Density Control of Dressed Four-wave Mixing and Super-fluorescence

Transcription

1 0.09/JQE , IEEE Journal of Quantum Electronics Density Control of Dressed Four-wave Mixing and Super-fluorescence Yuanyuan Li, Gaoping Huang, Dan Zhang,, Zhenkun Wu, Yiqi Zhang, Junling Che and Yanpeng Zhang,* Abstract For the first time, we study the fluorescence induced by spontaneous emission under three different kinds of atom densities (including proper, high and low atom densities). Apart from the fluorescence signal, we also present the characteristics of images and spectral of the probe transmission and four-wave mixing under proper atom density, such as the Autler-Townes splitting of the spectral and the images. Moreover, under other two improper atom densities, we give the observations of spectral of two super-fluorescence in order to understand the different contributions of high and low atom densities. The phenomena in spectral and images can be well controlled by adjusting the incident beam powers and frequency detunings. Such studies can be used in all-optical controlled spatial signal processings. Index Terms Aulter-Townes splitting, electromagnetically induced transparency, four-wave mixing, super-fluorescence. E I. INTRODUCTION LECTROMAGNETICALLY induced transparency (EIT) in multi-level atomic vapors attracted a lot of attention in last two decades [,]. It has been demonstrated that the nonlinearities can be significantly enhanced and modified by atomic coherence []. The self- and cross-kerr nonlinearities enhanced by such atomic coherence are crucial in generating large refractive index modulation [3]. By changing the nonlinear refractive index, laser induced-focusing [4] and pattern formation [5] have been extensively investigated with two laser beams propagating in atomic vapors. Recently, we have observed spatial shift [6], spatial Autler-Townes (A-T) splitting [7], gap and dipole solitons [8,9] of the four-wave mixing (FWM) beams generating in multi-level atomic systems with This work was supported by the 973 Program (0CB9804), NSFC (607800, , 044, 60807, 046, 605), RFDP ( , , ), FRFCU (0jdhz05, 0jdhz07, xjj0083, xjj0084, xjj0080, xjj03089), and CPSF (0M5773). The authors are with Institute of Applied Physics, Xi an University of Arts and Science, Xi an 70065, China and Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi an Jiaotong University, Xi an 70049, China (*Corresponding author: ypzhang@mail.xjtu.edu.cn) dressing effects [0-]. Such FWM processes can be well controlled by additional coupling laser beams via the cross-phase modulation (XPM) [6]. Studies on such spatial shift and splitting of the laser beams can be very useful in understanding the formation and dynamics of spatial solitons [3] in Kerr nonlinear systems and all optical spatial signal processing applications, such as spatial image storage [4], entangled spatial images [5], soliton pair generation [6], and influences of higher-order (such as fifth-order) nonlinearities [7]. In addition, the fluorescence signal induced by spontaneous emission under EIT conditions [8,9] is studied due to its potential applications in metrology and long-distance quantum communication and quantum correlation. Besides, the key point to observe EIT is that the frequency detunings of the probe and coupling fields in the atomic system should match the so-called enhancement and suppression conditions [,,8,9], and the evolution between enhancement and suppression of FWM has been observed through controlling additional laser fields [0]. In alkali atomic vapor, if probe is strong enough and far detuned, FWM process occurs where Stokes and anti-stokes photons will be parametrically generated, which is so-called super-fluorescence (SF) processes []. In this article, different from the previous literatures under certain atom densities, we investigate not only the images and spectral of the probe transmission and FWM that are induced by the atomic coherence under proper atom density, but also the spectral of SF propagating in two directions under high or low atom density. At the same time, we show the fluorescence induced by spontaneous emission under these three kinds of atom density. We present the spatial splitting, shift, focusing as well as defocusing effect, and some other characteristics of the images in detail. All of the spectral and images can be effectively Copyright (c) 03 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

2 0.09/JQE , IEEE Journal of Quantum Electronics controlled by adjusting the incident beam power and frequency detuning. The paper is organized as following: in Sec., we briefly introduce the theoretical model and experiment scheme; in Sec. 3, we discuss the experiment results in detail and give the reasonable explanations; in Sec. 4, we conclude the paper. II. EXPERIMENTAL SETUP AND BASIC THEORY A. Experimental Setup 3P 3/ 3S / z x 4D 3/ E y E E E E E E 3 E F E E & E E F E F Na E F E 3 R R E 3 E F G G () a ( a) ( b) 0, 3 0 k 3 ) 3( E E E E E s( s) E ks k s as ) 3( E E& E GG ( as ) as E GG E & E & E 3 Fig.. (a) FWM and fluorescence processes in a cascade three-level atomic system. (a) Dressed-state energy level diagrams involved in the FWM process. The primary and secondary dressed states are the dot-dashed and solid lines, respectively. (b) Spatial alignments of the incident beams. (c) A double-λ configuration with the phase-matching scheme for SF processes by taking the hyperfine structures F= ( 0) and F= ( ) of the ground state into account. (d) Spatial beam geometry in the experiment. HR: high reflective mirror, BS: half-transparent mirror (50%), PMT: photomultiplier tube. In our experiment, a cascade three-level atomic system involving the energy levels 0 (3S / ), (3P / ), and 3 (4D 3/ ) of sodium atoms is used, as shown in Fig. (a). The pump laser field