Abstract

We report an observation of the self- and external-dressed Autler-Townes (AT) splitting in six-wave mixing (SWM) within an electromagnetically induce transparency window, which demonstrates the interaction between two coexisting SWM processes. The multi-dressed states induced by the nested interactions between many dressing fields and the five-level atomic system lead to the primary, secondary and triple AT splittings in the experiment. Such controlled multi-channel splitting of nonlinear optical signals can be used in a range of applications, e.g. the wavelength-demultiplexer in optical communication and quantum information processing.

©2011 Optical Society of America

1. Introduction

Aulter-Townes (AT) splitting was first observed on a radio-frequency transition more than sixty years ago [1]. Such effect has been clearly demonstrated in a four-wave mixing on a simple atomic system dressed with a single laser beam [2]. With the cw triple-resonant spectroscopy and the ultrashort intense laser pulses, respectively, the AT splitting effect in lithium molecules [3] and a semiconductor material [4] was investigated. Theoretical studies also indicate that the AT-split Rydberg population can lead to an antiblockade effect [5] and such phenomenon was experimentally demonstrated with two-photon excitation in a three-level atomic system [6]. Recently, a great deal of attention has been paid to observe and understand the phenomenon of electromagnetically induced transparency (EIT) [710] and related effects in multi-level atomic systems interacting with two or more electromagnetic fields [11,12].

The interaction of double-dark states (nested scheme of doubly-dressing) and splitting of dark state (the secondarily-dressed state) in a four-level atomic system with EIT were studied theoretically by Lukin, et al [13]. Then doubly-dressed states in cold atoms were observed, in which triple-photon absorption spectrum exhibits a constructive interference between the excitation pathways of two closely-spaced, doubly-dressed states [14]. A similar result was obtained in the inverted-Y [15] and double-Λ [16] atomic systems.

In this letter, we present the first experimental observation of the self-, doubly- and triply-dressed AT splitting states of the SWM process within the EIT window in a five-level atomic system. Theoretical calculations are carried out and used to well explain the observed results, giving a full physical understanding of the interesting multiple AT splittings in the high-order nonlinear optical processes. On the basis of our previous study of the AT splitting in the four-wave mixing (FWM) process [17], we go further to investigate the complex AT splitting phenomena in the SWM process.

2. Theoretical model and experimental scheme

The experimental demonstration of the AT splitting of SWM within the EIT window is carried out in the atomic system of 85Rb. The energy levels of 5S1/2(F=3), 5S1/2(F=2), 5P3/2(F=3), 5D3/2, and 5D5/2 form the five-level atomic system, as shown in Fig. 1(b) . The atomic vapor cell temperature is set at 60C. The probe laser beam E1 (with frequency ω1, wave vector k1, Rabi frequency G1, and wavelength of 780.245 nm, connecting the transition 5S1/25P3/2) is from an external cavity diode laser (Toptica DL100L), which is horizontally polarized and has a power of about P11.3mW. The coupling laser beams E2 (ω2, k2, G2, and wavelength 775.978 nm, connecting the transition 5P3/25D5/2) and E4 (ω4, k4, G4, and wavelength 776.157 nm, connecting the transition 5P3/25D3/2) are from two external cavity diode lasers (Hawkeye Optoquantum and UQEL100), respectively. The pump laser beams E3 (ω3, k3, G3) and E3 (ω3,k3, G3), which are split from a tapered-amplifier diode laser (Thorlabs TCLDM9) with equal power (P3P3) and vertical polarization, drive the transition 5S1/25P3/2. The diameters of the probe, pump and coupling beams are about 0.3, 0.5, 0.5 mm at the cell center, respectively. The pump and coupling laser beams (E3, E3, E2, E4) are spatially aligned in a square-box pattern as shown in Fig. 1(a), which propagate through the atomic medium in the same direction with small angles (~0.3) between them (the angles are exaggerated in the figure). The probe beam (E1) propagates in the opposite direction with a small angle from the other beams. Under this configuration the diffracted FWM signal (EF) and two SWM signals (ES1 and ES2) with same horizontal polarization are in the directions determined by the phase-matching conditions kF=k1+k3k3, kS1=k1+k2k2+k3k3and kS2=k1+k4k4+k3k3, respectively. These signals are in the same direction as EF (at the lower right corner of Fig. 1(a)), and are detected by an avalanche photodiode detector. The transmitted probe beam is simultaneously detected by a silicon photodiode.

 

Fig. 1 (a) Phase-matching spatial beam geometry used in the experiment. (b) Five-level atomic system with one probe field , two pump fields E3 and E3, and two coupling (dressing) fields E2 and E4. EF is the generated FWM signal. ES1 and ES2 are the two generated SWM signals. (c)-(e) Corresponding dressed-state pictures of (b).

