Controlling cascade dressing interaction of four-wave mixing image

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1 Controlling cascade dressing interaction of four-wave mixing image Changbiao Li Yanpeng Zhang* Huaibin Zheng Zhiguo Wang Haixia Chen Suling Sang Ruyi Zhang Zhenkun Wu Liang Li and Peiying Li Key Laboratory for Physical lectronics and Devices of the Ministry of ducation and Shaanxi Key Lab of Information Photonic Technique Xi an Jiaotong University Xi an 749 China 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. 0 Optical Society of America OCIS codes: (90.480) Nonlinear optics four-wave mixing; (90.70) Kerr effect; (90.480) Multiphoton processes; (.570) Four-wave mixing; (70.670) Coherent optical effects References and links. S.. Harris lectromagnetically induced transparency Phys. Today 50(7) (997).. P. R. Hemmer D. P. Katz J. Donoghue M. Cronin-Golomb M. S. Shahriar and P. Kumar fficient low-intensity optical phase conjugation based on coherent population trapping in sodium Opt. Lett. 0(9) (995).. 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. (0) (998). 4. H. Li V. A. Sautenkov Y. V. Rostovtsev G. R. Welch P. R. Hemmer and M. O. Scully lectromagnetically induced transparency controlled by a microwave field Phys. Rev. A 80() 080 (9). 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) 0560 (7). 6. Y. Zhang B. Anderson A. W. Brown and M. Xiao Competition between two four-wave mixing channels via atomic coherence Appl. Phys. Lett. 9(6) 06 (7). 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) 5 8 (999). 8. M. Yan. G. Rickey and Y. F. Zhu Observation of doubly dressed states in cold atoms Phys. Rev. A 64() 04 (). 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) 0689 (8). 0. Y. P. Zhang Z. Q. Nie Z. G. Wang C. B. Li F. Wen and M. Xiao vidence of Autler-Townes splitting in high-order nonlinear processes Opt. Lett. 5(0) 40 4 ().. 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) 040 (9).. G. P. Agrawal Induced focusing of optical beams in self-defocusing nonlinear media Phys. Rev. Lett. 64() (990).. 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() 90 (). 4. 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. 7() 9 (99). 5. H. Wang D. Goorskey and M. Xiao nhanced Kerr nonlinearity via atomic coherence in a three-level atomic system Phys. Rev. Lett. 87(7) 0760 (). (C) 0 OSA 4 July 0 / Vol. 9 No. 4 / OPTICS XPRSS 675

2 6. W. Królikowski M. Saffman B. Luther-Davies and C. Denz Anomalous interaction of spatial solitons in photorefractive media Phys. Rev. Lett. 80(5) 40 4 (998). 7. 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 8(5) 0587 (). 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. () 90 (8). 9. V. Boyer A. M. Marino R. C. Pooser and P. D. Lett ntangled images from four-wave mixing Science (5888) (8). 0. W. Krolikowski. 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) (0).. 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. 0() 060 (9).. Introduction fficient four-wave mixing (FWM) processes enhanced by atomic coherence in multilevel atomic systems [ 4] 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 [78]. 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 (IT) 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 [0]. In addition we reported the evolution of suppression and enhancement of FWM signal by controlling an additional laser field []. 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 [] and pattern formation [] have been extensively investigated with two laser beams propagating in atomic vapors. Recently we have observed spatial shift [4] and spatial splitting [5 7] 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 [6] in the Kerr nonlinear systems and signal processing applications such as spatial image storage [8] entangled spatial images [9] soliton pair generation [0] and influences of higher-order (such as fifth-order) nonlinearities []. 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.. Theoretical model and experimental scheme The two relevant experimental systems are shown in Figs. (a) and (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. (c). In the Fig. (a) energy levels 0 ( S / ) and (C) 0 OSA 4 July 0 / Vol. 9 No. 4 / OPTICS XPRSS 676

