Coherently Enhanced Four-wave Mixing And Its Applications

This thesis introduced the non-degenerate four-wave mixing effect (NFWM) which based on electromagnetically induced transparency (EIT) effects of quantum interference and the research work of its application on quantum optical communications—all-optical switching.Research of efficient non-degenerate four-wave mixingThe energy model for NDFWM is shown in Fig.l. The first FWM channel (population flow:|1>→|3>→|2>→|4>→|1>) is the generation of internal FWM signal coming from the input probe field in EIT scheme; the second FWM channel (population flow:|1>→|4>→|2>→|3>→|1>) is caused by the reabsorption of the internally generated FWM signal. Fig.1 Theoretical model of the four-level double-Λsystem of 87Rb atomic.Fig.2 Schematic of experimental setup BS:beam splitter;λ/2:half-wave plate; PBS:polarizing beam splitter.The experimental setup is shown in Fig.2. A Ti:sapphire ring laser (Coherent 899 ring laser system) with a beam diameter of～2mm and power of～36mW is tuned to the transition acting as the coupling field. An external cavity diode laser-ECDL1 (DL100) with a beam diameter of～0.8mm and power of～0.8mW is tuned to the transition acting as the probe fieldΩp. Another external cavity diode laser-ECDL2 (DL100) with a beam diameter of～2mm and power of～10mW is tuned to the transition acting as the pump fieldΩ2. All three beams are vertically polarized and propagate collinearly with the help of 1/2 wave plate and a pair of polarization beam splitters (PBSx). All laser beams are focused upon a 7.5-cm-long temperature stabilized vapor cell that consists of both 85Rb and 87Rb isotopes.Fig.3 Measured (solid curves) and Calculated (dash and dot curve) FWM signal intensity as a function of the pump detuning. Here the probe and coupling detuningδ1=-160MHz. Inset:Calculated FWM signal intensity for only 87Rb atom versus the pump detuning with and without Doppler broadening.However, two unsymmetrical peaks appear in this experiment (as shown in the solid curve in Fig.3), which is different from the symmetric phenomenon as predicted by the theory. This difference is related to the sample comprising of two isotope 87Rb and 85Rb. In the axis of pump detuning of Fig.3, for the isotope 87Rb,δ2=0 is defined to describe the resonant transition |2>→|4>of pump fieldΩ2, however, for the isotope 85Rb,δ2(?)1.2GHz is the point. The applied pump fieldΩ2 is understood to drive the atomic transition|2>→|4> for both the isotope 87Rb and 85Rb. With different detuning in the region of 0<δ2<12GHz. The similar case also occurs for the other two applied fieldsΩ1 andΩp. Therefore in this experiment there are two systems coupled by the same applied fields with different detuning. We understand from the energy diagram that the FWM frequency corresponding to the positive pump detuning observing the maximum FWM intensity for the isotope 87Rb is very near the resonant region of the isotope 85Rb. Due to the reason that, for the given fieldsΩ1 andΩp, the two-photon resonance condition necessary for the FWM process is only satisfied for the isotope 87Rb but not for 85Rb,the FWM signal at the positive pump detuning observing the maximum FWM intensity for the isotope 87Rb could be absorbed by the isotope 85Rb to induce a much smaller signal compared with the case of negative pump detuning. The dash and dot curves in Fig.2 are the theoretical predictions with the consideration of two double-A systems under the effect of Doppler broadening with only overall amplitude adjustment. It is seen that the experimental result agrees well with the theoretical prediction.Fig.4 illustrates the absolute FWM intensity conversion efficiency If(z=l)/Ip(z=0) as a function of the temperature with fixed pump detuning. Clearly, the optimized FWM intensity conversion efficiency about 73% is observed during the temperature region from 65℃to 70℃, which is the region where constructive interference between two FWM channels occurs. Fig.4 The nonlinear frequency conversion efficiency as a function of the temperature. Here the probe and coupling detuningδ1=-160MHz and the pump detuningδ1=-1.16GHz.Research of all-optical wavelength conversion switching based on four-wave mixingThe atom-light interaction scheme for the proposed all-optical switching is shown in Fig.5. For 87 Rb atoms, a standard three-levelΛ-type EIT configuration is formed when a strong coupling fieldΩ1 with the detuning ofδ1 and a weak probe fieldΩp with the detuning of 8p are applied on the medium to drive respectively transitions |2>(?)|3>and|1>(?)|3>. A strong pump field Q2 with the detuning ofδ2 drives transition |2>(?)|4> to facilitate the generation of a FWM signalΩf with the detuning ofδf on transition|1>(?)