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For the five-level atomic system as shown in Fig. 1(b), if two strong coupling laser fields (E2 and E4) drive two separate upper transitions (|1> to |2> and |1> to |4>), respectively, and a weak laser field (..) probes the lower transition (|0> to |1>), two ladder-type EIT subsystems will form with two-photon Doppler-free configuration [8] and two EIT windows appear. Depending on the frequency detunings of the two coupling laser beams, these two EIT windows can either overlap or be separated in frequency on the probe beam transmission signal. On the other hand, if the probe field E1 drives the transition (|0> to |1>) and the two pump fields (E3 and E3) drive another transition (|3> to |1>) in the three-level Λ-type subsystem, as shown in Fig. 1(b), there will be a corresponding FWM signal generated at frequency ω1 (satisfying kF=k1+k3k3). However, the FWM signal without the EIT window (not satisfying the two-photon Doppler-free configuration [8]) can be neglected. When the two coupling laser fields E2 (connecting transition |1> to |2>) and E4 (connecting the transition |1> to |4>) are added, two SWM processes will occur [11]. First, without the strong coupling field E4, a simple SWM1 process (ES1) at frequency ω1 is generated from the probe beam (E1), the coupling field (E2), and two pump fields (E3 and E3), via the perturbation chain (I): ρ00(0)G1ρ10(1)G2ρ20(2)G2*ρ10(3)(G3)*ρ30(4)G3ρ10(5) (satisfying kS1=k1+k2k2+k3k3) [11]. When the power of E2 is strong enough, it will start to dress the energy level |1 to create the primarily-dressed states |+ and |, as shown in Fig. 1(c). This dressed SWM1 process can be described via the perturbation chain (II): ρ00(0)ω1ρ±0(1)ω2ρ20(2)ω2ρ±0(3)ω3ρ30(4)ω3ρ±0(5). Such self-dressing effect, i.e. one of the participating fields for generating SWM dresses the involved energy level |1, which then modifies the SWM process itself, is unique for such multi-wave mixing processes in multi-level systems. Similarly, for another SWM process (with fields E1, E4, E3 and E3), without the strong coupling field E2, it will generate a signal field ES2 at frequency ω1 via the perturbation chain (III): ρ00(0)G1ρ10(1)G4ρ40(2)G4*ρ10(3)(G3)*ρ30(4)G3ρ10(5) (satisfying kS2=k1+k4k4+k3k3). When the power of E4 is strong enough, it will start to dress the energy level |1 to create the primarily-dressed states |+ and |, as shown in Fig. 1(d). This dressed SWM2 process can be described via the perturbation chain (IV): ρ00(0)ω1ρ±0(1)ω4ρ40(2)ω4ρ±0(3)ω3ρ30(4)ω3ρ±0(5).

Next, when both coupling fields (E2 and E4) are on at the same time, they can dress the energy level |1> together. For the SWM1 process (ES1), E2 first produces the primarily-dressed states |±, then E4 produces the secondarily-dressed states |±± at a proper frequency detuning (i.e. either tuned to the upper or lower dressed state, |+> or |>), as shown in Fig. 1(e) via the perturbation chain (V): ρ00(0)ω1ρ±±0(1)ω2ρ20(2)ω2ρ±±0(3)ω3ρ30(4)ω3ρ±±0(5). This generates the secondary AT splitting for the SWM1 signal. The situation for the SWM2 (ES2) process is similar.

The two primarily-dressed states induced by E2 can be written as |±>=sinθ1±|1>+cosθ1±|2> (Fig. 1(c)). When E4 only couples to the dressed state |+>, the secondarily-dressed states are then given by |+±>=sinθ2±|+>+cosθ2±|4> (Fig. 1(e)), where tanθ1±=a1±/G2, tanθ2±=a2±/G4, a1±=Δ2λ±(1) and a2±=Δ4λ+(1)λ+±(1). One can obtain the eigenvalues λ±(1)=(Δ2±Δ22+4|G2|2)/2 (measured from level |1>) of |±>, and λ+±(1)=(Δ4±Δ42+4|G4|2)/2 (measured from level |+>) of |+±>, where Δ4=Δ4λ+(1). When E4 only couples to the dressed state |>, the secondarily-dressed states are given by |±>=sinθ2±|>+cosθ2±|4>, where a2±=Δ4λ(1)λ±(1), and other parameters are the same as before. Then, we obtain the same eigenvalues λ±(1), and λ±(1)=(Δ4±Δ42+4|G4|2)/2 (measured from level |>) of |±>, where Δ4=Δ4λ(1). Similarly, when E4 induces the two primarily-dressed states, and E2 acts as the external-dressing field, one can get the following corresponding eigenvalues: , λ+±(2)=(Δ2±Δ22+4|G2|2)/2 (Δ2=Δ2λ+(2)), and λ±(2)=(Δ2±Δ22+4|G2|2)/2 (Δ2=Δ2λ(2)).