E (with frequency ω, wave vector k and Rabi frequency G ) and E (ω, k and G ) drive the transition 0 to, and E with a small angle 0.3 from E propagates in the opposite direction of the probe field E 3 (ω, k 3 and G 3 ). The three laser beams are from the same near-transform-limited dye laser (0 Hz repetition rate, 5 ns pulse width, 0.04 cm - line width and 589.0nm wavelength) with the same ( d) E 3 () c as 0 frequency detuning Δ =Ω 0 ω, where Ω 0 is the resonant transition frequency between 0 and. The interaction between the three beams generates a degenerate FWM (DFWM) signal E F (ω F =ω ) satisfying the phase-matching condition kf k k k 3. Two additional pump fields E (ω, k, and G ) and E (ω, k, and G ) are from another similar dye laser with the same wavelength nm, and connect the transition to 3 with the same frequency detuning Δ =Ω 3 ω, where Ω 3 is the resonant transition frequency between and 3. The five beams (E, E, E, E and E 3 ) are all horizontally polarized. In general, the laser beam E co-propagates with E, and E propagates in yoz plane with a small angle (0.3 ) from E, as shown in Fig. (b). In this atomic system, if the probe is strong enough, Stokes and anti-stokes fields (satisfying k 3 =k s +k as ) can be obtained and respectively named as E s and E as, as depicted in Fig. (c). In addition, two fluorescence due to spontaneous emission can be obtained [Fig. (a)]. One fluorescence signal R comes from the spontaneous emission of photons in the decay from to 0, while the other one R is generated in the decay from 3 to. However, if we intentionally let E propagate in the same direction of E 3, the interaction between E, E, and E will generate an upper-fwm signal [] E F (ω F =ω ) emitted from upper branch of this atomic system via kf k k k. The signal E F is split into two equal components by a 50% beam splitter, one of which is captured by a CCD camera, and the other detected by a photomultiplier tube (PMT). The probe transmission signal is also detected by CCD and PMT, while fluorescence (R&R) and E F are recorded by PMT. For the spectral of SF, E as is detected by one PMT placed in the same direction with E, while E s is detected by another placed at the mirror side of E 3 and the experimental setup, as shown in Fig. (d). B. Theoretical Calculations for Probe, FWM, Upper FWM, SF and Fluorescence Theoretical calculations on the density matrix elements are carried out to interpret the following experimental results. Copyright (c) 03 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

3 0.09/JQE , IEEE Journal of Quantum Electronics 3 First, the density-matrix element () 0 can be obtained (Eq.) via the perturbation chain (A.) [3] () in Appendix A. The imaginary part of 0 (i.e. ρ ) determines the absorption in propagation, and ρ =G 3 Γ 0 /(Γ 0 +Δ ) where G i =μ i E i /ħ (i=,,3) is the Rabi frequency (μ and μ 3 is the dipole matrix element between energy levels 0 and, μ is the dipole matrix element between energy levels and 3), and Γ ij is the transverse relaxation rate between i and j. When the probe transmission signal is dressed by the fields E ( E, E 3) and E ( E ), the expression is modified into 0 DD (Eq.). As well known, we can obtain the intensity (I) of probe signal with any transmission length z as I(z) E(z,t) =E 0 exp( ω χ z/c) I 0 ( ω χ z/c), where χ is the imaginary part of electric susceptibility χ. After transmission length L in the sample and considering the atom density N (determined by the cell temperature), the intensity I T of probe transmission signal can be written as: L N 3 0 L IT I0 I0 I0( ), 3 0G 0 3 where λ 3 is the wavelength of E 3. Second, the FWM signal E F is related to 0 (Eq.3) described by the perturbation chain (A.3). The amplitude square of this third-order density matrix element proportionally determines the intensity of E F. When E F is also dressed by the fields E ( E, E 3) and E ( E ), the expression is modified into 0 DD (Eq.4) via the pathway (A.4). When the atom density N is taken into account, the intensity (I) of the E F signal is I P N. 0 Third, for the upper-fwm signal E F, via the pathway (A.5), the density matrix element corresponding to E F can be written as 3 (Eq.5). When dressed by the fields E ( E, E 3) and E ( E ), the expression is modified into 3 DD (Eq.6) described by the perturbation chain (A.6). In the expression, the subscript of () 0, 0 and 3 in (A.), (A.3) and (A.5) will be replaced by G±G ±, because fields E, E &E 3 dress the level into G+& G, and fields E &E dress the levels G± into G±G +& G±G. Finally, the identical coherence between 0 and will be affected, as shown in Fig. (a). Similarly, the intensity of the E F signal is I P N3. Moreover, for the SF E s with respect to ( s ) and E as with respect to ( as ) are described by the perturbation chains (A.7) and (A.8), respectively. Here, taken the dressing effects of E ( E, E 3) and E ( E ) into account, the modified formations are written as DD (Eq.7) and (Eq.8), (s) 0 DD (as) respectively. Considering the light propagation and gain processes in the nonlinear medium under the Hamiltonian of the system, the intensities [8] of E s and E as are I s N s =G and I as N as =G, respectively, where G=cosh(κ as L) is gain coefficient with nonlinear coefficient as Re[( ias / c) as E3 ], in which the third-order nonlinear susceptibility 3 * as ( N0as ) ( 0 G3Gs ). Finally, for the fluorescence, The intensity of R described by perturbation chain (A.9) is proportional to the amplitude square of () (Eq.9). The intensity of R is proportional to the amplitude square of (4) 33 (Eq.0), which can be obtained by the perturbation chain (A.0). The pumping process from 0 to 3 by the strong beams E ( E, E 3) and E ( E ) can both dress R and R. So the perturbation chains of (A.9) and (A.0) should be modified into (A.) and (A.), respectively. Considering the condition under proper () atom density N, the total dressed fluorescence (4) and () () 33 are rewritten as N (Eq.) and (4) (4) 33 N 33 (Eq.), respectively. After being absorbed in relatively high atom density, the total fluorescence signal would be modified as: () () 0 N ( ) (a) 0 N ( ) (b) (4) (4) C. Theoretical Model of the Spatial Nonlinear Propagation of Probe and DFWM Beams The sodium vapor is an EIT-enhanced Kerr medium for our experimental conditions. The mathematical description of the propagation Copyright (c) 03 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