3 ( P / ) form a two-level atomic system. Coupling field (with wave vector k and the Rabi frequency G ) together with ( k and G ) (connecting the transition between 0 and ) having a small angle ( 0. ) propagates in the opposite direction of the probe field ( k and G ) (also connecting the transition between 0 and ). These three laser beams come from the same near-transform-limited dye laser (with a 0 Hz repetition rate 5 ns pulse width and 0.04 cm linewidth) with the same frequency detuning 0 where 0 is the transition frequency between 0 and. The coupling fields and induce a population grating between states 0 to which is probed by. This generates a DFWM process (Fig. (a)) satisfying the phase-matching condition of kf = k k +k. Then two additional coupling fields ( k G ) and ( k G ) are applied as scanning fields connecting the transition from 0 to with the same frequency detuning 0 ; the two additional coupling fields are from another similar dye laser set at to dress the energy level. The fields and produce a non-degenerate FWM (NDFWM) signal k F (satisfying kf = k k +k ). When the five laser beams are all on there also exist other two FWM processes k F (satisfying kf = k k +k ) and k F4 (satisfying kf4 = k k +k ) in the same directions as F and F respectively. Under the experimental condition (or ) with detuning depletes two groups of atoms with different velocities at the same time such as negative velocities group and positive velocities group. At 0 the positive velocities group will see (or ) with detuning kv and with detuning kv. The frequency of the DFWM F in this case will be f kv kv kv kv due to the conservation of energy. Correspondingly at 0 negative velocities group will see (or ) with detuning kv and with detuning kv. The frequency of F will be f kv kv kv kv. Such changing implies that a group of atoms with certain velocities can satisfy the condition kv where is the detuning of (or ) based on both saturation excitation and atomic coherence effect. As a result the self-dressing field (or ) can be considered as the outer dressing field and separates the level 0 into two dressing states G as shown in Fig.. In addition the Doppler effect and the power broadening effect on the weak FWM signals need to be considered. D/ Na a P / FWM S/ 0 b P FWM / S/ 0 CCD D & F& F F F4 D c & F F4 z x y & F F Na Fig.. (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. (C) 0 OSA 4 July 0 / Vol. 9 No. 4 / OPTICS XPRSS 677

4 When and are open the DFWM process F and NDFWM F and F 4 are generated simultaneously and there exists interplay processes F among these four FWM signals in the two-level atomic system. These generated FWM signals have the frequencies F F F and F 4. 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 ( D or D ) 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 (F) (0) ( )* () ( ')* () () (0) ( ')* () () () (F) (F) 0 0 (0) () ( ')* () () (0) () ( ')* () () and (F4) respectively. For the DFWM signal F in fact this DFWM generation process can be viewed as a series of transitions: the first step is from 0 to with absorption of a coupling photon and the final state of this process can be dressed by the dressing field (or ). The second step is the transition from to 0 and the final state cannot be dressed by any field. The third step is the transition from 0 to with the emission of a probe photon and the final state of this process can be dressed by (or ). Then the last transition is from to 0 which emits a FWM photon at frequency. Thus we can obtain the dressed perturbation chain (0) ( )* () ( ')* () () G 0 G 0. Similarly we can obtain the other dressed (0) () perturbation chains as (DF) ( ')* () () (DF) (0) () ( ')* () () G0 G0 G0 G0 (0) () ( ')* and (DF4) () () G 0 G 0 respectively. The expressions of the corresponding density matrix elements () * related to the four FWM processes are F igg ( G ) / ( B ) () * () * () * F igg ( G ) / ( db ) F igg ( G ) / ( d4b ) F 4 igg ( G ) / ( d5d6b ) respectively where d 0 i d i( / m ) d 0 i d4 i( ) d5 0 i( ) d6 [ i( )] A G / d A G / A G / B d A B d A B d A. Here Gi ii / (i = ) is the Rabi frequency; 0 0 and are the transverse relaxation rates and i ( i ) is the detuning factor. The experiments are carried out in a vapor cell containing sodium. The cell 8-cm long is heated up to a temperature of about 0 C and crossed by linearly polarized laser beams which interact with the atoms. In the two-level atomic system the coupling fields and (with diameter of 0.8 mm and power of 9 μw) and the probe field (with diameter of 0.8 mm and power of μw) are tuned to the line center (589.0 nm) of the 0 to transition which generate the DFWM signal F at frequency. The coupling fields and (with diameter of. mm and powers of 0 μw and μw respectively) are scanned simultaneously around the 0 to transition to dress the DFWM process F. (C) 0 OSA 4 July 0 / Vol. 9 No. 4 / OPTICS XPRSS 678