In general for arbitrary strengths of the fields E1, E3, E3, E2 and E4, one needs to solve the coupled density-matrix equations to obtain ρ10(5) for the SWM processes, which we have done in simulating the experimental results later on. For simplicity, we have solved the coupled equations with perturbation chain (I) to obtain the nonlinear density-matrix element for the multi-dressed SWM processes (including self-dressing and external-dressing) as: ρ10(5)=iGS1/(ABCDE), where, A=d1+G12/Γ1+G12/Γ0+G22/d2+G42/d4, B=d2+G12/d2, C=d1+G12/Γ1+G22/d2+G32/d3+G42/d4, D=d3+G12/d3, E=d1+G12/Γ1+G12/Γ0+G32/d3+G42/d4,d1=Γ10+iΔ1, d2=Γ20+i(Δ1+Δ2), d2=iΔ2+Γ21, d3=Γ30+i(Δ1Δ3), d3=Γ31iΔ3, d4=Γ40+i(Δ1+Δ4) with Δi=Ωiωi and Γij being the transverse relaxation rate between states |i and |j. For the SWM1 signal (due to the weak probe field), the expression can be simplified as: ρS1(5)=iGS1/[(d1+G22/d2)d2(d1+G22/d2+G32/d3)d3(d1+G32/d3)]. Similarly, for the SWM2 signal, the expression is simplified as: ρS2(5)=iGS2/[(d1+G42/d4)d4(d1+G32/d3+G42/d4)d3(d1+G32/d3)], where GS2=G1G3*G3G4G4*.

There exist two ladder-type EIT windows in Fig. 1(b), i.e., the |0>|1>|2> EIT1 window satisfying Δ1+Δ2=0 (induced by the coupling field E2) and the |0>|1>|4> EIT2 window satisfying Δ1+Δ4=0 (induced by the coupling field E4). The EIT1 and EIT2 windows contain the SWM1 signal (ES1) and the SWM2 signal (ES2), respectively. Next, we will consider the AT splitting of the SWM signals within the EIT windows (Figs. 2 -4 ).

 

Fig. 2 (a1), (b1) and (c1) are the measured SWM1 self-dressing AT splitting signals versus Δ1 for Δ2=50MHz under differentP1, P2 and P3 powers, respectively. (a1) is increasing P1=0.30, 0.36, 0.43, 0.90, 1.37, 1.85, 2.32, 3.66, 5.33, 8.18, 10.3, 13.61, 15.46, 22.5, 24.2, 25.3, 28.8 and 29.5mW from bottom to top. (b1) is increasing P2=0.3, 0.6, 0.9, 1.2, 1.5, 2.1, 4.5, 7.5, 12.5, 17.2, 25.5 and 31.4mW from bottom to top. (c1) is increasing P3=1.8, 3.9, 6.3, 7.7, 11.4, 16.7, 22.2, 33.1 and 52.2mW from bottom to top. (a2), (b2) and (c2) are the corresponding power dependences of (a1), (b1) and (c1), respectively. Here Δa, Δb and Δc are the increments of distance between the two A-T splitting peaks when P1, P2 and P3 are increased, respectively, and the squares are the experimental results, while the solid lines in (a2, b2, c2) are the theoretical calculations. The fixed powers in (a1,2), (b1,2) and (c1,2) are (P2=32.0mW & P3=55.0mW), (P1=13.0mW & P3=55.0mW), and (P1=13.0mW & P2=32.0 mW), respectively.

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Fig. 4 Measured SWM1 moving towards SWM2 signal (lower-curves) and the corresponding EIT (upper-curves) versus Δ1 for Δ4=0, Δ2=150 (a1), Δ2=15 (a2), Δ2=15MHz (a3). (b3) is the SWM1 signal splitting the right peak of the SWM2 signal versus Δ1 for increasing , 2.5, 3.5, 4.5, 5.5 and 6.5 mW from bottom to top when P1=6 .5mW, P3=38 .5mW and P4=22 .6mW. (b5) is the SWM1 splitting the left peak of SWM2 signals versus Δ1 under the same power of (b3). (b1) is the double-peaked SWM1 signals versus Δ1 with Δ2=150MHz. (b2), (b4) and (b6) are the corresponding power dependences. Here Δb1, Δb3 and Δb5 are the increments of the distances between the two large peaks in (b1), right two peaks in (b3), left two peaks in (b5), respectively, when P2 is increased, and the squares are the experimental results, while the solid lines in (b2, b4, b6) are the theoretical calculations.

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3. Autler-Townes Splitting

When the external-dressing field E4 is blocked, we get the SWM1 signal within the EIT1 window (which is an inverted-Y system) [15]. Figure 2 (a1, b1, c1) presents the SWM1 signal intensity versus the probe field detuning (Δ1) for different field powers of P1, and P3 with the same frequency detuning of Δ2=50MHz. Obviously, the SWM1 signal shows two peaks due to multi-dressing effects (Fig. 1(c)). With the power increases, the intensity of the SWM1 signal increases accordingly, while the left peak height is always greater than the height of the right peak. Meanwhile, the increments of the AT splitting separations Δi=λ+(1)λ(1)2|Gj|2+|Gi0|2 (i=a, b, c corresponds to j=1, 2, 3, respectively, and |Ga0|2=|G20|2+|G30|2, |Gb0|2=|G10|2+|G30|2, |Gc0|2=|G10|2+|G20|2), increase obviously with increased powers (Rabi frequencies) P1 (G1), P2 (G2) and P3 (G3), respectively and fixed P2&P3 (G20&G30), P1&P3 (G10&G30) and P1&P2 (G10&G20), respectively. The two peaks of the double-peak SWM1 signal (Figs. 2(a1), (b1) and (c1)) correspond, from left to right, to the primarily-dressed states |+ and |, respectively (Fig. 1(c)). Moreover, the experimentally measured (peak separation) results in Figs. 2(a1), (b1) and (c1) are in good agreement with our theoretical calculations (solid curves), as shown in Figs. 2(a2), (b2) and (c2), respectively.