4 0.09/JQE , IEEE Journal of Quantum Electronics 4 properties of E 3 and E F with the self- and cross-kerr nonlinearities induced by the control and pump beams (E, E, E, and E ) can be obtained through numerically solving the following coupled equations: u3 i u3 ik3 S X ( n u3 n u z k3 n0 (a) X X3 X 4 n u n u n u ) u 3 uf i uf ikf S X5 ( n uf n u z kf n0 (b) X6 X7 X8 n u n u n u ) u F where = xx + yy is the transverse Laplacian, z is the longitudinal coordinate in the propagation direction, and u, and u, are the slowly varying envelope amplitudes of the fields E, and E,, respectively. The wave numbers are k 3 =k F =ω n 0 /c and n 0 is the linear refractive index at ω. At the S S right-hand sides of Eqs. (a) and (b), n are the X X8 self-kerr nonlinear coefficients of E 3,F and n [9] are the cross-kerr nonlinear coefficients due to the fields E, and E,, respectively. Moreover, nonlinear phase shift XEi ( i) / k zn I e /( n I ) i 3, F i 0 3, F XEi ( i) / ( i k3, Fzn Iie /( n0i 3, F), i=,) is introduced by strong field E i ( E i ) with i ( i ) being the center coordinate of E i ( E i ) in the transverse dimension relative to the center coordinate of E 3,F. The nonlinear phase shift shows that stronger spatial focusing/defocusing, shift and splitting can be achieved by larger nonlinear XEi XEi XEi XEi refractive index n n I i ( n n I i, i=,) and smaller intensity I 3,F of fields E 3,F. The Kerr nonlinear coefficient can be defined by a general expression as n Re 0 / ( 0cn 0) and D 0, where 4 3 S, S D N /( 0G3, F, F G3, F, F ) for n and 4 3 X X8 D N /( 0G3, F, F Gi ) for n. The element 0 can be obtained by solving the coupled density-matrix equations, e.g., 0a (Eq.3) X for n (induced by the strong E ) in Appendix B, X 4 0b (Eq.4) for n (induced by the strong E ), X 6 and 0c (Eq.5) for n (induced by the strong E ), X 8 0d (Eq.6) for n (induced by the strong E ). III. EXPERIMENTAL RESULTS AND DISCUSSIONS First, we experimentally investigate the probe transmission, FWM and fluorescence with proper atom density, because the detected will be enhanced due to enhanced quantum effect. In addition, we also study other attractive issue includes the properties of measured fluorescence and SF due to the atomic coherent effect at high or low atom density, but the quantum effect associated with the probe transmission and FWM vanishes. A. With Proper Atom Density The spectral of the probe transmission, E F and fluorescence versus Δ with different Δ, are shown in Figs. (a)-(c). For probe transmission, when Δ is set as 60 GHz, 30 GHz, 0, 30 GHz and 50 GHz successively, Figs. (a)-(a5) present a moving EIT window with Δ and a fixed EIT window within the Doppler absorption dip. This fixed EIT means a self-dressed EIT satisfying the single-photon resonant condition Δ =0 due to the term G /[Γ 00 + G /(iδ +Γ 0 )] in Eq.(). The moving EIT represents an external-dressed EIT satisfying the two-photon resonant condition Δ +Δ =0 due to the term G /[Γ 30 +i(δ +Δ )] in Eq.(). Thus, the self-dressed EIT is fixed, while the external-dressed one moves with Δ changing. It is worth mentioning that the self-dressed EIT and external-dressed one coincide at Δ =0, as shown in Fig. (a3). For E F signal in Fig. (b), the expression of the corresponding density matrix element related to FWM process is Eqs.(4, 6, 7, 8), in which the dressing effects can be denoted by the terms G /[Γ 00 + G /(iδ +Γ 0 )] and G /[Γ 30 +i(δ +Δ )]. The two terms mean a single-photon emission peak called primary A-T splitting and a two-photon emission peak called secondary A-T splitting in the spectral signal, respectively. The primary A-T splitting is caused by self-dressing fields E, E and E 3 which first split into two primary dressed () states G±. We can obtain the eigenvalues =±G of G±. And then, the secondary A-T splitting is caused by the external-dressing fields E and E Copyright (c) 03 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

5 0.09/JQE , IEEE Journal of Quantum Electronics 5 Probe transmission FWM Fluorescence (a) (a) (a3) (a4) (a5) (b) (b) (b3) (b4) (b5) (c) (c) (c3) (c4) (c5) Fluo. sig. n x0-5 (d) (d) (d3) (d4) (d5) (g) (g) (g3) (g4) (g5) Fig.. (a), (b) and (c) Measured spectral of E 3 transmission, E F and fluorescence versus Δ by setting () Δ =60 GHz, () 30 GHz, 0, (4) 30 GHz, (5) 50 GHz, respectively. (d) Theoretical calculations of fluorescence signal with the same condition in (a). (e) and (f) Measured images of E 3,F corresponding to (a) and (b), respectively. (g) Cross-Kerr XE, XE nonlinear refractive index n of E &E (solid curve) XE, XE and n of E &E (dashed curve) versus Δ with the same condition in (a). Probe transmission FWM Fluorescence (a) (b) (c) x0-5 n (f) (g) Δ (GHz) Δ (GHz) Fig. 3. (a), (b) and (c) Measured spectral of the E 3 transmission, E F and fluorescence versus Δ at Δ = 78 GHz when the E &E powers (P ) are 38 μw, 33 μw, 8 μw, μw, 8 μw, 3 μw and 8 μw from top to bottom. (d) and (e) Measured XE, XE images of E 3,F related to (a) and (b), respectively. (f) n XE, XE with the same condition in (a), and the inset is n. (g) Theoretical calculations of fluorescence signal with the same condition in (a). which split the primary dressed state G+ into G+G ± if Δ >0 or G into G G ± if Δ <0 as shown in Fig. (a). The corresponding eigenvalues are () ( 4 () G )/ ( ), () () and ( 4 G )/ ( ), which are measured from the level G+ and G, respectively. The splitting distance of primary A-T splitting is G, and that of secondary one is 4 G. As shown in Figs. (b)-(b5), when Δ is changed, the primary A-T splitting is fixed at Δ =±G, while the secondary one moves from the left to right due to the term 4 G. For the fluorescence signal, a similar moving can be observed in Figs. (c)-(c5). The fluorescence signal shows two dips: one is the dressed two-photon suppression dip moving from left to right with Δ changing from positive to negative because of G /[Γ 30 +i(δ +Δ )] in Eq.