, M.

M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001).
[Crossref]

Yelin, S. F.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999).
[Crossref]

Yin, G. Y.

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93(18), 183601 (2004).
[Crossref] [PubMed]

Zhang, Y.

Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011).
[Crossref]

Zhang, Y. P.

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009).
[Crossref]

B. Anderson, Y. P. Zhang, U. Khadka, and M. Xiao, “Spatial interference between four- and six-wave mixing signals,” Opt. Lett. 33(18), 2029–2031 (2008).
[Crossref] [PubMed]

Zheng, H.

Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011).
[Crossref]

Zheng, H. B.

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009).
[Crossref]

Zhu, Y.

H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70(6), 061804 (2004).
[Crossref]

Zhu, Y. F.

M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001).
[Crossref]

Zibrov, A. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82(26), 5229–5232 (1999).
[Crossref]

Zoller, P.

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
[Crossref] [PubMed]

Zuo, Z. C.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

C. B. Li, H. B. Zheng, Y. P. Zhang, Z. Q. Nie, J. P. Song, and M. Xiao, “Observation of enhancement and suppression in four-wave mixing processes,” Appl. Phys. Lett. 95(4), 041103 (2009).
[Crossref]

J. Chem. Phys. (1)

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, “Competitive events in fifth order time resolved coherent Raman scattering: Direct versus sequential processes,” J. Chem. Phys. 108(10), 3897–3902 (1998).
[Crossref]

Nature (4)

L.-M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414(6862), 413–418 (2001).
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Opt. Lett. (4)

Phys. Rev. A (4)

H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A 70(6), 061804 (2004).
[Crossref]

Z. Wang, Y. Zhang, H. Chen, Z. Wu, Y. Fu, and H. Zheng, “Enhancement and suppression of two coexisting six-wave-mixing processes,” Phys. Rev. A 84(1), 013804 (2011).
[Crossref]

M. Yan, E. G. Rickey, and Y. F. Zhu, “Observation of doubly dressed states in cold atoms,” Phys. Rev. A 64(1), 013412 (2001).
[Crossref]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60(4), 3225–3228 (1999).
[Crossref]

Phys. Rev. Lett. (5)

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86(5), 783–786 (2001).
[Crossref] [PubMed]

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97(19), 193904 (2006).
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[Crossref]

D. A. Braje, V. Balić, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93(18), 183601 (2004).
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[Crossref]

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Figures (7)