When the external-dressing field E2 is blocked, we get the SWM2 signal in the EIT2 window. Figure 3 presents the SWM2 signal intensity versus the probe field detuning (Δ1) for different powers of P1, P3 and P4 with the same frequency detuning of Δ4=0MHz. Figure 3(a) depicts the measured EIT windows induced by the self-dressing field E4 versus Δ1 (satisfying Δ1+Δ4=0). Such EIT window increases with P4 power increasing. The SWM2 signal has three peaks. In general, when the power increases, the intensity of the SWM2 signal also increases accordingly. However, the states of AT splittings change differently for different power changes. If only P1 power increases, the right peak first increases and then decreases, while the height of the middle peak is always larger than the height of either the left or right peak. If only P3 power increases, the right peak always increases, while the height of the middle peak is always larger than the height of either the left or right peak. If only P4 power increases, the height of the right peak increases monotonously to approach the height of the middle peak. The two primarily-dressed states |+>and |> are induced by E4. When E1 and E3 couples to the dressed state |>, the secondarily-dressed states |+ and | appear. The three peaks in the SWM2 signal (Figs. 3(b1), (c1) and (d1)) correspond, from left to right, to the primarily-dressed state |+>, the secondarily-dressed states |+ and |, respectively (Fig. 1(d)). Based on our theoretical analysis, the two primarily-dressed states dressed by E4 can be written as |±>=sinα1±|1>+cosα1±|4>, and the secondarily-dressed states dressed by E3are given by |±>=sinα2±|>+cosα2±|3>, where tanα1±=b1±/G4, tanα2±=b2±/|G1|2+|G3|2, b1±=Δ4λ±(3), and b2±=Δ3λ(3)λ±(3). One can obtain the eigenvalues λ±(3)=(Δ4±Δ42+4|G4|2)/2 (measured from level |1>) of |±>, and λ±(3)=(Δ3±Δ32+4(|G1|2+|G3|2))/2 (measured from level |>) of |±>, where Δ3=Δ3λ(3).

 

Fig. 3 (a) is the measured EIT2 induced by the field E4 versus Δ1. (b1), (c1) and (d1) are the measured SWM2 self-dressing AT splitting signals versus Δ1 for Δ4=0 under different P1, P3 and P4 powers, respectively. (b1) is increasing P1=0 .4, 0.9, 1.4, 1.8, 3.7, 5.3, 9.3, 10.3, 13.6, 15.5, 24.7 and 29.5 mW from bottom to top. (c1) is increasing P3=1.2, 1.4, 2.9, 4.6, 6.6, 8.2, 9.5 and 27.2 mW from bottom to top. (d1) is increasing P4=0.12, 0.48, 0.6, 1.36, 2.47, 3.1, 5.4, 7.7, 14.0, 23.0, 39.0, 71.0, 116.0, 142.0, 184.0, 205.0, 225.0, 242.0 and 258.0 mW from bottom to top. (b2), (c2) and (d2) are the corresponding power dependences of (b1), (c1) and (d1), respectively. Here Δb, Δc and Δd are the increments of the distance between the right (for Δb and Δc) or left (for Δd) two A-T splitting peaks, respectively, when P1, P3 and P4 are increased, respectively, and the squares are the experimental results, while the solid lines in (b2, c2, d2) are the theoretical calculations. The fixed powers in (b1, 2), (c1, 2) and (d1, 2) are (P3=30.0mW & P4=150.0mW), (P1=1.0 mW & P4=150.0mW), and (P1=1.0 mW & P3=30.0mW), respectively.

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Meanwhile, the increments of the AT splitting separations Δb=λ-+(3)-λ--(3)=2|G1|2+|G30|2, Δc=λ+(3)λ(3)=2|G3|2+|G10|2, and Δd=λ+(3)λ+(3)=2G4|G10|2+|G30|22G4 (G4>>G10,30) increase obviously with increased powers (Rabi frequencies) of P1 (G1), P3 (G3) and P4 (G4), respectively and fixed P3&P4 (G30&G40), P1&P3 (G10&G30) and P1&P4 (G10&G40), respectively. When the self-dressing P4 power changes, the state of the AT splitting obviously has an essential distinction from the former two states as the powers of P1 and P3 change. The experimentally measured results in Figs. 3(b1), (c1) and (d1) are in good agreement with our theoretical calculations shown in Figs. 3(b2), (c2) and (d2), respectively.

