Abstract

We report our observations on enhancement and suppression of spatial four-wave mixing (FWM) images and the interplay of four coexisting FWM processes in a two-level atomic system associating with three-level atomic system as comparison. The phenomenon of spatial splitting of the FWM signal has been observed in both x and y directions. Such FWM spatial splitting is induced by the enhanced cross-Kerr nonlinearity due to atomic coherence. The intensity of the spatial FWM signal can be controlled by an additional dressing field. Studies on such controllable beam splitting can be very useful in understanding spatial soliton formation and interactions, and in applications of spatial signal processing.

© 2011 OSA

1. Introduction

Efficient four-wave mixing (FWM) processes enhanced by atomic coherence in multilevel atomic systems [14] are of great current interest. Recently, destructive and constructive interferences in a two-level atomic system [5] and competition via atomic coherence in a four-level atomic system [6] with two coexisting FWM processes were studied. Also, the interactions of doubly dressed states and the corresponding effects of atomic systems have attracted many researchers in recent years [7,8]. The interaction of double-dark state and splitting of a dark state in a four-level atomic system were studied theoretically in an electromagnetically induced transparency (EIT) system by Lukin et al. [7]. The triple-peak absorption spectrum, which was observed later in the N-type cold atomic system by Zhu et al., verified the existence of the secondarily dressed states [8]. Recently, we had theoretically investigated three types of doubly dressed schemes in a five-level atomic system [9] and observed three-peak Autler-Townes (AT) splitting of the secondary dressing FWM signal [10]. In addition, we reported the evolution of suppression and enhancement of FWM signal by controlling an additional laser field [11].

As two or more laser beams pass through an atomic medium, the cross-phase modulation (XPM), as well as modified self-phase modulation (SPM), can potentially affect the propagation and spatial patterns of the incident laser beams. Laser beam self-focusing [12] and pattern formation [13] have been extensively investigated with two laser beams propagating in atomic vapors. Recently, we have observed spatial shift [14] and spatial splitting [1517] of the FWM beams generated in multi-level atomic systems, which can be well controlled by additional dressing laser beams via XPM. Studies on such spatial shift and splitting of the laser beams can be very useful in understanding the formation and interactions of spatial solitons [16] in the Kerr nonlinear systems and signal processing applications, such as spatial image storage [18], entangled spatial images [19], soliton pair generation [20], and influences of higher-order (such as fifth-order) nonlinearities [21].

In this paper, we first report our experimental studies of the interaction of four coexisting FWM processes in a two-level atomic system by blocking different laser beams. Next, we investigate the various suppression/enhancement of the degenerate-FWM (DFWM) signals and two dispersion centers, which are caused by the cascade dressing interaction of two dressing fields. The experimental results clearly show the evolutions of the enhancement and suppression, from pure enhancement to partial enhancement/suppression, then to pure suppression, further to partial enhancement/suppression, and finally to enhancement, which are in good agreement with the theoretical calculations. In addition, we also observe the spatial splitting in the x and y directions of DFWM signal due to different spatially alignment of the probe and coupling beams.

2. Theoretical model and experimental scheme

The two relevant experimental systems are shown in Figs. 1(a) and 1(b). Three energy levels from sodium atom in heat pipe oven are involved in the experimental schemes. The pulse laser beams are aligned spatially as shown in Fig. 1(c). In the Fig. 1(a), energy levels |0〉 (3S1/2) and |1〉 (3P3/2) form a two-level atomic system. Coupling field E1 (with wave vector k1 and the Rabi frequency G1) together with E1 (k1 and G1) (connecting the transition between |0〉 and |1〉) having a small angle (0.3) propagates in the opposite direction of the probe field E3 (k3 and G3) (also connecting the transition between |0〉 and |1〉). These three laser beams come from the same near-transform-limited dye laser (with a 10 Hz repetition rate, 5 ns pulse width, and 0.04 cm1 linewidth) with the same frequency detuning Δ1=ω10ω1, where ω10 is the transition frequency between |0〉 and |1〉. The coupling fields E1 and E1 induce a population grating between states |0〉 to |1〉, which is probed by E3. This generates a DFWM process (Fig. 1(a)) satisfying the phase-matching condition of kF1=k1k1+k3. Then, two additional coupling fields E2 (k2, G2) and E2 (k2, G2) are applied as scanning fields connecting the transition from |0〉 to |1〉 with the same frequency detuning Δ2=ω10ω2; the two additional coupling fields are from another similar dye laser set at ω2 to dress the energy level |1〉. The fields E2, E2, and E3 produce a non-degenerate FWM (NDFWM) signal kF2 (satisfying kF2=k2k2+k3). When the five laser beams are all on, there also exist other two FWM processes kF3 (satisfying kF3=k2k1+k3) and kF4 (satisfying kF4=k1k2+k3) in the same directions as EF1 and EF2, respectively.

 

Fig. 1 (a) and (b) The diagram of relevant Na energy levels. (c) The scheme of the experiment. Inset gives the spatial alignments of the incident beams.