(0), and the other one is the single-photon suppression dip fixed at Δ =0 due to the term (Γ 0 +iδ ) in Eq.(0). It is worth noting that the two suppression dips coincide with each other at Δ =0 and form a larger suppression dip. Figure (d) shows the theoretical calculations of fluorescence signal at discrete Δ and agree with the experimental results [Fig. (c)]. Figures (e) and (f) show the spatial images of E 3 and E F versus Δ with different Δ. Figure (g) is the corresponding calculation of nonlinear refractive ' XE, XE index Δn including n (solid curve) and XE, XE n (dashed curve). The spatial shifts of E 3,F images that are mainly induced by E are investigated. The spatial shift curves [Fig. (e) and XE (f)] agree with n [Fig. (g)] well that E 3,F images shift up due to the attraction from E XE ( n 0 ) in Δ <0, and down due to repulsion XE ( n 0 ) in Δ >0, respectively. Moreover, the spatial shift behaves more distinct around Δ +Δ =0 because the absolute value of n XE ' reaches its maximum in Fig. (g). In other words, the spatial XE shift is distinct when n ' reaches its peak around Δ = 60 GHz, 30 GHz, 0, 30 GHz and 50 GHz, as shown in Figs. (e)-(e5) and (f)-(f5). Furthermore, the extent of focusing/defocusing of E 3,F images induced by E and E is proportional to XE, XE' n. As an example, the images of E 3,F in Figs. (e) and (f) focus more distinctly around Δ +Δ =0 than exactly at this point, because, ' n XE XE shows a peak around that point while a dip at that point. Besides, E F image has spatial splitting and shows approximate symmetry with respect to Δ =0 [Figs. (f)-(f5)]. These phenomena Copyright (c) 03 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

6 0.09/JQE , IEEE Journal of Quantum Electronics 6 can be explained by the XPM effect, as well as the relative location between the strong and weak beams [Fig. (b)]. The cross-kerr nonlinear refractive index Δn X,X is approximately symmetrical about Δ =0, resulting in the symmetrical spatial splitting. Since Δn X,X of the images reaches its maximum around the two peaks in spectral of E F, we can obtain more significant spatial splitting here. From the aspect of the spatial alignment [Fig. (b)], E F overlaps with E mainly in x-direction, which leads to the splitting of E F images in x-direction. As a result, the splitting in x-direction is observed at two sides of Δ =0, as shown in Fig. (f). In particular, the splitting of E F images in y-direction is obtained around Δ = 5 GHz. The reason is that E spatially attracts E F when Δn X > 0 so that E F and E will overlap with each other mainly in y-direction. It can be seen that there exists correspondence between the spectral and spatial images of probe transmission and E F. Then, we consider the power dependence (P ) of the probe transmission, E F and fluorescence versus Δ, both in spectral and spatial images. In fact, we can infer from the Eqs.(, 4, 6, 7, 8, 0, ) that the areas of the EITs of probe transmission, of the A-T splitting of FWM signal and of the suppression dip fluorescence signal can be controlled by the atom density N. Here, the areas include the height (i.e. amplitude) and the width (i.e. distance) of these spectral. The density control is able to influence the amplitude rather than the distance of these, since the distance is of little sensitivity to the atom density. In this subsection, our experiment is implemented at one constantly proper atom density, resulting in the constant density control effect upon the amplitude of these. Thus, we pay attention to the power dependence upon the amplitude of these. Specifically, for the probe transmission, the amplitude of the EITs at Δ =0 decreases from the top to bottom curves as shown in Fig. 3(a). When the dressing effects of E (E ) and E 3 are considered, the self-dressed term in Eq. () is G /[Γ 00 + G /(iδ +Γ 0 )]. The self-dressed effects become weaker with decreasing P because the Rabi frequency is related to the power, following the equation G i =E i /ћ=(p i /ε 0 ca) / /ћ, i=,,3. However, the external-dressed EIA remains invariant because G does not change with P at fixed P due to the term G /[Γ 30 +i(δ +Δ )]. Besides, the EIT splits the dip at Δ =0 into two small dips, which means that they are caused by the dressing influences of E (E ) and E 3. Accordingly, we can obtain the () eigenvalues as =±G. When the Rabi frequency G becomes smaller with P decreasing, the distance G becomes smaller from the top to bottom curves, as shown in Fig. 3(a). This is the reason why we mention above that the distance is not sensitive to the atom density but to the power. Probe transmission FWM Flourescence (a) (a) (a3) (a4) (a5) (b) (b) (b3) (b4) (b5) (d) (d) (d3) (d4) (d5) (e) (e) (e3) (e4) (e5) (c) (f) (c) (f) (c3) (f3) (c4) (f4) (c5) (f5) (GHz) (GHz) Fig. 4. (a)-(c) Measured spectral of E 3 transmission, E F and fluorescence versus Δ with Δ =0 when the power of E 3 (P 3 ) is () 9.95 μw, () 6.54 μw,.4 μw, (4) 7.0 μw, (5).48 μw. (d)-(f) Measured spectral of E p transmission, E F and fluorescence versus Δ with Δ =40 GHz when the power of E (E ) (P ) is () 5.3 μw, () 9.74 μw, 3.58 μw, (4) 8.0 μw, (5) 3.7 μw. Then, in Fig. 3(b), the primary A-T splitting of FWM decreases due to the term G /[Γ 00 + G /(iδ +Γ 0 )], and the overall signal intensity (proportional to 0 ) also becomes smaller due to the decreasing G in the term * g igg 3 ( G ) in Eqs.(4, 6, 7, 8). Moreover, as displayed in Fig. (b), the primary A-T splitting stands at Δ =±G, thus it approaches to Δ =0 with the P decreasing. Finally, in Fig. 3(c), the spectral signal of fluorescence presents the similar diminishing tendency of single-photon suppression dip at Δ =0 and two-photon one at Δ +Δ =0. The evolution of A-T splitting in fluorescence is clearly depicted by theoretical simulation in Fig. 3(g), which agrees well with the experiment. Figures 3(d) and 3(e) separately show the corresponding images of E 3 and E F. Here, the Copyright (c) 03 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