After studying the self-dressing AT splitting of the individual SWM1 or SWM2 signal, we will now consider the cross-dressing AT splitting between the two SWM signals. Figures 4(a1) - 4(a3) present the interplay between the two SWM signals versus the probe field detuning (Δ1) for different external-dressing field detunings (Δ2) with Δ4=0MHz. Here, we consider the case with G2<G4. The upper-curve in each figure is the probe transmission with two ladder-type EIT windows and the lower-curve gives the measured SWM signals. In Fig. 4(a1), the left EIT window (|0>|1>|4> satisfying Δ1+Δ4=0) is induced by the coupling field E4,which contains the SWM2 signal (ES2), and the right one (|0>|1>|2> satisfying Δ1+Δ2=0, Δ2 = -15MHZ) is induced by the coupling field E2, which contains the SWM1 signal (ES1). Since the right EIT window (Δ2=150MHz) is quite far from the left EIT window, these two SWM signals have little effect on each other (Fig. 4(a1)). When the frequency of E2 is tuned to move the right EIT window (|0>|1>|2>) towards the left one, the two EIT windows overlap at Δ2=15MHz, which leads to the triple AT splitting for SWM2, i.e., the right peak of SWM2 signal is further split into two peaks (Fig. 4(a2), satisfying Δ2=λ(3)). It is the coupling field E2 that couples the secondarily-dressed state | dressed by E3 and splits it into two triply-dressed states |+> and |>. The four peaks of the SWM2 signal in Fig. 4(a2) correspond, from left to right, to the primarily-dressed state |+>, the secondarily-dressed states |+, the triply-dressed states |+> and |>, respectively (Fig. 1(e)). We can write the triply-dressed states as |±>=sinα3±|+cosα3±|2>, where tanα3±=b3±/G2, b3±=Δ2λ(3)λ(3)λ±(3), and the other parameters are the same as before. One can obtain the eigenvalues λ±(3)=(Δ2±Δ22+4|G2|2)/2 (measured from level |) for the dressed states |±>, where Δ2=Δ2λ(3)λ(3). With the right EIT window (|0>|1>|2>) continuously moving to the left, the SWM1 signal splits the left peak of the SWM2 signal when Δ2=15MHz, as shown in Fig. 4(a3). Corresponding to the moving SWM1 signal in Fig. 4(a1), Fig. 4(b1) presents the measured self-dressing double-peak SWM1 signal versus Δ1 with Δ2=0MHz. Corresponding to the fixed SWM2 signal in Figs. 4(a2) and 4(a3), Figs. 4(b3) and 4(b5) show the measured SWM2 signals, whose right and left peaks are split by the SWM1 signal, versus Δ1 with an increasing external-dressing P2 power, respectively. Figures 4(b2), 4(b4) and 4(b6) give the corresponding power dependences of the AT-splitting separations. The corresponding separations are determined by Δb1=λ+(1)λ(1)2G2, Δb3=λ+(3)λ(3)2G2, and Δb52G2, respectively.

4. Conclusion

In summary, we have observed the self- and externally-dressed AT splittings of the SWM processes within EIT windows in a five-level atomic system. Such AT splitting demonstrates the interactions between two coexisting SWM processes. The controlled multi-channel splitting signals in nonlinear optical processes can find potential applications in optical communication and quantum information processing, such as wavelength-demultiplexer [1820].

Acknowledgments

This work was supported by NSFC (10974151, 61078002, 61078020), NCET (08-0431), RFDP (20100201120031), 2009xjtujc08, XJJ20100100, XJJ20100151.

References and links

1. S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100(2), 703–722 (1955). [CrossRef]  

2. W. Chalupczak, W. Gawlik, and J. Zachorowski, “Four-wave mixing in strongly driven two-level systems,” Phys. Rev. A 49(6), 4895–4901 (1994). [CrossRef]   [PubMed]  

3. J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999). [CrossRef]  

4. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002). [CrossRef]   [PubMed]  

5. C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007). [CrossRef]   [PubMed]  

6. T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010). [CrossRef]   [PubMed]  

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

8. M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995). [CrossRef]   [PubMed]  

9. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency-observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74(5), 670–673 (1995). [CrossRef]   [PubMed]  

10. S. Wielandy and A. L. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A 58(3), 2500–2505 (1998). [CrossRef]  

11. Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007). [CrossRef]   [PubMed]  

12. 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]  

13. 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]  

14. 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]  

15. R. Drampyan, S. Pustelny, and W. Gawlik, “Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization,” Phys. Rev. A 80(3), 033815 (2009). [CrossRef]  

16. G. Wasik, W. Gawlik, J. Zachorowski, and Z. Kowal, “Competition of dark states: Optical resonances with anomalous magnetic field dependence,” Phys. Rev. A 64(5), 051802 (2001). [CrossRef]  

17. 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]  

18. K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009). [CrossRef]   [PubMed]  

19. R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009). [CrossRef]  

20. 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]  

