ISSN: 0256-307X 中国物理快报 Chinese Physics Letters A Series Journal of the Chinese Physical Society Distributed by IOP Publishing Online: http://www.iop.org/journals/cpl http://cpl.iphy.ac.cn CHINESE PHYSICAL SOCIETY CHIN. PHYS. LETT. Vol. 27, No. 7 (2010) 074212 Enhancement and Suppression of Four-Wave Mixing in a Four-Level Atomic System * CHEN Ru-Lin(陈[霖), YUAN Chen-Zhi(袁晨智), WANG Zhi-Guo(王志I), NIE Zhi-Qiang(m志r), LI Yuan-Yuan(o院院), ZHANG Yan-Peng(张彦+)** Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi'an Jiaotong University, Xi'an 710049 (Received 16 April 2010) We report observations of the enhancement and suppression of four-wave mixing (FWM) in an electromagnetically induced transparency window in a Y-type 85Rb atomic system. The results show the evolution of the dressed effects (from pure enhancement to partial enhancement/suppression, and finally into pure suppression) inthe degenerate-FWM processes. Moreover, we use the perturbation chain method to describe the FWM process. Finally, we observe the polarization dependence of the enhancement and suppression of the FWM signal. PACS: 42. 50. Gy, 42. 65. Jx, 42. 65. Tg DOI: 10.1088/0256-307X/27/7/074212 0 In recent years, it has been experimentally demon- condition kF = k1 + k2 − k2. At the same time, the strated that under electromagnetically induced trans- strong dressing laser beam E3 with a wavelength of [1] parency (EIT) conditions multi-wave mixing can 776.157 nm (!3, k3 and ∆3 = !31 − !3) propagates in be selectively enhanced or suppressed and emit with the same direction as beam E2 to influence this FWM [2;3] small absorption by the medium. Such laser- signal while E3 drives the transition j1i to j3i. Fi- induced atomic coherence has a strong influence on nally, the generated FWM signal and the transmitted singly and doubly dressing schemes in multi-level probe beam are detected by an avalanche photodiode systems.[4] On the other hand, due to the multi- detector and a photodiode, respectively. Zeeman energy levels of the atomic systems,[5;6] po- 5 5 larizations of involved fields can largely control four- D5/2, D3/2, wave mixing (FWM) processes.[7−14] In this Letter, F/,, F/,, > > experimental observation of the evolutions of the en- ω ω hancement and suppression, from pure enhancement 2 3 E3 5 to partial enhancement/suppression, and finally into > P3/2, F/ E ' E pure suppression at resonance, is reported. Also, ac- ω1 ωF 2 2 cording to the selective transitions among polarization E1 EF 5 > S1/2, F/ (b) dark states of degenerate Zeeman sublevels, we can (a) modulate polarization of the weak probe field to con- Fig.1. (a) Relevant 85Rb energy levels, (b) spatial box trol enhancement and suppression of FWM processes schematic diagram of the experiment. by the dressing field. The experiment was carried out in a 85Rb vapor We can obtain the results of the FWM process by solving the coupled density-matrix equations in cell, whose energy levels 5S1=2 (F = 3), 5P3=2 (F = 3), general for arbitrary strengths of the fields E1, E2, 5D3=2 and 5D5=2 (F = 2; 3; 4) form such a Y-type sys- 0 tem (Fig. 1(a)). The laser beams are aligned spatially E2 and E3. The simple FWM (with E1, E2 and 0 (0) !1 as shown in Fig. 1(b). A weak probe beam E1 with a E2 on, and field E3 off) process via chain 휌00 −! (1) !2 (2) −!2 (3) (3) 2 wavelength of 780 nm (!1, k1 and frequency detuning 휌10 −! 휌20 −−−! 휌10 can give 휌10 = Ga=(d1d2), 0 * ∆1 = !10 − !1) is modulated by a quarter wave plate where Ga = −iG1G2(G2) exp(ikF ·r), d1 = Γ10 +i∆1 (QWP). The laser beam E1 probes the lower tran- and d2 = Γ20 + i(∆1 + ∆2), with Γij being the trans- sition j0i to j1i. Two pump beams E2 (!2, k2 and verse relaxation rate between states jii and jji. Next, 0 0 ∆2 = !21 − !2) and E2 (!2, k2 and ∆2) have a wave- we add the dressing field E3 with strong pumping field 0 length of 775.978 nm and propagate in the opposite E2, E2 and strong probe field E1, so the simple FWM ∘ 0 direction with small angle (0:3 ) and they drive the process above can be dressed by fields E2, E2, E3 upper transition j1i to j2i. One FWM signal beam and even E1, a perturbative approach for this spe- EF is generated among them with phase matching cific interaction can be further