7 0.09/JQE , IEEE Journal of Quantum Electronics 7 spatial shift and splitting are obtained with some properties. The first property is that the spatial shift of E 3,F images gradually weakens with the powers of E and E decreasing from the top to bottom, as shown in Fig. 3(d). This is because the nonlinear XE XE refractive index n n I and nonlinear phase i shift ( ) / k XE 3, Fzn Iie /( n0i3, F) are both proportional to the powers of E and E. The second one is that the spatial splitting of E F images is also obtained and transforms from significant to negligible with decreasing powers of E and E, XE, XE since the absolute value of n changes diminishingly. The last one is that the spatial splitting behaves the most significantly at the position where the left peak of the spectral signal of E F in Fig. 3(b) is as well as the left maximum point XE, XE of n in Fig. 3(f) is. One can also find the correspondence between the spectral [Figs. 3(a) and (b)] and the spatial images [Figs. 3(d) and (e)], respectively. Furthermore, we consider the power dependences (P 3 and P ) of the probe transmission, E F and fluorescence versus Δ only in the spectral. Here, the corresponding images of E 3 and E F are omitted for simplicity. In Fig. 4(a), one can see that the height of EIT of the probe transmission at Δ =0 becomes smaller from top to bottom (dashed line). Here, the EIT at Δ =0 is the combination of self-dressed and external-dressed EIT. This is because the self-dressed effects, as mentioned above, become weaker with decreasing P 3 (G 3 ), even though the external-dressed EIT remains invariant. Similar to Fig. 3(a), the EIT splits the dip at Δ =0 into two small dips, which means that they are caused by the dressing influences of E &E 3 and E ( G /[Γ 00 + G /(iδ +Γ 0 )] and G /[Γ 30 +i(δ +Δ )]). Accordingly, we can obtain the eigenvalues as () =±(G+G ) with a distance (G+G ) between them. When the Rabi frequency G becomes smaller with P 3 decreasing, the distance becomes smaller from the top to bottom curves, as shown in Fig. 4(a). Then, in Fig. 4(b), the FWM signal shows the similar decreasing phenomena of the primary A-T splitting and the background intensity with the case in Fig. 3(b), because there are similarities between P and P 3 in the terms G /[Γ 00 + G /(iδ +Γ 0 )] and * g igg 3 ( G ). But it is different that the left two peaks are secondary A-T splitting [Fig. 4(b)], which are almost constant because their distance is 4 G without relationship of P 3. In Fig. 4(c), the spectral signal of fluorescence presents unobvious changing of single-photon suppression dip and two-photon one that coincide at Δ =0, which is because (Γ 0 +iδ ) and G /[Γ 30 +i(δ +Δ )] do not relate with P 3, as shown in Fig. 4(c). Probe transmission FWM Flourescence (a) (a) (a3) (a4) (a5) (d) (d) (d3) (d4) (d5) (b) (b) (b3) (b4) (b5) (e) (e) (e3) (e4) (e5) (c) (c) (c3) (c4) (c5) (f) (f) (f3) (f4) (f5) (GHz) (GHz) Fig. 5. (a)-(c) Spectral of E 3 transmission, E F and fluorescence versus Δ with Δ = 0 GHz when the power of E ( E ) is ().4 μw, () 7.04 μw,.3 μw, (4) 6.74 μw, (5) 9.98 μw. (d)-(f) Spectral of E P transmission, E F and fluorescence versus Δ with Δ = 0 GHz when the power of E 3 (P 3 ) is () 5.4 μw, () 9.63 μw, 3.85 μw, (4) 8.45 μw, (5).9 μw. Figures 4(d)-(f) show the spectral versus Δ with the powers of E and E increasing from top to bottom. The amplitude of EIA in probe transmission close to Δ = 40 GHz becomes larger because the dressing effects of E and E are denoted by G /[Γ 30 +i(δ +Δ )] and increase gradually from top to bottom curves. The dip distance and secondary A-T splitting distance increase due to the terms (G+G ) and 4 G, respectively. The fluorescence spectral signal in Fig. 4(f) shows that the amplitude of left suppression dip at Δ = 40 GHz enlarges when the powers of E and E increase from the top to bottom curves. Lastly, the self-dressed EIT of E 3, primary A-T splitting of E F and the right suppression dip of fluorescence signal at Δ =0 do not change with E and E, Copyright (c) 03 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

8 0.09/JQE , IEEE Journal of Quantum Electronics 8 because they are mainly caused by the dressing effects of E, E and E 3. Besides investigating the power dependences upon spectral versus Δ, we also study them versus Δ in Fig. 5. First, we turn to the power dependence P in Figs. 5(a)-(c). The EIA of E 3 transmission and the enhancement of E F are obtained, and their strengths are determined by the strength of the dressing effects of E and E. So, as the powers of E and E increase from the top to bottom curves, the EIA and enhancement enlarge gradually in Fig. 5(a). Besides, the suppression dip of fluorescence signal at Δ =0 determined by G /(Γ 3 +iδ ) in Eq.(0) becomes deeper, which is similar to the suppression dip at Δ +Δ =0 that is determined by the combined dressing effects of E (E ) and E (E ). Correspondingly, Figs. 5(d)-(f) show power dependence P 3. For E p transmission in Fig. 5(d), the overall signal intensity becomes stronger due to the enlarging numerator G 3 of () 0 in Eq.