5 Relative Intensity of DFWM signals. 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 (or ) the DFWM signal F (or the FWM signal F ) is suppressed by the coupling field as can be seen from the upper triangle points [or the right triangle points in Fig. (a)] compared to the pure DFWM signal F (or the FWM signal F ). Next when laser beams and are turned on two coexisting FWM processes ( F and F ) 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 ( F and F ). Finally when all the five laser beams are turned on the DFWM signal F and the FWM signal F 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. (a)..0.0 (a) G (a) 0.5 G (b).5 (b).0.0 G 0.5 G (GHz) (GHz) Fig.. (Color online) The interplay and mutual suppression/enhancement between two coexisting FWM signals ( and ). (a) the upper curves: pure DFWM signal (with F F F both and blocked) (squares) singly dressed DFWM signal (with blocked) F (triangles) coexisting singly dressed DFWM signal and FWM signal (with F F blocked) (reverse triangles) and coexisting dressed DFWM signal and FWM signal F F (circles);lower curves: pure FWM signal (with both and F blocked) (left triangle) singly-dressed FWM signal (with blocked) (right triangle); 0. The inserted plot: corresponding to the dressed-state picture. (b) the condition are the same to that in (a) except = 5.9GHz. The inserted plot: corresponding to the dressed-state picture. (a) and (b) theoretical plots corresponding to the experimental parameters of (a) and (b) respectively. These effects can be explained effectively by the dressed-state picture. The dressing field couples the transition 0 to and creates the dressed states G which leads to single-photon transition 0 off-resonance [the inserted plot in Fig. (a)]. At exact single-photon resonance with 0 the DFWM signal F intensity is greatly suppressed by the means of scanning the dressing field across the resonance ( 0 ) as the upper (C) 0 OSA 4 July 0 / Vol. 9 No. 4 / OPTICS XPRSS 679

6 Relative Intensity of DFWM signals triangle points in Fig. (a) shows. At the same time the FWM signal F experiences similar process [the right triangle points in Fig. (a)]. Furthermore an appropriate value at which chosen in the investigation. In this case compared to the pure DFWM signal points in Fig. (b)] the dressed DFWM signal F is either enhanced or suppressed is F [square is enhanced [the upper and low triangle points in Fig. (b)]. However the dressed FWM signal F is suppressed due to the destructive interference [right triangle points in Fig. (b)] compared to the pure signal [left triangle points in Fig. (b)]. The upper triangle in Fig. (b) combines the two FWM processes ( F and F ) which are dressed by laser beams and respectively. After () () calculating F and F under the above experiment conditions good agreements are obtained between the theoretical calculations and the experimental results as shown in Figs. (a) and (b) respectively. After that we investigate the evolutions of the interaction between these two coexisting FWM signals by the means of setting different frequency detuning values where the fixed spectra corresponds to the suppression and enhancement of DFWM signal F F and the shifting spectra corresponds to the FWM signal F as shown in Figs. (a)-(a7). It is obvious in Figs. (a)-(a) that as the frequency detuning varies from 0 to zero from up to down the DFWM signal F shows the evolution from enhancement to partial enhancement/suppression and then to suppression. At the same time the FWM signal F varies from intense to weak (when two FWM signals F and F overlap) and shifts from left side to right side which satisfies the two-photon resonant condition ( 0 ). When changes further to be positive a symmetric process is observed [i.e. suppression in Fig. (a5) partial suppression/enhancement in Fig. (a6) and pure enhancement in Fig. (a7)]. It should be noted here that FWM signal F still shifts from left side to right side. Figure (a4) shows the weakened FWM signal due to the strong effect of the Doppler absorption. specially (a) (a) (a) (a4) (a5) (a6) (a7) (GHz) (b) (b) (b) (b4) (b5) (b6) (b7) (GHz) Fig.. (a) and (b) Measured evolution of the four FWM signals [( and ) and ( and F F F ) respectively] versus for different values. (a)-(a7) and (b)-(b7): -9. F GHz respectively. (C) 0 OSA 4 July 0 / Vol. 9 No. 4 / OPTICS XPRSS 680