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Under the experimental condition, E1 (or E1) with detuning Δ1 depletes two groups of atoms with different velocities at the same time, such as negative velocities group and positive velocities group. At Δ1<0, the positive velocities group will see E1 (or E1) with detuning Δ1+k1v and E3 with detuning Δ1k3v. The frequency of the DFWM EF1in this case will be ωf=(ω1kv)(ω1kv)+(ω1+k3v)=ω1+k3v due to the conservation of energy. Correspondingly, at Δ1>0, negative velocities group will see E1 (or E1) with detuning Δ1k1v and E3 with detuning Δ1+k3v. The frequency of EF1 will be ωf=(ω1+kv)(ω1+kv)+(ω1k3v)=ω1k3v. Such changing implies that a group of atoms with certain velocities can satisfy the condition Δ1=Δ1±k1v, where Δ1 is the detuning of E1 (or E1) based on both saturation excitation and atomic coherence effect. As a result, the self-dressing field E1 (or E1) can be considered as the outer dressing field and separates the level |0〉 into two dressing states |G1±>, as shown in Fig. 2 . In addition, the Doppler effect and the power broadening effect on the weak FWM signals need to be considered.

 

Fig. 2 (Color online) The interplay and mutual suppression/enhancement between two coexisting FWM signals (EF1 and EF3). (a1) the upper curves: pure DFWM signal EF1 (with both E2and E2 blocked) (squares), singly dressed DFWM signal EF1 (with E2 blocked) (triangles), coexisting singly dressed DFWM signal EF1 and FWM signal EF3 (with E2 blocked) (reverse triangles), and coexisting dressed DFWM signal EF1 and FWM signal EF3 (circles);lower curves: pure FWM signal EF3 (with both E1and E2 blocked) (left triangle), singly-dressed FWM signal (with E1 blocked) (right triangle); Δ1=0. The inserted plot: corresponding to the dressed-state picture. (b1) the condition are the same to that in (a1) except Δ1=25.9  GHz. The inserted plot: corresponding to the dressed-state picture. (a2) and (b2) theoretical plots corresponding to the experimental parameters of (a1) and (b1), respectively.

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When E1, E1, E2, E2 and E3 are open, the DFWM process EF1and NDFWM processes EF2, EF3 and EF4 are generated simultaneously, and there exists interplay among these four FWM signals in the two-level atomic system. These generated FWM signals have the frequencies ωF1=ωF2=ω1, ωF3=ω2, and ωF4=2ω1ω2. They are split into two equal components by a 50% beam splitter before being detected. One is captured by the CCD camera, and the other is detected by photomultiplier tubes (D1 or D2) and a fast gated integrator (gate width of 50 ns). Also, they are monitored by digital acquisition card.

In order to interpret the following experimental results, we perform the theoretical calculation on the four coexisting FWM processes. First, we consider four FWM processes to be or perturbed by corresponding laser beams. In two-level configuration, there exist the transition paths to generate FWM signals. They can be described by perturbation chains (F1) ρ00(0)(E1)*ρ10(1)(E1')*ρ00(2)E3ρ10(3), (F2) ρ00(0)(E2')*ρ10(1)E2ρ00(2) E3ρ10(3), (F3) ρ00(0)E2ρ10(1)(E1')*ρ00(2)E3ρ10(3), and (F4) ρ00(0)E1ρ10(1) (E2')*ρ00(2)E3ρ10(3), respectively. For the DFWM signal EF1, in fact, this DFWM generation process can be viewed as a series of transitions: the first step is from |0〉 to |1〉 with absorption of a coupling photon E1, and the final state of this process can be dressed by the dressing field E2 (or E2). The second step is the transition from |1〉 to |0〉, and the final state cannot be dressed by any field. The third step is the transition from |0〉 to |1〉 with the emission of a probe photon E3, and the final state of this process can be dressed by E2 (or E2). Then, the last transition is from |1〉 to |0〉, which emits a FWM photon at frequency ω1. Thus, we can obtain the dressed perturbation chain ρ00(0)(E1)*ρG2±0(1)(E1')* ρ00(2)E3ρG2±0(3). Similarly, we can obtain the other dressed perturbation chains as (DF2) ρ00(0)E2 ρG1±0(1)(E2')*ρ00(2)E3ρG1±0(3), (DF3) ρ00(0)E2ρG2±0(1)(E1')*ρ00(2)E3ρG2±0(3), and (DF4) ρ00(0)E1 ρG1±0(1)(E2')* ρ00(2)E3ρG1±0(3), respectively. The expressions of the corresponding density matrix elements related to the four FWM processes are ρF1(3)=iG3G1(G1)*/(Γ00B12), ρF2(3)=iG3G2(G2)*/(Γ00d3B2), ρF3(3)=iG2G3(G1)*/(d4B32), ρF4(3)=iG1G3(G2)*/(d5d6B1), respectively, whered1=Γ10+iΔ1, d2=Γ00+i(Δ1/mΔ2), d3=Γ10+iΔ2, d4=Γ00+i(Δ2Δ1), d5=Γ10+i(2Δ1Δ2), d6=[Γ00+i(Δ1Δ2)], A1=|G2|2/d2, A2=G12/Γ00, A3=|G2|2/Γ00, B1=d1+A1, B2=d1+A2, B3=d3+A3. Here Gi=μiEi/ (i = 1, 2, 3) is the Rabi frequency; Γ10, Γ20, and Γ00 are the transverse relaxation rates, and Δi (i=1,2) is the detuning factor.