(). Thus the amplitude of EIA at Δ +Δ =0 becomes larger accordingly from top to bottom, as shown in Fig. 5(d). For E F, the overall signal intensity also becomes stronger with the enlarging G 3 in * g ig3gg of 0, leading to the increasing of the amplitude of enhancement, as shown in Fig. 5(e). However, as to the fluorescence in Fig. 5(f), Probe transmission ( a) FWM ( b) (GHz) (GHz) D3/ 3 3P3/ 3S 0 Fig. 6. (a) and (b) Spectral of E 3 transmission, E F versus Δ by setting Δ as 40 GHz ~ 5 GHz, from top to bottom. (c) Energy level diagrams involved in the upper-fwm process. two suppression dips at the positions Δ =0 and Δ +Δ =0 both show unobvious variation, because their expressions (Eq.(0) and Eq.()) do not contain the term G 3. Next, under the proper atom density, we are also able to obtain the upper-fwm signal E F emitted from the upper branch within the EIT window. Here, the propagating direction of E is purposely switched / E E ( c) E ' E F into the same direction of E 3. Figures 6(a) and (b) show the probe transmission and E F signal versus Δ with several discrete Δ from positive to negative. For E 3 (in fact E acting as E 3 ) transmission, Fig. 6(a) displays the evolution from EIA, to first-eia-then-eit, to EIT, next to first-eit-then-eia, and finally EIA. For E F signal in Fig. 6(b), the spectral signal evolutes from single emission peak to twin emission peaks and to single emission peak from top to bottom. The density-matrix element of upper-fwm is depicted by Eq.(6), thus the conditions for twin peaks are ( 4 G )/ ( 4 G )/0. From which we can deduce the distance of these twin peaks Δ a = 4 G. The twin peaks become more distinct around Δ =-Δ =0 since Δ a reaches its maximum. But they merge into one single peak at large detuning since Δ a approaches to 0. Meanwhile, the amplitude of the emission peak is the largest at Δ =0, because the dressing influence of E on FWM signal is the largest at this time. Besides, the locations of EIT in E 3 transmission and dip in between the peaks in E F signal change with different Δ (dashed lines in Figs. 6(a) and (b)), which alter rightwards from the top to bottom curves corresponding to G /[Γ 30 +i(δ +Δ )] in Eq.() and Eq.(6), respectively. In this subsection A, we have investigated the images and the spectral of the probe transmission, FWM, and fluorescence with proper atom density. We will continue to investigate the fluorescence signal and super-fluorescence with relatively high (Fig. 7) or low atom density (Figs. 8 and 9) in the following subsections (B and C). B. Relatively High Atom Density With relatively high or low atom density in our experiment, we have found that the EIT/EIA of probe transmission and enhancement/suppression of FWM do not exist any longer. But the fluorescence and SF can be still observed. This is not only because the fluorescence and SF are not sensitive to the atom density, but also because the atomic coherence effect, which causes the EIT/EIA of probe and enhancement/suppression of FWM, will be destroyed by the improper atom density. At this time, the typical emission FWM signal, which is not induced by atomic Copyright (c) 03 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

9 0.09/JQE , IEEE Journal of Quantum Electronics 9 coherence effect, will generate and affect the SF, thus we choose to eliminate it by blocking several beams. So in a sense, the control effect of atom density plays a role as a switch: proper atom density is on status so that we are able to control the areas of these induced by atomic coherence effect, while the improper density is off status so that we cannot obtain these. Specifically, we present the SF signal E s, normal fluorescence signal and the SF signal E as with the power of E decreasing under relatively high atom density, as shown in Fig. 7. First, for the normal fluorescence (i.e. R), its baseline height is determined by the density-matrix element that is proportional to the atom density and the square of G. When the power of E decreases from the left to right curves, the baseline height declines exponentially depicted by the triangle points in Fig. 7(b). However, one can also find that the baseline heights of the SF decline in the similar tendency with the normal fluorescence [Figs. 7(a) and (c)], against the fact that their heights are not mainly determined by G. Thus, we infer that both E s [Fig. 7(a)] and E as [Fig. 7(c)] have the leaky light of normal fluorescence. Second, for each curve of the normal fluorescence signal in Fig. 7(b), a deep dip is obtained. The dip combines the contributions of the SF signal E s (g) (g) (j) (j) (g3) (j3) (a) Dip depth (j4) P (μw) (g4) d x (g5) (j5) Fluorescence signal (h) (k) (k) (b) (h) (k3) Dip depth (h3) (h4) e x (h5) (k4) (k5) P (μw) SF signal E as (i) Dip depth (l) (i) (l) (i3) (l3) (c) f x (i4) (l4) (i5) (l5) P (μw) Fig. 7. (a)-(c) Measured spectral of (a) SF signal E s, (b) normal fluorescence signal and (c) SF signal E as versus Δ with E, E and E blocked and the power of E (P ) changing from 5 μw to 5 μw. Insets of (a), (b) and (c) are the dip depth representing the differences between the triangles and dots, which are defined as d x =g x j x, e x =h x k x and f x =i x l x (x=,, 3, 4, 5), respectively. suppression from E and of the large absorption with high atom density N. The former contribution can be depicted by term G /[Γ 00 + G /(iδ +Γ 0 )] in Eq.(0), while the latter one can be depicted by Eq.(a). We use the dip depth (defined as e x ) to reflect the decreasing tendency of combined contributions with P, as shown in the inset of Fig. 7(b). Similarly, d x and f x are used to reflect the decreasing tendency of the combined SF and leaky light of normal fluorescence signal, as shown in the insets of Figs. 7(a) and (c), respectively. One can see that decreasing tendency of d x and f x are more gentle than e x, which is due to the diminishingly contradictive dressing effect of E ( G /A in Eq.