References

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  1. S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100(2), 703–722 (1955).
    [Crossref]
  2. W. Chalupczak, W. Gawlik, and J. Zachorowski, “Four-wave mixing in strongly driven two-level systems,” Phys. Rev. A 49(6), 4895–4901 (1994).
    [Crossref] [PubMed]
  3. J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999).
    [Crossref]
  4. O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002).
    [Crossref] [PubMed]
  5. C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007).
    [Crossref] [PubMed]
  6. T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010).
    [Crossref] [PubMed]
  7. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (1997).
    [Crossref]
  8. M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
    [Crossref] [PubMed]
  9. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency-observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74(5), 670–673 (1995).
    [Crossref] [PubMed]
  10. S. Wielandy and A. L. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A 58(3), 2500–2505 (1998).
    [Crossref]
  11. Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007).
    [Crossref] [PubMed]
  12. 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]
  13. 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]
  14. 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]
  15. R. Drampyan, S. Pustelny, and W. Gawlik, “Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization,” Phys. Rev. A 80(3), 033815 (2009).
    [Crossref]
  16. G. Wasik, W. Gawlik, J. Zachorowski, and Z. Kowal, “Competition of dark states: Optical resonances with anomalous magnetic field dependence,” Phys. Rev. A 64(5), 051802 (2001).
    [Crossref]
  17. 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]
  18. K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
    [Crossref] [PubMed]
  19. R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
    [Crossref]
  20. 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]

2010 (2)

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010).
[Crossref] [PubMed]

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]

2009 (3)

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[Crossref] [PubMed]

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

R. Drampyan, S. Pustelny, and W. Gawlik, “Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization,” Phys. Rev. A 80(3), 033815 (2009).
[Crossref]

2008 (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]

2007 (2)

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007).
[Crossref] [PubMed]

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007).
[Crossref] [PubMed]

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]

2002 (1)

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002).
[Crossref] [PubMed]

2001 (2)

G. Wasik, W. Gawlik, J. Zachorowski, and Z. Kowal, “Competition of dark states: Optical resonances with anomalous magnetic field dependence,” Phys. Rev. A 64(5), 051802 (2001).
[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]

1999 (2)

J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (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]

1998 (1)

S. Wielandy and A. L. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A 58(3), 2500–2505 (1998).
[Crossref]

1997 (1)

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

1995 (2)

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[Crossref] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency-observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74(5), 670–673 (1995).
[Crossref] [PubMed]

1994 (1)

W. Chalupczak, W. Gawlik, and J. Zachorowski, “Four-wave mixing in strongly driven two-level systems,” Phys. Rev. A 49(6), 4895–4901 (1994).
[Crossref] [PubMed]

1955 (1)

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100(2), 703–722 (1955).
[Crossref]

Amthor, T.

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010).
[Crossref] [PubMed]

Ates, C.

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007).
[Crossref] [PubMed]

Autler, S. H.

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100(2), 703–722 (1955).
[Crossref]

Boyd, R. W.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[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. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007).
[Crossref] [PubMed]

Camacho, R. M.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

Chalupczak, W.

W. Chalupczak, W. Gawlik, and J. Zachorowski, “Four-wave mixing in strongly driven two-level systems,” Phys. Rev. A 49(6), 4895–4901 (1994).
[Crossref] [PubMed]

Dolgaleva, K.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[Crossref] [PubMed]

Drampyan, R.

R. Drampyan, S. Pustelny, and W. Gawlik, “Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization,” Phys. Rev. A 80(3), 033815 (2009).
[Crossref]

Dunn, M. H.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency-observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74(5), 670–673 (1995).
[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]

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]

Fulton, D. J.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency-observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74(5), 670–673 (1995).
[Crossref] [PubMed]

Gaeta, A. L.

S. Wielandy and A. L. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A 58(3), 2500–2505 (1998).
[Crossref]

Gawlik, W.

R. Drampyan, S. Pustelny, and W. Gawlik, “Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization,” Phys. Rev. A 80(3), 033815 (2009).
[Crossref]

G. Wasik, W. Gawlik, J. Zachorowski, and Z. Kowal, “Competition of dark states: Optical resonances with anomalous magnetic field dependence,” Phys. Rev. A 64(5), 051802 (2001).
[Crossref]

W. Chalupczak, W. Gawlik, and J. Zachorowski, “Four-wave mixing in strongly driven two-level systems,” Phys. Rev. A 49(6), 4895–4901 (1994).
[Crossref] [PubMed]

Gea-Banacloche, J.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[Crossref] [PubMed]

Giese, C.

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010).
[Crossref] [PubMed]

Harris, S. E.

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

Hofmann, C. S.

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010).
[Crossref] [PubMed]

Howell, J. C.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

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]

Jin, S.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[Crossref] [PubMed]

Kärtner, F. X.

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002).
[Crossref] [PubMed]

Kowal, Z.

G. Wasik, W. Gawlik, J. Zachorowski, and Z. Kowal, “Competition of dark states: Optical resonances with anomalous magnetic field dependence,” Phys. Rev. A 64(5), 051802 (2001).
[Crossref]

Lazarov, G.