The experiments are carried out in a vapor cell containing sodium. The cell, 18-cm long, is heated up to a temperature of about 230C and crossed by linearly polarized laser beams which interact with the atoms. In the two-level atomic system, the coupling fields E1 and E1 (with diameter of 0.8 mm and power of 9 μW), and the probe field E3 (with diameter of 0.8 mm and power of 3 μW) are tuned to the line center (589.0 nm) of the |0 to |1 transition, which generate the DFWM signal EF1 at frequency ω1. The coupling fields E2 and E2 (with diameter of 1.1 mm and powers of 20 μW and 100 μW, respectively) are scanned simultaneously around the |0 to |1 transition to dress the DFWM process EF1.

3. Cascade dressing interaction

We first investigate the interaction of four coexisting FWM signals in the two-level atomic system by blocking different laser beams. Firstly, by blocking E2 (or E1), the DFWM signal EF1 (or the FWM signal EF3) is suppressed by the coupling field E2 as can be seen from the upper triangle points [or the right triangle points in Fig. 2(a1)], compared to the pure DFWM signal EF1 (or the FWM signal EF3). Next, when laser beams E1, E1, E2 and E3 are turned on, two coexisting FWM processes (EF1 and EF3) couple to each other (the lower triangle points), and the intensities of total FWM signals are increased, as can be attributed to the combination of two FWM signal processes (EF1 and EF3). Finally, when all the five laser beams are turned on, the DFWM signal EF1 and the FWM signal EF3 are both greatly suppressed by corresponding dressing fields. So the intensities of total FWM signals are extremely decreased, as shown in the circles points in Fig. 2(a1).

These effects can be explained effectively by the dressed-state picture. The dressing field E2 couples the transition |0> to |1> and creates the dressed states |G2±>, which leads to single-photon transition |0>|1> off-resonance [the inserted plot in Fig. 2(a1)]. At exact single-photon resonance with Δ1=0, the DFWM signal EF1 intensity is greatly suppressed by the means of scanning the dressing field E2 across the resonance (Δ2=0), as the upper triangle points in Fig. 2(a1) shows. At the same time, the FWM signal EF3 experiences similar process [the right triangle points in Fig. 2(a1)].

Furthermore, an appropriate Δ1 value at which EF1 is either enhanced or suppressed is chosen in the investigation. In this case, compared to the pure DFWM signal EF1 [square points in Fig. 2(b1)], the dressed DFWM signal EF1 is enhanced [the upper and low triangle points in Fig. 2(b1)]. However, the dressed FWM signal EF3 is suppressed due to the destructive interference [right triangle points in Fig. 2(b1)] compared to the pure signal [left triangle points in Fig. 2(b1)]. The upper triangle in Fig. 2(b1) combines the two FWM processes (EF1 and EF3), which are dressed by laser beams E1 and E2, respectively. After calculating ρF1(3) and ρF3(3) under the above experiment conditions, good agreements are obtained between the theoretical calculations and the experimental results as shown in Figs. 2(a2) and 2(b2), respectively.

After that, we investigate the evolutions of the interaction between these two coexisting FWM signals by the means of setting different frequency detuning Δ1 values, where the fixed spectra corresponds to the suppression and enhancement of DFWM signal EF1, and the shifting spectra corresponds to the FWM signal EF3 as shown in Figs. 3 (a1)–3(a7). It is obvious in Figs. 3(a1)–3(a3) that, as the frequency detuning Δ1 varies from Δ1<0 to zero from up to down, the DFWM signal EF1 shows the evolution from enhancement to partial enhancement/suppression, and then to suppression. At the same time, the FWM signal EF3 varies from intense to weak (when two FWM signals EF1 and EF3 overlap) and shifts from left side to right side, which satisfies the two-photon resonant condition (Δ1Δ2=0). When Δ1 changes further to be positive, a symmetric process is observed [i.e., suppression in Fig. 3(a5), partial suppression/enhancement in Fig. 3(a6), and pure enhancement in Fig. 3(a7)]. It should be noted here that FWM signal EF3 still shifts from left side to right side. Figure 3(a4) shows the weakened FWM signal due to the strong effect of the Doppler absorption. Especially, the DFWM signal EF1 at a large one-photon detuning is extremely weak when G2=0. However, the strong dressing field can cause the resonant excitation of one of the dressed states if the enhanced condition Δ1Δ2±G2=0 is satisfied. In such case, the DFWM signal EF1 is strongly enhanced [Fig. 3(a1)], mainly due to the one-photon resonance (|0>|G2+|) [the insert plot in Fig. 2(b1)]. As Δ1=0, the intensity of the DFWM signal EF1 is greatly suppressed [Fig. 3(a3)], similar to the case of the upper triangle curves in Fig. 2(a1). Also, we can observe the FWM signal EF3 is suppressed due to the destructive interference. In addition, Figs. 3(b1)–3(b7) show the interaction of another two coexisting the FWM processes (EF2 and EF4), in which the fixed spectra corresponds to the FWM signal EF2, and the shifting spectra corresponds to FWM signal EF4 for different frequency detuning Δ1 values.