(7) for E s or G /A 5 in Eq.(8) for E as ). C. Relatively Low Atom Density By contrast, we study these under relatively low density. Figures 8(a)-(c) respectively show E s, fluorescence spectral and E as versus Δ with different Δ, respectively. Compare Fig. 8(b) with Fig. 7(b), one can see that the fluorescence signal only has an emission peak with tiny absorption and ignorable suppression (because of low atom density). The profile (dashed line) of fluorescence signal is maximal around Δ =0 due to Γ 0 +iδ in Eq.(0) and Eq.(), and the signal intensity is stronger at the off-resonance region than that at the near-resonance region because the fluorescence signal R is suppressed around the resonant point due to the term d + G /d in Eq.(). On the other hand, E s and E as both experience successively one bright state ( / 4 G / 0 ) at off-resonance region, one bright state ( / 4 G / 0) and one dark state (Δ +Δ =0) at near-resonance region, and one dark state (Δ +Δ =0) at resonant region as shown in Figs. 8(a) and (c). Besides, the baseline heights of these SF reach the maximum at Δ =0, and their intensities also reach the maximum at Δ =0, which is due to G /A in Eq.(7) and G /A 6 in Eq.(8). Since we can observe the bright state of the SF signal under relatively low density, the SF prefer proper atom density [6] to low and high ones, and the high one is the worst case. SF signal E s (a) (GHz) Fluorescence signal (b) (GHz) (GHz) Fig. 8. (a)-(c) Measured spectral of (a) SF signal E s, (b) normal fluorescence signal and (c) SF signal E as versus Δ and with E and E blocked and setting Δ from positive to negative rightward as 99. GHz, GHz, 38.8 GHz, SF signal E as (c) Copyright (c) 03 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

10 0.09/JQE , IEEE Journal of Quantum Electronics 0.57 GHz, 0, 4.3 GHz,.94 GHz,.56 GHz, and 38.8 GHz, respectively. The dashed lines are the profiles of the SF and fluorescence signal fitted by their baseline heights, respectively. Finally, we give other experimental results versus Δ with different Δ. Figure 9(b) is the normal fluorescence signal (i.e. R and R) with no absorption and two emission peaks induced by G /[Γ 30 +i(δ +Δ )] and (Γ 0 +iδ ) in Eq.(0) and Eq.(). Accordingly, one can obtain the conditions for emission peaks as / 4 G /, and the distance between the two peaks as 4 b G. Thus, we find that the distance becomes larger with larger Δ from Fig. 9(b) to Fig. 9(b3). Figures 9(a) and (c), similar to Figs. 8(a) and (c), show one bright state ( / 4 G /0) and one dark state (Δ +Δ =0) at resonant point, respectively. SF signal E s Fluo. signal SF signal E as (a) (b) (c) (GHz) (a) (b) (c) (GHz) (a3) (b3) (c3) (GHz) Fig. 9. (a)-(c) Measured spectral of (a) E s, (b) normal fluorescence signal and (c) E as versus Δ when E, E and E are blocked by setting () Δ =5 GHz, () GHz, and GHz, respectively. IV. CONCLUSION In summary, we have investigated the fluorescence induced by spontaneous emission with three different atom densities. Besides, in the proper atom density, we also present the characteristics of images and spectral of the probe transmission and FWM, such as A-T splitting of the spectral and the spatial splitting, shift, focusing as well as defocusing of the images. Also, we demonstrate the evolution of enhancement of upper-fwm signal with different Δ when the atom density is proper. Moreover, under other two improper atom densities, we give the spectral of two SF in order to understand the contribution of high atom density (strong absorption) and low atom density (little absorption). Such phenomena in spectral and images can be effectively controlled by adjusting the incident beam powers and frequency detunings, and have potential applications in quantum signal processing. APPENDIX A: THE PERTURBATION CHAINS AND CORRESPONDING DENSITY MATRIX ELEMENTS IN SECTIONS II-B. For probe transmission (0) 3 () perturbation chain: 00 0 (A.) (0) G3 () 00 ( GG )0 (A.) with the corresponding density matrix elements being : () ig / d (Eq.) 0 3 ig 3 0 d G /( 00 G / d) G / d (Eq.). For four-wave mixing and upper four-wave mixing. For four-wave mixing perturbation chain: (0) G * () G () G (A.3) (0) () ( )* () 3 00 G ( )0 G 00 G G G ( GG )0 (A.4) with the corresponding density matrix elements being: * 0 ig3gg /( 00d ) (Eq.3) * ig3g( G ) 0 00 (Eq.4) [ d G /( G / d ) G / d ] 00. For upper four-wave mixing perturbation chain: (0) G () G () ( G )* (A.5) * (0) G () G () ( G ) G G G G (A.6) 00 ( )0 30 3( ) (0) G 3 () G * as () G 3 0 ( s) (A.7) (0) G 3 () G * s () G ( as) (A.8) with the corresponding density matrix elements being: * ig ( G) G / d d d (Eq.5) 3 3 Copyright (c) 03 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

11 0.09/JQE , IEEE Journal of Quantum Electronics * ig( G ) G 3 d( d3 G / d G / 33) (Eq.6) [ d G /( G / d ) G / d ] 00 * igasg3 (s) ( d G / A G / A ) (Eq.7) d0 ( d G / A3 G / A4 ) * igsg3 0(as) ( d0 G / A5 G / A6 ) (Eq.8) d ( d G / A G / A ) For the Fluorescence perturbation chain: (0) G () ( G)* () 00 0 (A.9) (0) G () ( G )* () (A.0) 00 ( GG)0 ( GG)( GG) (0) () () ( )* ( )* (4) G G G G (A.) G G G G (A.) (0) () () ( )* ( )* (4) (0) G () G () ( G)* 00 ( GG)0 ( G)0 3( GG) ( G )* (4) 33 (A.3) with the corresponding density matrix elements being: () G /( d ) (Eq.9) () () N G N [ d G /( 00 G / d) G / d] ( G / d G / d G / d G / d ) * * 3 3 (4) (Eq.0) G G /( d d d ) (Eq.) (4) (4) N G G 33 N 33 [ d G /( 00 G / d) G / d] ( d G / d )( d G / d G / ) (Eq.) APPENDIX B: THE PERTURBATION CHAINS AND CORRESPONDING DENSITY MATRIX ELEMENTS IN SECTIONS II-C /[ 00 ( a N a ing G d G / 00 G / d ) ] (Eq.3) /[ ( b N b ing G d d G / 00 G / d ) ] (Eq.4) 0 0 c N c ingf G /[ 00 ( d G / 00 G / d ) ] (Eq.5) 0 0 d N d ingf G /[ d ( d G / 00 G / d ) ] (Eq.6) where d 0 =Γ 0 +i(δ Δ s ), d 0 =Γ 0 +iδ, d =Γ +i(δ Δ 0 ), d 0 =Γ 0 +i(δ Δ 0 Δ as ), d 0 =Γ 0 +i(δ Δ 0 Δ s ), d =Γ +i(δ Δ 0 Δ as ), A =Γ + G /d, A =Γ 3 +i(δ Δ 0 +Δ ), A 3 =Γ +i(δ Δ 0 Δ as )+ G /d, A 4 =Γ 3 +i(δ Δ 0 Δ as +Δ ), A 5 =Γ 00 + G /d 0, A 6 =Γ 30 +i(δ +Δ ), A 7 =Γ 00 +i(δ Δ s )+ G /d 0, A 8 =Γ 30 +i(δ Δ 0 Δ s +Δ ), and Δ 0 =.7 GHz. REFERENCES [] S. E. Harris, Electromagnetically induced transparency, Phys. Today., vol. 50, no. 7, pp. 36-4, 997. [] 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., vol. 0, no. 9, pp , 995. [3] H. Wang, D. Goorskey, and M. Xiao, Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system, Phys. Rev. Lett., vol. 87, no. 7, p , 00. [4] G. P. Agrawal, Induced focusing of optical beams in self-defocusing nonlinear media, Phys. Rev. Lett., vol. 64, no., pp , 990. [5] R. S. Bennik, V. Wong, A. M. Marino, D. L. Aronstein, R. W. Boyd, C. R. Stroud, Jr., and S. Lukishova and D. J. Gauthier, Honeycomb pattern formation by laser-beam filamentation in atomic sodium vapor, Phys. Rev. Lett., vol. 88, no., p. 390, 00. [6] 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., vol. 7, no., pp. 9-, 99. [7] G. P. Huang, J. S, W. K. Feng, J. M. Yuan, Z. K. Wu, M. Z. Qin, Y. Q. Zhang, and Y. P. Zhang, (03, April). Observations of Autler-Townes spatial splitting of four-wave mixing image, Appl. Phys. B, [Online] Available: [8] M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, Quantum interference effects induced by interacting dark resonances, Phys. Rev. A, vol. 60, no. 4, pp , 999. [9] M. Yan, E. G. Rickey, and Y. F. Zhu, Observation of doubly dressed states in cold atoms, Phys. Rev. A, vol. 64, no., p. 034, 00. [0] Y. P. Zhang, Z. Q. Nie, H. B. Zheng, C. B. Li, J. P. Song, and M. Xiao, Electromagnetically induced spatial nonlinear dispersion of four-wave mixing, Phys. Rev. A, vol. 80, no., p , 009. [] Y. P. Zhang, C. C. Zuo, H. B. Zheng, C. B. Li, Z. Q. Nie, J. P. Song, H. Chang, and M. Xiao, Controlled spatial beam splitter using four-wave-mixing images, Phys. Rev. A, vol. 80, no. 5, p , 009. [] 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. Copyright (c) 03 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.

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Lazarov, X. 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., vol. 83, no., pp. 88-9, 999. [9] J. Qi, F. C. Spano, T. Kirova, A. Lazoudis, J. Magnes, L. Li, L. M. Narducci, R. W. Field, and A. M. Lyyra, Measurement of transition dipole moments in molecular lithium through electromagnetically induced transparency, Phys. Rev. Lett., vol. 88, no. 7, p , 00. [0] 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., vol. 95, no. 4, p. 0403, 009. [] H. B. Zheng, X. Zhang, C. B. Li, H. Y. Lan, J. L. Che, Y. Zhang and Y. P. Zhang, Suppression and enhancement of coexisting super-fluorescence and multi-wave mixing processes in sodium vapor, J. Chem. Phys., vol. 38, no. 0, p. 0435, 03. [] H. B. Zheng, X. Zhang, J. Sun, C. B. Li, Z. Y. Zhang, H. X. Chen, and Y. P. Zhang, Dressed four-wave mixing from upper branch in a sodium atomic vapor, IEEE J. Quantum Electron., vol. 49, no., pp. -6, 03. [3] Z.Q. Nie, H. B, Zheng, P. Z. Li, Y. M. Yang, and Y. P. Zhang Interacting multiwave mixing in a five-level atomic system, Phys. Rev. A., vol. 77, no. 6, p , 008; Y. P. Zhang, and M. Xiao Generalized dressed and doubly-dressed multi-wave mixing, Opt. Express., vol. 5, no., p. 78, 007. Yuanyuan Li was born in Shaanxi, China, in 970. He received the Ph.D. degree in physics from Northwest University, Xi an, China, in 009. He is currently a professor at Xi an University of Arts and Sciences. She is currently with the Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi an Jiaotong University. Her current research interests include nonlinear optics and quantum optics. Zhenkun Wu was born in Henan, China, in 988. He is a PhD student in electronics science and technology from Xi an Jiaotong University, Xi an, China. He is currently with the Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi an Jiaotong University. His current research interests include nonlinear optics and quantum optics. Yiqi Zhang was born in Shandong, China, on October 9, 983. He received the PhD degree from Chinese Academy of Sciences, Xi an, China, in 0. He is currently with the Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi an Jiaotong University. His current research interests include nonlinear optics and quantum optics. Junling Che was born in Shanxi, China, in 985. He received the Master degree from Shanxi University in 0. He is currently with the Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi an Jiaotong University. His current research interests include nonlinear optics and quantum optics. Yanpeng Zhang was born in Shanxi, China, on May 5, 969. He received the Ph.D. degree in electronics engineering from Xi an Jiaotong University, Xi an, China, in 000. He is currently with the Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi an Jiaotong University. His current research interests include nonlinear optics and quantum optics. Gaoping Huang was born in Chongqing, China, on August 8, 99. He received the B.S. degree in electronics science and technology from Xi an Jiaotong University, Xi an, China, in 03. He is currently with the Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi an Jiaotong University. His current research interests include nonlinear optics and quantum optics. Dan Zhang was born in Henan, China, on May 8, 990. She received the B.S. degree from Xi an University of Arts and Sciences, Xi an, China, in 03. Copyright (c) 03 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by ing pubs-permissions@ieee.org.