Fig. 1
Fig. 1 (a) The diagram of the K-type five-level atomic system. (b) Spatial beam geometry used in the experiment. (c) The diagram of the ladder-type three-level atomic subsystem when the fields E 3 , E 3 , E 4 and E 4 are blocked and E 1 , E 2 and E 2 are turned on. (d) The diagram of the Y-type four-level atomic subsystem when the fields E 3 and E 3 are blocked and other beams are turned on. (e) The diagram of the K-type five-level atomic system when the fields E 2 and E 4 are blocked only.
Fig. 2
Fig. 2 The probe transmission (the upper curves) and measured MWM signals (the bottom curves) with different ways of blocking laser beams. The left peaks show the EIT window and MWM signals related to E 4 ( E 4 ) and the right peaks are related to E 2 ( E 2 ). (a) Measured total MWM signals with all beams turned on. (b) Measured MWM signals related to E 4 ( E 4 ) and SWM signal E S2 , with E 2 blocked. (c) Measured MWM signals related to E 4 ( E 4 ) and SWM signal E S2 , with E 2 blocked. (d) Measured MWM signals related to E 2 ( E 2 ) with E 4 and E 4 blocked. (e) Measured FWM signal E F2 and E F4 with E 3 and E 3 blocked. The experimental parameters are Δ 2 =150MHz , Δ 4 =140MHz , Δ 3 =0MHz , and the powers of all laser beams are 5.3mW ( E 1 ), 40.9mW ( E 2 ), 5mW ( E 2 ), 44mW ( E 3 and E 3 ), 21mW ( E 4 and E 4 ).
Fig. 3
Fig. 3 (a) The measured intensity of (a1) the probe transmission and (a2) the singly-dressed FWM signal E F2 versus Δ 2 at discrete probe detunings Δ 1 =80, 20, 0, 20 and 80 MHz , and the measured intensity of (a3) the probe transmission and (a4) the singly-dressed FWM signal E F2 versus Δ 1 at discrete dressing detunings Δ 2 =80, 20, 0, 20 and 80 MHz . (b1), (b3), (b4), (b5) are theoretical calculations corresponding to (a1)-(a4). (b2) is the theoretical calculations of enhancement and suppression of singly-dressed E F2 . (c) The dressed energy level diagrams corresponding to (a). Powers of participating laser beams are 4mW ( E 1 ), 34.5mW ( E 2 ), 8.7mW ( E 2 ).The detuning range is 200MHz when scanning Δ 1 , 60MHz when scanning Δ 2 .
Fig. 4
Fig. 4 (a) The measured intensity of (a1) the probe transmission and (a2) the doubly-dressed FWM signal E F2 versus Δ 2 at discrete probe detunings Δ 1 =80, 40, 20, 10, 0, 10, 20, 40 and 80 MHz , and the measured intensity of (a3) the probe transmission and (a4) the doubly-dressed FWM signal E F2 versus Δ 1 at discrete self-dressing detunings Δ 2 =80, 40, 20, 10, 0, 10, 20, 40 and 80 MHz ( Δ 4 is fixed at Δ 4 =0 ). (b1), (b3), (b4), (b5) are theoretical calculations corresponding to (a1)-(a4). (b2) is the theoretical calculations of enhancement and suppression of doubly-dressed E F2 . (c) The energy level diagrams corresponding to (a). (d) The measured intensity of (d1) the probe transmission and (d2) the doubly-dressed FWM signal E F2 versus Δ 4 at discrete probe detunings Δ 1 =80, 40, 20, 10, 0, 10, 20, 40 and 80 MHz , and the measured intensity of (d3) the probe transmission and (d4) the doubly-dressed FWM signal E F2 versus Δ 1 at discrete external-dressing detunings Δ 4 =80, 40, 20, 10, 0, 10, 20, 40 and 80 MHz ( Δ 2 is fixed at Δ 2 =0 ). (e1)-(e4) Theoretical calculations corresponding to (d1)-(d4). (f) The energy level diagrams corresponding to (d). Powers of participating laser beams are 4.6mW ( E 1 ), 33mW ( E 2 ), 8.4mW ( E 2 ), 39mW ( E 4 ).
Fig. 5
Fig. 5 The spatiotemporal interferograms of E F2 and E F4 in the Y-type atomic subsystem. (a) A three-dimensional spatiotemporal interferogram of the total FWM signal intensity I(τ,r) versus time delay τ of beam E 2 and transverse position r. (b) The temporal interference with a much longer time delay of beam E 2 . (c) Measured beat signal intensity I(τ,r) versus time delay τ together with the theoretically simulated result (solid curve).
Fig. 6
Fig. 6 (a1) The probe transmission signal and (a2) the SWM signal with the enhancement and suppression effect versus Δ 2 for different Δ 1 with the laser beams E 2 and E 4 blocked when Δ 3 is at large detuning. (b) The doubly-dressed state diagram of the SWM signal. Powers of participating laser beams are 3mW ( E 1 ), 4.6mW ( E 2 ), 44mW ( E 3 and E 3 ), 65mW ( E 4 ).
Fig. 7
Fig. 7 (a) Measured total MWM signal versus Δ 2 at discrete Δ 1 when all seven laser beams on. (b) Measured FWM signals versus Δ 2 at discrete Δ 1 . (b1) Signal obtained with the laser beams E 3 and E 3 blocked and others on. (b2) The enhancement and suppression of the FWM signal E F4 when the laser beams E 3 , E 3 and E 2 are blocked. (b3) The FWM signal when the laser beams E 3 , E 3 and E 4 are blocked. (c) Measured SWM signals versus Δ 2 at discrete Δ 1 . (c1) Signal obtained with laser beams E 2 , E 4 blocked and others on. (c3) Signal obtained with the laser beams E 2 , E 4 and E 4 blocked. (c2) The sum of E S4 D E S4 and E S2 D E S2 . Powers of all laser beams are 3.7mW ( E 1 ), 55mW ( E 2 ), 5.3mW ( E 2 ), 44mW ( E 3 and E 3 ), 85mW ( E 4 ), 8.6mW ( E 4 ).

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