 

Fig. 3 (a) and (b) Measured evolution of the four FWM signals [(EF1and EF3) and (EF2 and EF4), respectively] versus Δ2 for different Δ1 values. (a1)-(a7) and (b1)-(b7): Δ1=-139.1, −103.87, −29.5, 0, 29.8, 100.1, 155.7GHz, respectively.

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Now, we concentrate on the cascade dressing interaction and the two dispersion centers of FWM images with two dressing fields E1 and E2 in the two-level atomic system. In order to investigate the cascade dressing interaction, the power of the coupling field E1 is set at 80μW. So the DFWM signal EF1 shows a spectrum of the AT splitting due to self-dressed effect [10] induced by beam k1 when Δ1 is scanned and the dressing field E2 is off, as shown in the dashed curve of Fig. 4(a) . When the beam k2 is on, the DFWM signal EF1 is dressed by both E1 and E2, and therefore shows the cascade dressing interaction, as shown in Figs. 4(a) and 4(c). Specifically, by discretely choosing different detuning values within Δ1<0 and scanning Δ2, the DFWM signal EF1shows the evolution of the successively occurring pure enhancement, partial suppression/enhancement, pure suppression, partial enhancement/suppression and enhancement processes, as shown in the left side of Fig. 4(a). When Δ1 changes to be positive, a symmetric process occurs, in the right side of Fig. 4(a), which is well described by the theoretical curves [Fig. 4(b)].

 

Fig. 4 (Color online) (a) Measured suppression and enhancement of DFWM signal EF1 versus Δ2 for different Δ1values in the two-level system. Δ1=-69.1, −55.5, −38.7, −19.2, 0, 14.7, 28.8, 42.2 and 57.3 GHz, respectively. The dashed curve is the double-peak DFWM signal EF1 versus Δ1. (b) Theoretical plots corresponding to the experimental parameters in (a). (c) The same measures to (a) with the same condition, except that the laser beams E1, E1 overlap in the middle of heat oven. (d1)-(d9) the dressed-state pictures of the suppression or enhancement of the DFWM signal. The states |G1±> (dashed lines) and the states |G1+±> or |G1±> (dot-dashed lines), respectively.

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In order to explain this phenomenon, the dressed-state picture is adopted, as shown in Fig. 4(d). First, the DFWM signal EF1is dressed by both fields E2 and E1. The corresponding expression of the modified density matrix element of DFWM EF1 process is ρEF1(3)=iG3G1(G1)*/(B4B52), where d6=Γ00+A5, d7=Γ10iΔ2, A4=G12/B1, A5=G22/d7, A6=G12/d6, B4=Γ00+A4 and B5=B1+A6. Next, the inner dressing field E1 dresses the state |0> to create two new dressing states |G1±>, and then the strong dressing field E2 creates new states |G1+±> or |G1±> around states |G1±>, as scanning the frequency detuning Δ2. As a result of this dressing scheme, the DFWM signal EF1 is extremely small when G2=0 and Δ1 is set far away from the resonance point at both Δ1<0 and Δ1>0, respectively. Another result is that the strong fields can cause resonant excitation of one of the dressed state (i.e., |G1> or |G1++> [Fig. 4(d1) and Fig. 4(d9), respectively], which can lead to the enhancement of FWM signals. Specifically, if the condition Δ1Δ2=G2 and Δ1Δ2=G2 [corresponding to the dressed states shown in Figs. 4(d1) and 4(d9)] is satisfied, the DFWM signal EF1 is obviously enhanced, as shown in the curves of Fig. 4(a1) and 4(a9), respectively. As Δ1 changes to be near the resonance point, we can get a partial enhancement/suppression of DFWM signal EF1. The first and second transition states satisfy suppression condition Δ1Δ2=0 and enhancement condition Δ1Δ2=G2 (Fig. 4(d2)), [enhancement condition Δ1Δ2=G2 and suppression condition Δ1Δ2=0, as shown in Fig. 4(d4)], as leads to the first suppression and next enhancement (the curve of Fig. 4(a2)) [or the first enhancement and next suppression, as shown in the curve of Fig. 4(a4)]. When Δ1 reaches the point Δ1Δ2=0, the suppression effect gets dominant due to the dressed states |G1> [Fig. 4(d3)], so the DFWM signal EF1 is purely suppressed, as shown in the curve of Fig. 4(a3). For the point Δ1=Δ2=0 between the two resonance points, the curve of Fig. 4(a5) shows a pair of suppressed peaks. In fact, they are induced by the outer dressing field E2 which can largely weaken the suppression effect of the inner dressing field E1 on DFWM signal. Furthermore, the other cascade dressing field E2 splits such suppressed peak into a pair of suppressed peaks, as shown in the curve of Fig. 4(a5). Figure 4(a) shows the various suppression/enhancement of the DFWM signal EF1 and its two dispersion centers, which is caused by the cascade dressing interaction of the two dressing fields E1 and E2.