J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999).
[Crossref]

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.

Li, L.

J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999).
[Crossref]

Li, Y.

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[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, 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]

Lyyra, A. M.

J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999).
[Crossref]

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]

Morgner, U.

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002).
[Crossref] [PubMed]

Moseley, R. R.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency-observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74(5), 670–673 (1995).
[Crossref] [PubMed]

Mücke, O. D.

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002).
[Crossref] [PubMed]

Narducci, L. M.

J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999).
[Crossref]

Nie, Z. Q.

Pattard, T.

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007).
[Crossref] [PubMed]

Pohl, T.

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007).
[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]

Pustelny, S.

R. Drampyan, S. Pustelny, and W. Gawlik, “Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization,” Phys. Rev. A 80(3), 033815 (2009).
[Crossref]

Qi, J. B.

J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999).
[Crossref]

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]

Rost, J. M.

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007).
[Crossref] [PubMed]

Scully, M. O.

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]

Shepherd, S.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency-observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74(5), 670–673 (1995).
[Crossref] [PubMed]

Shin, H.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[Crossref] [PubMed]

Sinclair, B. D.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency-observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74(5), 670–673 (1995).
[Crossref] [PubMed]

Spano, F. C.

J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999).
[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]

Townes, C. H.

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100(2), 703–722 (1955).
[Crossref]

Tritschler, T.

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002).
[Crossref] [PubMed]

Vudyasetu, P. K.

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

Wang, X. J.

J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999).
[Crossref]

Wang, Z. G.

Wasik, G.

G. Wasik, W. Gawlik, J. Zachorowski, and Z. Kowal, “Competition of dark states: Optical resonances with anomalous magnetic field dependence,” Phys. Rev. A 64(5), 051802 (2001).
[Crossref]

Wegener, M.

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002).
[Crossref] [PubMed]

Weidemüller, M.

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010).
[Crossref] [PubMed]

Wen, F.

Wielandy, S.

S. Wielandy and A. L. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A 58(3), 2500–2505 (1998).
[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]

Xiao, M.

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, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007).
[Crossref] [PubMed]

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[Crossref] [PubMed]

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]

Zachorowski, J.

G. Wasik, W. Gawlik, J. Zachorowski, and Z. Kowal, “Competition of dark states: Optical resonances with anomalous magnetic field dependence,” Phys. Rev. A 64(5), 051802 (2001).
[Crossref]

W. Chalupczak, W. Gawlik, and J. Zachorowski, “Four-wave mixing in strongly driven two-level systems,” Phys. Rev. A 49(6), 4895–4901 (1994).
[Crossref] [PubMed]

Zhang, Y. P.

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, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007).
[Crossref] [PubMed]

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]

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]

Nat. Photonics (1)

R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Four-wave-mixing stopped light in hot atomic rubidium vapour,” Nat. Photonics 3(2), 103–106 (2009).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (1)

S. H. Autler and C. H. Townes, “Stark effect in rapidly varying fields,” Phys. Rev. 100(2), 703–722 (1955).
[Crossref]

Phys. Rev. A (6)

W. Chalupczak, W. Gawlik, and J. Zachorowski, “Four-wave mixing in strongly driven two-level systems,” Phys. Rev. A 49(6), 4895–4901 (1994).
[Crossref] [PubMed]

S. Wielandy and A. L. Gaeta, “Investigation of electromagnetically induced transparency in the strong probe regime,” Phys. Rev. A 58(3), 2500–2505 (1998).
[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]

R. Drampyan, S. Pustelny, and W. Gawlik, “Electromagnetically induced transparency versus nonlinear Faraday effect: Coherent control of light-beam polarization,” Phys. Rev. A 80(3), 033815 (2009).
[Crossref]

G. Wasik, W. Gawlik, J. Zachorowski, and Z. Kowal, “Competition of dark states: Optical resonances with anomalous magnetic field dependence,” Phys. Rev. A 64(5), 051802 (2001).
[Crossref]

Phys. Rev. Lett. (9)

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103(11), 113902 (2009).
[Crossref] [PubMed]

Y. P. Zhang, A. W. Brown, and M. Xiao, “Opening four-wave mixing and six-wave mixing channels via dual electromagnetically induced transparency windows,” Phys. Rev. Lett. 99(12), 123603 (2007).
[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).
[Crossref] [PubMed]

M. Xiao, Y. Li, S. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74(5), 666–669 (1995).
[Crossref] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency-observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74(5), 670–673 (1995).
[Crossref] [PubMed]

J. B. Qi, G. Lazarov, X. J. Wang, L. Li, L. M. Narducci, A. M. Lyyra, and F. C. Spano, “Autler-Townes splitting in molecular lithium: prospects for all-optical alignment of nonpolar molecules,” Phys. Rev. Lett. 83(2), 288–291 (1999).
[Crossref]