described by the follow- *Supported by the National Natural Science Foundation of China under Grant No 10974151, the New Century Excellent Talent Project of the Ministry of Education of China under Grant No 08-0431, and the Cross-Disciplinary Project of Xi'an Jiaotong University under Grant No 2009xjtujc08. **To whom correspondence should be addressed. Email: [email protected] ○c 2010 Chinese Physical Society and IOP Publishing Ltd 074212-1 CHIN. PHYS. LETT. Vol. 27, No. 7 (2010) 074212 ing coupling equations @휌10=@t = −d1휌10 + iG1휌00 + tion dips corresponding to the hyperfine-level transi- b * * * 87 0 i(G2) 휌20 + iG3휌30, @휌00=@t = −Γ0휌00 + iG1휌10, tions from Rb j5S1=2;F = 2i to j5P3=2;F = 1; 2; 3i, b 85 85 @휌20=@t = −d2휌20 + iG2휌10, @휌30=@t = −d3휌30 + Rb j5S1=2;F = 3i to j5P3=2;F = 2; 3; 4i, Rb * 0 87 iG3휌10 and @휌21=@t = −d4휌21 − iG1휌20, where d3 = j5S1=2;F = 2i to j5P3=2;F = 1; 2; 3i, and from Rb 0 Γ30 + i(∆1 + ∆3) and d4 = Γ21 + i∆2. These coupling j5S1=2;F = 1i to j5P3=2;F = 0; 1; 2i, respectively. In equations can be solved when combined with chain I to Fig. 2(a), there are two peaks on the absorption dips give the nonlinear density matrix for the multi-dressed in the up-curve. The right one of the two peaks is the 0 FWM process: EIT window created by the pump fields E2 and E2 in the system j0i − j1i − j2i, which satisfies the condi- [︂(︂ jG j2 )︂(︂ jGb j2 휌(3) = G × d + 1 d + 2 tion ∆ + ∆ = 0 and corresponds to the double-peak 10 a 2 d 1 d 1 2 4 2 FWM signal, while the left one is created by the dress- 2 )︂(︂ 2 2 )︂]︂−1 jG3j jG1j jG3j ing field E3 in the system j0i − j1i − j3i and satisfies + d1 + + : d3 Γ0 d3 the condition ∆1 + ∆3 = 0. In Fig. 2(b), each peak of the pure FWM signal corresponding to the right j0i − j1i − j2i EIT window is split into two peaks due to the dressing effect of E2 (a) 0 and E2. Figure 3 arranges the enhancement and suppres- sion of the FWM signal and corresponding EIT win- dows by scanning ∆3 for different ∆1. The height of FWM signals FWM (b) EIT peaks in Fig. 3(a) represents the transparent de- Probetransmission gree of probe field E1. The EIT peaks on the transpar- -6 -4 -2 0 2 ent curves are caused by the dressing field E . Such D (GHz) 3 1 EIT peaks satisfy the condition ∆1 + ∆3 = 0. As Fig.2. (a) Probe beam transmission with two EIT shown in Fig. 3(a), the heights of the EIT peaks de- windows versus the probe detuning Δ . (b) Measured 1 crease when j∆ j ! 0 and the EIT peaks fall to the FWM signals. The experimental parameters are G1 = 1 0 11:68 MHz, G2 = G2 = 25:39 MHz, G3 = 51:52 MHz, lowest height at point ∆1 = 0. This is because the Δ = 0 and Δ = 250 MHz. 2 3 interaction effect between E2 and E3 increases when Curve a in Fig. 2 is the probe transmission with j∆1j ! 0, so the dressing effect of E3 is greatly sup- EIT windows[12] and curve b is the measured FWM pressed, and the EIT transmission peaks are lower at signal. Figure 2(a) gives the four apparent spec- this point ∆1 = 0 than that at any other larger de- tra. From the left to right, there are four absorp- tuning positions. 1.5 1.4 (a) (c) 1.2 nsmission Tra 1.0 1.0 -100 0 100 0 50 100 150 (d) 4 (b) 2 2 Normalized 1 FWM signal FWM 0 -100 0 100 -100 0 100 200 D1 (MHz) D3 (MHz) Fig.3. (a) The EIT windows and (b) the enhancement and suppression of the FWM signal obtained by scanning Δ3 for different1 Δ increasing with the step of 11 MHz from Δ1 = 132 MHz to Δ1 = −132 MHz. (c) The theoretical EIT window by scanning Δ3 when Δ1 = −77 MHz. (d) The corresponding enhancement and suppression of the FWM 0 signal to the theoretical EIT window. The other parameters are Δ2 = 0, G1 = 11:68 MHz, G2 = G2 = 25:39 MHz, G3 = 51:52 MHz. 074212-2 CHIN. PHYS. LETT. Vol. 27, No. 7 (2010) 074212 The curve in Fig. 3(b) represents the FWM signal agree quite well with the experimental observations. normalized by the FWM without any dressing field We also investigate the enhancement and sup- E3. Therefore, the constant background 1 represents pression of the FWM signal intensities by scanning the common FWM signals without dressing field E3 the dressing field detuning ∆3 for different probe while the dips lower than the constant background field detuning ∆1, as shown in Figs. 4(a){4(c).