In addition, the spatial splitting in x-direction of the FWM signal beams induced by additional dressing laser beams is observed simultaneously as shown in Fig. 5(a) . It is observed that, the number of the splitting spots increases when the FWM intensity is suppressed. To understand these phenomena, we need to consider the cross-phase modulation (XPM) on the FWM signals. As described in our previous investigation [17], the spatial splitting of the FWM beam can be controlled by the intensities of the involved laser beams, the cross-Kerr nonlinear coefficients and the atomic density, according to the nonlinear phase shift ϕ=2kF1n2zI1er2/2/(n0IF1). Here the additional transverse propagation wave-vector is δkr=ϕ/r. The change of phase (ϕ) distribution in the laser propagating equations determines the spatial splitting of the laser beams. In theoretical calculation, we can obtain the intensity of the EF1 beam by IF1|ρEF1(3)|2=|iG3Fa|2 [17], with Fa=G1(G1)*/(B4B52) and the nonlinear cross-Kerr refractive index n2Re(iμGF1Fa2/h). When Δ2 is scanned in the experiment, the intensity I1 of the laser beam E1 and n2 almost stays constant for different detuning Δ2. So ϕ is primarily determined by IF1. When the suppression condition (Δ1Δ2=0) is satisfied, and the intensity of FWM signal IF1 reaches its minimum, the spatial splitting will become stronger as shown in Fig. 5(a) (the suppression positions located at Δ212GHz). While in the enhancement condition with the larger IF1, ϕ is decreased, and therefore the splitting is weakened correspondingly, as shown in Fig. 5(a), where the enhancement condition is located at Δ228.3GHz.

 

Fig. 5 (Color online) (a) DFWM signal EF1 images when Δ1=-69.1, −55.5, −38.7GHz. (b) DFWM signal images when Δ1=-55.5, −38.7, −19.2GHz.

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Specially, we observed the y-direction spatial splitting images of the DFWM signal EF1 [Fig. 5(b)] by carefully arranging laser beams k1 andk1. In the experiment, the beams E1 and E1 are deliberately aligned in y-z plane with an angle θ (0.05) to induce a grating in the same plane with the fringe spacing Λ=λ1/θ. Because θ is far less than the angle of E1 and E1 in the x-z plane, Λ is big enough for observing the splitting caused by the induced grating. Furthermore when E1and E1 are set in the middle of the oven, EF1and E1 overlap in y-direction due to the phase matching condition. As a result, the splitting of EF1 in x-direction due to the nonlinear cross-Kerr effect from E1 disappears simultaneously. Because Λ remains nearly the same for the changeless θ and λ1, a larger spot of the EF1 beam with larger intensity will be split to more parts. In Fig. 5(b), the field E3 is stronger than that in Fig. 5(a), which leads to stronger FWM signals passing through the grating in y-direction. So we can easily obtain the splitting in y-direction. Moreover, in the enhanced position, the profile of the FWM signal become larger, and more split parts induced by the grating can be obtained. Here, Figs. 5(b1)-5(b3) show the experimental spots corresponding to the curves in Figs. 4(c1)-4(c3). However, the effects of suppression and enhancement of the DFWM signal EF1 are much worse due to the special spatial alignment of the laser beams, as shown in Fig. 4(c) compared to that in Fig. 4(a). In Fig. 4(a), theE1, E1 and E2, E2 are all set at the back of the heat oven. But in Fig. 4(c), only E1and E1 are deliberately moved to the middle of the oven to demonstrate the splitting of EF1 in the y-direction. So the dressing effect on EF1 by E2 in Fig. 4(c) appears worse than that in Fig. 4(a).

In order to verify the cascade dressing interaction and two dispersion centers of FWM image. The dresses field E2 is tuned to the line center (568.8 nm) of the |1> to |2> (4D3/2,5/2) transition, and a ladder type three-level atomic system forms, as shown in Fig. 1(b). With the dressed perturbation chains, we can obtain IEF1|ρEF1(3)|2, where ρEF1(3)=iG3G1(G1)*/(B6B72), with d8=Γ00+i(Δ1+Δ2), d9=Γ21+iΔ2,d10=Γ11+A9, d11=d1+A7, A7=G22/d8, A8=G12/d11, A9=G22/d9, A10=G12/d10, B6=Γ00+A8 and B7=d1+A7+A10.

We repeated above the experiment with the same experimental conditions [the data points in Fig. 4(a)], and obtained the results as shown in Fig. 6(a) . Comparing the results in Fig. 6(a) with those in Fig. 4(a), we can obtain the similar observations of suppression and enhancement of the DFWM signal EF1, except the shapes of partial suppressions/ enhancement. For instance, the curve of Fig. 4(a2) shows first suppression, and next enhancement, is different from the curve of Fig. 6(a2), which shows first enhancement, and next suppression. The reason for this contrast is the difference of levels structure. As Δ1 is set near the resonance point (Δ1=55.8GHz), the new dressed-state |G1> moves from upper to lower as Δ2 is scanned from positive to zero [Fig. 4(d2)]. So the DFWM signal EF1 is first enhanced as the condition Δ1+Δ2=G2 is satisfied, and then suppressed (the suppression condition Δ1+Δ2=0), as shown in the curve of Fig. 6(a2). Simultaneously, we obtain the corresponding suppressions and enhancements of x direction spatial splitting of DFWM signal EF1 images, as shown in Fig. 6(c). Here Figs. 6(c1)–6(c9) show the experimental spots corresponding to the curves in Figs. 6(a1)–6(a9).