7 the DFWM signal F at a large one-photon detuning is extremely weak when G 0. However the strong dressing field can cause the resonant excitation of one of the dressed states if the enhanced condition G 0 is satisfied. In such case the DFWM signal F is strongly enhanced [Fig. (a)] mainly due to the one-photon resonance ( 0 G ) [the insert plot in Fig. (b)]. As 0 the intensity of the DFWM signal F is greatly suppressed [Fig. (a)] similar to the case of the upper triangle curves in Fig. (a). Also we can observe the FWM signal F is suppressed due to the destructive interference. In addition Figs. (b)-(b7) show the interaction of another two coexisting the FWM processes ( F and F 4 ) in which the fixed spectra corresponds to the FWM signal F and the shifting spectra corresponds to FWM signal F 4 for different frequency detuning values. Now we concentrate on the cascade dressing interaction and the two dispersion centers of FWM images with two dressing fields and in the two-level atomic system. In order to investigate the cascade dressing interaction the power of the coupling field is set at 80 W. So the DFWM signal F shows a spectrum of the AT splitting due to self-dressed effect [0] induced by beam k when is scanned and the dressing field is off as shown in the dashed curve of Fig. 4(a). When the beam k is on the DFWM signal F is dressed by both and and therefore shows the cascade dressing interaction as shown in Figs. 4(a) and 4(c). Specifically by discretely choosing different detuning values within 0 and scanning the DFWM signal F shows 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 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)]. In order to explain this phenomenon the dressed-state picture is adopted as shown in Fig. 4(d). First the DFWM signal is dressed by both fields and. The corresponding F expression of the modified density matrix element of DFWM F process is () * igg ( G ) / ( B4 B5 ) where d6 A5 d7 0 i A4 G / B F A5 G / d7 A6 G / d6 B4 A4 and B5 B A6. Next the inner dressing field dresses the state 0 to create two new dressing states G and then the strong dressing field creates new states G or G around states G as scanning the frequency detuning. As a result of this dressing scheme the DFWM signal F is extremely small when G 0 and is set far away from the resonance point at both and 0 respectively. Another result is that the strong fields can cause resonant 0 excitation of one of the dressed state (i.e. G or G [Fig. 4(d) and Fig. 4(d9) respectively] which can lead to the enhancement of FWM signals. Specifically if the condition G and G [corresponding to the dressed states shown in Figs. 4(d) and 4(d9)] is satisfied the DFWM signal F is obviously enhanced as shown in the curves of Fig. 4(a) and 4(a9) respectively. As changes to be near the resonance point we can get a partial enhancement/suppression of DFWM signal F. The first and second transition states satisfy suppression condition 0 and enhancement condition G (Fig. 4(d)) [enhancement condition G and suppression condition 0 as shown in Fig. 4(d4)] as leads to the first suppression and next enhancement (the curve of Fig. (C) 0 OSA 4 July 0 / Vol. 9 No. 4 / OPTICS XPRSS 68

8 DFWM signal Intensity 4(a)) [or the first enhancement and next suppression as shown in the curve of Fig. 4(a4)]. When reaches the point 0 the suppression effect gets dominant due to the dressed states G [Fig. 4(d)] so the DFWM signal F is purely suppressed as shown in the curve of Fig. 4(a). For the point 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 which can largely weaken the suppression effect of the inner dressing field on DFWM signal. Furthermore the other cascade dressing field 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 F and its two dispersion centers which is caused by the cascade dressing interaction of the two dressing fields and (a) (b) (c) (GHz) (GHz) (GHz) G 0 G G d G d d d4 d5 d6 d7 d8 d9 Fig. 4. (Color online) (a) Measured suppression and enhancement of DFWM signal versus F for different values in the two-level system. = and 57. GHz respectively. The dashed curve is the double-peak DFWM signal F versus. (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 overlap in the middle of heat oven. (d)-(d9) the dressed-state pictures of the suppression or enhancement of the DFWM signal. The states G (dashed lines) and the states G or G (dot-dashed lines) respectively. 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 [7] the spatial splitting of the FWM beam can be controlled by the intensities of the involved laser beams the cross-kerr nonlinear (C) 0 OSA 4 July 0 / Vol. 9 No. 4 / OPTICS XPRSS 68