|4>. Here the detuned probe and coupling fields are kept in two-photon resonanceδp=δ1, thus another two-photon resonant conditionδf=δ2 is also satisfied due to the energy-conservation and phase-matching requirements. On the other hand, for 85Rb atoms, the coupling fieldΩ1 drives transition |2'>(?)3'> with the detuning ofδ'2=δ2-913MHz and the pump fieldΩ2 drives transition |2'>(?)|4'> with the detuning ofδ'2=δ2-1218MHz when the probe fieldΩp is applied on transition |1'>(?)|3'> with the detuning ofδ'p and the two-photon resonanceδ'p=δ'1 is satisfied, the second generated FWM signalΩ'f with the detuning ofδ'f=δ'2 may be observed due to the energy-conservation phase matching requirements.Fig.5 Diagrams of the four-level double-Λsystem of 85Rb and 87Rb atom for strong nonlinear interactions. The two laser fieldsΩ1 andΩp drive the transitions in 85Rb and 87Rb atom as shown. When the probe fieldΩp (orΩp) is applied to the transition 87Rb (or85Rb) atom and two-photon resonance is formed in lower-A configuration, a FWM signalΩf(orΩf) is observed at the end of the vapor cell.An experimental setup is depicted in Fig.2 where a Ti:sapphire ring laser (Coherent 899 ring laser system) with a power of～24mW, acting as the coupling fieldΩ1, simultaneously drives transition|2>(?)|3>of 87Rb atoms and |2'>(?)|3'> of 85Rb atoms. An external cavity diode laser (ECDL1, DL100) with a power of～0.5mW, acting as the probe fieldΩp(Ωp) is scanned across the D1 line of 85Rb and 87Rb atoms. Another external cavity diode laser (ECDL2, DL100) with a power of～10mW, acting as the pump fieldΩ2, simultaneously drives transition |2>(?)|4> of 87Rb atom and|2'>(?)|4'>of 85Rb atoms. All laser beams are linearly polarized and collinearly propagate inside the vapor cell with the help of a half-wave plate and a polarization beam splitter (PBS1).Fig.6 The output FWM signals spectra of 87Rb atom (red square) and 85Rb atom (black circle) versus the pump detuningδ2. The red and black solid curves are the guideline for the measured data. The points A, B, C, and D demonstrate the four statuses of this proposed optical switching, which are marked by the dash lines at different pump detuning.The measured FWM signals as a function of the pump detuning are shown in Fig.6. Let's pay more attention to the tick points A, B, C, and D in Fig.6. With the gradual departure from the pump resonance, four different output statuses are shown in turn. With a small pump detuning, a maximal FWM signal of 85Rb atoms is shown at point A while the FWM signal of 87Rb is small enough to be negligible. With increased pump detuning, the FWM signal intensity of 85Rb atoms decreases while that of 87Rb atoms increases instead. This leads to the same FWM signal intensities for both 85Rb and 87Rb atoms at point B, as well as the phenomena of the maximum FWM signal for 87Rb atoms and the negligible FWM signal for 85Rb atoms at point C. As the pump detuning is larger enough, both FWM signals become even hard to be seen at point D.For a clear sight on this dual-channel optical switching, we present now the experimental results as viewed from the channel statuses. A series of measured FWM signals as a function of the probe detuning are plotted in Fig.7. For these measurements, the pump detuning is fixed sequentially at the tick points A, B, C, and D as shown in Fig.7. The channel I (the FWM signal of 85Rb atoms depicted as the left part in Fig.7) is switched on (Fig.7A) and off (Fig.7D) when the pump detuning is set as --96MHz (point A) and～-1.127GHz (point D) in turn, with frequency conversion efficiencyη= If(z=l)/Ip(z=0) respectively to be～65% and～2%. During the process of switching on and off channel I, the output of channelⅡ(the FWM signal of 87Rb atoms depicted as the right part in Fig.7) is always small (η≤2%). On the other hand, the channel II is switched on (Fig.7C) and off (Fig.7D) when the pump detuning is set as～-1.127GHz (point C) and～-1.826GHz (point D) in turn, with frequency conversion efficiencies respectively to be～72% and～2%. During this switching process, the output of channelⅠis also very small (η≤5%).Furthermore, both channelⅠand channelⅡare switched on (Fig.7B,η～30%) when the pump detuning is set as～-838MHz (point B),and are switched off (Fig.7D) when the pump detuning is set as～-1.826GHz (point D). As discussed above, this dual-channel optical switch has four distinct statuses:only channelⅠopen, only channelⅡopen, both channels open, and both channels closed, which are mainly determined by the pump detuning. Fig.7 (Color Online) The output FWM signal spectra of 85Rb atom and 87Rb atom versus the probe detuningδ1. These FWM signals (from upper to lower) denote the four switching statuses corresponding to the marked point A, B, C, and D in Fig.6.