 

Fig. 6 (a) Measured suppression and enhancement of DFWM signal EF1 versus Δ2 for different Δ1 values. Δ1=-70.5, −55.8, −32.7, −15.4, 0, 16.5, 32.5, 48.2 and 72.1 GHz, respectively. The dashed curve is the double-peak DFWM signal EF1 versus Δ1. (b) Theoretical plots corresponding to the experimental parameters in (a). (c1)-(c9) DFWM signal EF1 images. The condition here is the same as that in (a).

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4. Conclusion

In conclusion, we have experimentally observed the suppression and enhancement of the spatial FWM signal by the controlled cascade interaction of additional dressing fields, and the corresponding controlled spatial splitting of FWM signal caused by the enhanced cross-Kerr nonlinearity due to atomic coherence in two- and three-level atomic systems. In addition, we report the interplay between the two coexisting FWM signals, which can be tuned to overlap or separate by varying frequency detunings. Such controllable FWM processes can have important applications in wavelength conversion for spatial signal processing and optical communication.

Acknowledgments

This work was supported by NSFC (10974151, 61078002, 61078020), NCET (08-0431), RFDP (20100201120031), 2009xjtujc08, xjj20100100, xjj20100151.

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9. Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008). [CrossRef]  

10. Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010). [CrossRef]   [PubMed]  

11. 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]  

12. G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. 64(21), 2487–2490 (1990). [CrossRef]   [PubMed]  

13. R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud Jr, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002). [CrossRef]   [PubMed]  

14. A. J. Stentz, M. Kauranen, J. J. Maki, G. P. Agrawal, and R. W. Boyd, “Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium,” Opt. Lett. 17(1), 19–21 (1992). [CrossRef]   [PubMed]  

15. H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001). [CrossRef]   [PubMed]  

16. W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80(15), 3240–3243 (1998). [CrossRef]  

17. Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010). [CrossRef]  

18. P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor,” Phys. Rev. Lett. 100(12), 123903 (2008). [CrossRef]   [PubMed]  

19. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008). [CrossRef]   [PubMed]  

20. W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000). [CrossRef]   [PubMed]  

21. Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009). [CrossRef]   [PubMed]  

References

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  1. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–9999 (1997).
    [Crossref]
  2. 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]
  3. B. Lü, W. H. Burkett, and M. Xiao, “Nondegenerate four-wave mixing in a double-Lambda system under the influence of coherent population trapping,” Opt. Lett. 23(10), 804–806 (1998).
    [Crossref] [PubMed]
  4. H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
    [Crossref]
  5. S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98(5), 053601 (2007).
    [Crossref] [PubMed]
  6. Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91(6), 061113 (2007).
    [Crossref]
  7. 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]
  8. 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]
  9. Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).
    [Crossref]
  10. Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010).
    [Crossref] [PubMed]
  11. 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]
  12. G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. 64(21), 2487–2490 (1990).
    [Crossref] [PubMed]
  13. R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
    [Crossref] [PubMed]
  14. A. J. Stentz, M. Kauranen, J. J. Maki, G. P. Agrawal, and R. W. Boyd, “Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium,” Opt. Lett. 17(1), 19–21 (1992).
    [Crossref] [PubMed]
  15. H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
    [Crossref] [PubMed]
  16. W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80(15), 3240–3243 (1998).
    [Crossref]
  17. Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010).
    [Crossref]
  18. P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor,” Phys. Rev. Lett. 100(12), 123903 (2008).
    [Crossref] [PubMed]
  19. V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
    [Crossref] [PubMed]
  20. W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000).
    [Crossref] [PubMed]
  21. Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
    [Crossref] [PubMed]

2010 (2)

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010).
[Crossref] [PubMed]

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010).
[Crossref]

2009 (3)

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]

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

2008 (3)

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).
[Crossref]

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor,” Phys. Rev. Lett. 100(12), 123903 (2008).
[Crossref] [PubMed]

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref] [PubMed]

2007 (2)

S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98(5), 053601 (2007).
[Crossref] [PubMed]

Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91(6), 061113 (2007).
[Crossref]

2002 (1)

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

2001 (2)

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]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[Crossref] [PubMed]

2000 (1)

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000).
[Crossref] [PubMed]

1999 (1)

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]

1998 (2)

B. Lü, W. H. Burkett, and M. Xiao, “Nondegenerate four-wave mixing in a double-Lambda system under the influence of coherent population trapping,” Opt. Lett. 23(10), 804–806 (1998).
[Crossref] [PubMed]

W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80(15), 3240–3243 (1998).
[Crossref]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–9999 (1997).
[Crossref]

1995 (1)

1992 (1)

1990 (1)

G. P. Agrawal, “Induced focusing of optical beams in self-defocusing nonlinear media,” Phys. Rev. Lett. 64(21), 2487–2490 (1990).
[Crossref] [PubMed]

Agrawal, G. P.