9 DFWM Images coefficients and the atomic density according to the nonlinear phase shift r / kfn zie / ( n0i F ). Here the additional transverse propagation wave-vector is kr / r. The change of phase ( ) distribution in the laser propagating equations determines the spatial splitting of the laser beams. In theoretical calculation we can obtain the () * intensity of the F beam by I F ig F F a [7] with Fa G ( G ) / ( B4 B5 ) and the nonlinear cross-kerr refractive index n Re( igffa / h). When is scanned in the experiment the intensity I of the laser beam and n almost stays constant for different detuning. So is primarily determined by I F. When the suppression condition ( 0 ) is satisfied and the intensity of FWM signal I F reaches its minimum the spatial splitting will become stronger as shown in Fig. 5(a) (the suppression positions located at GHz ). While in the enhancement condition with the larger I F is decreased and therefore the splitting is weakened correspondingly as shown in Fig. 5(a) where the enhancement condition is located at 8.GHz. (a) (a) (a) (b) (b) (b) (GHz) (GHz) Fig. 5. (Color online) (a) DFWM signal images when = GHz. (b) F DFWM signal images when = GHz. Specially we observed the y-direction spatial splitting images of the DFWM signal [Fig. 5(b)] by carefully arranging laser beams k and k. In the experiment the beams and are deliberately aligned in y-z plane with an angle ( 0.05 ) to induce a grating in the same plane with the fringe spacing /. Because is far less than the angle of and in the x-z plane is big enough for observing the splitting caused by the induced grating. Furthermore when and are set in the middle of the oven F in y-direction due to the phase matching condition. As a result the splitting of x-direction due to the nonlinear cross-kerr effect from F and overlap F in disappears simultaneously. Because remains nearly the same for the changeless and a larger spot of the F beam with larger intensity will be split to more parts. In Fig. 5(b) the field 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(b)-5(b) show the experimental spots corresponding to the curves in Figs. 4(c)-4(c). However the effects of suppression and enhancement of the DFWM signal F 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) the and are all set at the back of the heat oven. But in Fig. 4(c) only and are deliberately moved to the middle of the oven to demonstrate the splitting of F in the y-direction. So the dressing effect on F by in Fig. 4(c) appears worse than that in Fig. 4(a). (C) 0 OSA 4 July 0 / Vol. 9 No. 4 / OPTICS XPRSS 68

10 In order to verify the cascade dressing interaction and two dispersion centers of FWM image. The dresses field is tuned to the line center (568.8 nm) of the to ( 4D /5/ ) transition and a ladder type three-level atomic system forms as shown in Fig. (b). () With the dressed perturbation chains we can obtain I where F F ig G ( G) / ( B B ) with d8 i( ) d9 i d0 A9 () * F 6 7 d d A7 A7 G / d8 B d A A A G / d 8 A G / d 9 9 A0 G / d0 B6 A8 and Fig. 6. (a) Measured suppression and enhancement of DFWM signal versus F for different values and 7. GHz respectively. The dashed curve is the double-peak DFWM signal versus. (b) F Theoretical plots corresponding to the experimental parameters in (a). (c)-(c9) DFWM signal images. The condition here is the same as that in (a). F 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 F except the shapes of partial suppressions/ enhancement. For instance the curve of Fig. 4(a) shows first suppression and next enhancement is different from the curve of Fig. 6(a) which shows first enhancement and next suppression. The reason for this contrast is the difference of levels structure. As is set near the resonance point ( 55.8GHz ) the new dressed-state G moves from upper to lower as is scanned from positive to zero [Fig. 4(d)]. So the DFWM signal F is first enhanced as the condition G is satisfied and then suppressed (the suppression condition 0 ) as shown in the curve of Fig. 6(a). Simultaneously we obtain the corresponding suppressions and enhancements of x direction spatial splitting of DFWM signal F images as shown in Fig. 6(c). Here Figs. 6(c)-6(c9) show the experimental spots corresponding to the curves in Figs. 6(a)-6(a9). 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 (C) 0 OSA 4 July 0 / Vol. 9 No. 4 / OPTICS XPRSS 684

11 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 ( ) NCT (08-04) RFDP () 9xjtujc08 xjj0 xjj05. (C) 0 OSA 4 July 0 / Vol. 9 No. 4 / OPTICS XPRSS 685