O. D. Mücke, T. Tritschler, M. Wegener, U. Morgner, and F. X. Kärtner, “Role of the carrier-envelope offset phase of few-cycle pulses in nonperturbative resonant nonlinear optics,” Phys. Rev. Lett. 89(12), 127401 (2002).
[Crossref] [PubMed]

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in Rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007).
[Crossref] [PubMed]

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold Rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010).
[Crossref] [PubMed]

Phys. Today (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36 (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 (4)

Fig. 1
Fig. 1 (a) Phase-matching spatial beam geometry used in the experiment. (b) Five-level atomic system with one probe field , two pump fields E 3 and E 3 , and two coupling (dressing) fields E 2 and E 4 . E F is the generated FWM signal. E S 1 and E S 2 are the two generated SWM signals. (c)-(e) Corresponding dressed-state pictures of (b).
Fig. 2
Fig. 2 (a1), (b1) and (c1) are the measured SWM1 self-dressing AT splitting signals versus Δ 1 for Δ 2 = 50 MHz under different P 1 , P 2 and P 3 powers, respectively. (a1) is increasing P 1 = 0.30, 0.36, 0.43, 0.90, 1.37, 1.85, 2.32, 3.66, 5.33, 8.18, 10.3, 13.61, 15.46, 22.5, 24.2, 25.3, 28.8 and 29.5mW from bottom to top. (b1) is increasing P 2 = 0.3, 0.6, 0.9, 1.2, 1.5, 2.1, 4.5, 7.5, 12.5, 17.2, 25.5 and 31.4mW from bottom to top. (c1) is increasing P 3 = 1.8, 3.9, 6.3, 7.7, 11.4, 16.7, 22.2, 33.1 and 52.2mW from bottom to top. (a2), (b2) and (c2) are the corresponding power dependences of (a1), (b1) and (c1), respectively. Here Δ a , Δ b and Δ c are the increments of distance between the two A-T splitting peaks when P 1 , P 2 and P 3 are increased, respectively, and the squares are the experimental results, while the solid lines in (a2, b2, c2) are the theoretical calculations. The fixed powers in (a1,2), (b1,2) and (c1,2) are ( P 2 = 32.0mW & P 3 = 55.0mW), ( P 1 = 13.0mW & P 3 = 55.0mW), and ( P 1 = 13.0mW & P 2 = 32.0 mW), respectively.
Fig. 4
Fig. 4 Measured SWM1 moving towards SWM2 signal (lower-curves) and the corresponding EIT (upper-curves) versus Δ 1 for Δ 4 = 0 , Δ 2 = 150 (a1), Δ 2 = 15 (a2), Δ 2 = 15 MHz (a3). (b3) is the SWM1 signal splitting the right peak of the SWM2 signal versus Δ 1 for increasing , 2.5, 3.5, 4.5, 5.5 and 6.5 mW from bottom to top when P 1 =6 .5mW , P 3 =38 .5mW and P 4 =22 .6mW . (b5) is the SWM1 splitting the left peak of SWM2 signals versus Δ 1 under the same power of (b3). (b1) is the double-peaked SWM1 signals versus Δ 1 with Δ 2 = 150 M H z . (b2), (b4) and (b6) are the corresponding power dependences. Here Δ b1 , Δ b3 and Δ b5 are the increments of the distances between the two large peaks in (b1), right two peaks in (b3), left two peaks in (b5), respectively, when P 2 is increased, and the squares are the experimental results, while the solid lines in (b2, b4, b6) are the theoretical calculations.
Fig. 3
Fig. 3 (a) is the measured EIT2 induced by the field E 4 versus Δ 1 . (b1), (c1) and (d1) are the measured SWM2 self-dressing AT splitting signals versus Δ 1 for Δ 4 = 0 under different P 1 , P 3 and P 4 powers, respectively. (b1) is increasing P 1 =0 .4 , 0.9, 1.4, 1.8, 3.7, 5.3, 9.3, 10.3, 13.6, 15.5, 24.7 and 29.5 mW from bottom to top. (c1) is increasing P 3 = 1.2 , 1.4, 2.9, 4.6, 6.6, 8.2, 9.5 and 27.2 mW from bottom to top. (d1) is increasing P 4 = 0.12, 0.48, 0.6, 1.36, 2.47, 3.1, 5.4, 7.7, 14.0, 23.0, 39.0, 71.0, 116.0, 142.0, 184.0, 205.0, 225.0, 242.0 and 258.0 mW from bottom to top. (b2), (c2) and (d2) are the corresponding power dependences of (b1), (c1) and (d1), respectively. Here Δ b , Δ c and Δ d are the increments of the distance between the right (for Δ b and Δ c ) or left (for Δ d ) two A-T splitting peaks, respectively, when P 1 , P 3 and P 4 are increased, respectively, and the squares are the experimental results, while the solid lines in (b2, c2, d2) are the theoretical calculations. The fixed powers in (b1, 2), (c1, 2) and (d1, 2) are ( P 3 = 30.0mW & P 4 = 150.0mW), ( P 1 = 1.0 mW & P 4 = 150.0mW), and ( P 1 = 1.0 mW & P 3 = 30.0mW), respectively.

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