Anderson, B.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91(6), 061113 (2007).
[Crossref]

Aronstein, D. L.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Bennink, R. S.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Boyd, R. W.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

A. J. Stentz, M. Kauranen, J. J. Maki, G. P. Agrawal, and R. W. Boyd, “Induced focusing and spatial wave breaking from cross-phase modulation in a self-defocusing medium,” Opt. Lett. 17(1), 19–21 (1992).
[Crossref] [PubMed]

Boyer, V.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref] [PubMed]

Brown, A. W.

Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91(6), 061113 (2007).
[Crossref]

Burkett, W. H.

Camacho, R. M.

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor,” Phys. Rev. Lett. 100(12), 123903 (2008).
[Crossref] [PubMed]

Cronin-Golomb, M.

Denz, C.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000).
[Crossref] [PubMed]

W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80(15), 3240–3243 (1998).
[Crossref]

Donoghue, J.

Du, S. W.

S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98(5), 053601 (2007).
[Crossref] [PubMed]

Fleischhauer, M.

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]

Gauthier, D. J.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Geisser, M.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000).
[Crossref] [PubMed]

Goorskey, D.

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[Crossref] [PubMed]

Harris, S. E.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–9999 (1997).
[Crossref]

Hemmer, P. R.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

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]

Howell, J. C.

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor,” Phys. Rev. Lett. 100(12), 123903 (2008).
[Crossref] [PubMed]

Katz, D. P.

Kauranen, M.

Khadka, U.

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

Kivshar, Y. S.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000).
[Crossref] [PubMed]

Krolikowski, W.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000).
[Crossref] [PubMed]

Królikowski, W.

W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80(15), 3240–3243 (1998).
[Crossref]

Kumar, P.

Lett, P. D.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref] [PubMed]

Li, C. B.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010).
[Crossref]

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010).
[Crossref] [PubMed]

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, H.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

Li, P. Z.

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).
[Crossref]

Lu, K. Q.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010).
[Crossref]

Lü, B.

Lukin, M. D.

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]

Lukishova, S.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Luther-Davies, B.

W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80(15), 3240–3243 (1998).
[Crossref]

Luther-Davies, B. L.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000).
[Crossref] [PubMed]

Maki, J. J.

Marino, A. M.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref] [PubMed]

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

McCarthy, G.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000).
[Crossref] [PubMed]

Nie, Z. Q.

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010).
[Crossref] [PubMed]

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]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).
[Crossref]

Ostrovskaya, E. A.

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000).
[Crossref] [PubMed]

Pooser, R. C.

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[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. V.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

Rubin, M. H.

S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98(5), 053601 (2007).
[Crossref] [PubMed]

Saffman, M.

W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80(15), 3240–3243 (1998).
[Crossref]

Sautenkov, V. A.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

Scully, M. O.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[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]

Stentz, A. J.

Stroud, C. R.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Vudyasetu, P. K.

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor,” Phys. Rev. Lett. 100(12), 123903 (2008).
[Crossref] [PubMed]

Wang, H.

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[Crossref] [PubMed]

Wang, Z. G.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010).
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W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000).
[Crossref] [PubMed]

Welch, G. R.

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[Crossref]

Wen, F.

Wen, J. M.

S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98(5), 053601 (2007).
[Crossref] [PubMed]

Wong, V.

R. S. Bennink, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, S. Lukishova, and D. J. Gauthier, “Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor,” Phys. Rev. Lett. 88(11), 113901 (2002).
[Crossref] [PubMed]

Xiao, M.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010).
[Crossref]

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010).
[Crossref] [PubMed]

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]

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).
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Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91(6), 061113 (2007).
[Crossref]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
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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]

Yang, Y. M.

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).
[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.

S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98(5), 053601 (2007).
[Crossref] [PubMed]

Yuan, C. Z.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010).
[Crossref]

Zhang, Y.

Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91(6), 061113 (2007).
[Crossref]

Zhang, Y. P.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010).
[Crossref]

Y. P. Zhang, Z. Q. Nie, Z. G. Wang, C. B. Li, F. Wen, and M. Xiao, “Evidence of Autler-Townes splitting in high-order nonlinear processes,” Opt. Lett. 35(20), 3420–3422 (2010).
[Crossref] [PubMed]

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

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]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).
[Crossref]

Zheng, H. B.

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010).
[Crossref]

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]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).
[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]

Appl. Phys. Lett. (2)

Y. Zhang, B. Anderson, A. W. Brown, and M. Xiao, “Competition between two four-wave mixing channels via atomic coherence,” Appl. Phys. Lett. 91(6), 061113 (2007).
[Crossref]

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]

Opt. Lett. (4)

Phys. Rev. A (5)

H. Li, V. A. Sautenkov, Y. V. Rostovtsev, G. R. Welch, P. R. Hemmer, and M. O. Scully, “Electromagnetically induced transparency controlled by a microwave field,” Phys. Rev. A 80(2), 023820 (2009).
[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]

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]

Z. Q. Nie, H. B. Zheng, P. Z. Li, Y. M. Yang, Y. P. Zhang, and M. Xiao, “Interacting multi-wave mixing in a five-level atomic system,” Phys. Rev. A 77(6), 063829 (2008).
[Crossref]

Y. P. Zhang, Z. G. Wang, H. B. Zheng, C. Z. Yuan, C. B. Li, K. Q. Lu, and M. Xiao, “Four-wave-mixing gap solitons,” Phys. Rev. A 82(5), 053837 (2010).
[Crossref]

Phys. Rev. Lett. (8)

P. K. Vudyasetu, R. M. Camacho, and J. C. Howell, “Storage and retrieval of multimode transverse images in hot atomic Rubidium vapor,” Phys. Rev. Lett. 100(12), 123903 (2008).
[Crossref] [PubMed]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87(7), 073601 (2001).
[Crossref] [PubMed]

W. Królikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80(15), 3240–3243 (1998).
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[Crossref] [PubMed]

S. W. Du, J. M. Wen, M. H. Rubin, and G. Y. Yin, “Four-wave mixing and biphoton generation in a two-level system,” Phys. Rev. Lett. 98(5), 053601 (2007).
[Crossref] [PubMed]

W. Krolikowski, E. A. Ostrovskaya, C. Weilnau, M. Geisser, G. McCarthy, Y. S. Kivshar, C. Denz, and B. L. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85(7), 1424–1427 (2000).
[Crossref] [PubMed]

Y. P. Zhang, U. Khadka, B. Anderson, and M. Xiao, “Temporal and spatial interference between four- wave mixing and six-wave mixing channels,” Phys. Rev. Lett. 102(1), 013601 (2009).
[Crossref] [PubMed]

Phys. Today (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–9999 (1997).
[Crossref]

Science (1)

V. Boyer, A. M. Marino, R. C. Pooser, and P. D. Lett, “Entangled images from four-wave mixing,” Science 321(5888), 544–547 (2008).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

(a) and (b) The diagram of relevant Na energy levels. (c) The scheme of the experiment. Inset gives the spatial alignments of the incident beams.

Fig. 2
Fig. 2

(Color online) The interplay and mutual suppression/enhancement between two coexisting FWM signals ( E F 1 and E F 3 ). (a1) the upper curves: pure DFWM signal E F 1 (with both E 2 and E 2 blocked) (squares), singly dressed DFWM signal E F 1 (with E 2 blocked) (triangles), coexisting singly dressed DFWM signal E F 1 and FWM signal E F 3 (with E 2 blocked) (reverse triangles), and coexisting dressed DFWM signal E F 1 and FWM signal E F 3 (circles);lower curves: pure FWM signal E F 3 (with both E 1 and E 2 blocked) (left triangle), singly-dressed FWM signal (with E 1 blocked) (right triangle); Δ 1 = 0 . The inserted plot: corresponding to the dressed-state picture. (b1) the condition are the same to that in (a1) except Δ 1 = 25.9   GHz . The inserted plot: corresponding to the dressed-state picture. (a2) and (b2) theoretical plots corresponding to the experimental parameters of (a1) and (b1), respectively.

Fig. 3
Fig. 3

(a) and (b) Measured evolution of the four FWM signals [( E F 1 and E F 3 ) and ( E F 2 and E F 4 ), respectively] versus Δ 2 for different Δ 1 values. (a1)-(a7) and (b1)-(b7): Δ 1 = -139.1, −103.87, −29.5, 0, 29.8, 100.1, 155.7GHz, respectively.

Fig. 4
Fig. 4

(Color online) (a) Measured suppression and enhancement of DFWM signal E F 1 versus Δ 2 for different Δ 1 values in the two-level system. Δ 1 = -69.1, −55.5, −38.7, −19.2, 0, 14.7, 28.8, 42.2 and 57.3 GHz, respectively. The dashed curve is the double-peak DFWM signal E F 1 versus Δ 1 . (b) Theoretical plots corresponding to the experimental parameters in (a). (c) The same measures to (a) with the same condition, except that the laser beams E 1 , E 1 overlap in the middle of heat oven. (d1)-(d9) the dressed-state pictures of the suppression or enhancement of the DFWM signal. The states | G 1 ± > (dashed lines) and the states | G 1 + ± > or | G 1 ± > (dot-dashed lines), respectively.

Fig. 5
Fig. 5

(Color online) (a) DFWM signal E F 1 images when Δ 1 = -69.1, −55.5, −38.7GHz. (b) DFWM signal images when Δ 1 = -55.5, −38.7, −19.2GHz.

Fig. 6
Fig. 6

(a) Measured suppression and enhancement of DFWM signal E F 1 versus Δ 2 for different Δ 1 values. Δ 1 = -70.5, −55.8, −32.7, −15.4, 0, 16.5, 32.5, 48.2 and 72.1 GHz, respectively. The dashed curve is the double-peak DFWM signal E F 1 versus Δ 1 . (b) Theoretical plots corresponding to the experimental parameters in (a). (c1)-(c9) DFWM signal E F 1 images. The condition here is the same as that in (a).

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