Enhancement Of Raman Signal Via Fractional Stimulated Raman Adiabatic Passage In A Pr: YSO Crystal

By choosing the proper time dependence of a pair of short coupling pulses which adiabatically interact with an atomic or molecular system, a 100% population transfer between lower levels can be achieved. This is referred to as stimulated Raman adiabatic passage (STIRAP). However, using the pulses with the same back edge, referred to as fractional STIRAP (F-STIRAP) we can create maximal coherence between the lower levels. After some time, a probe pulse arrives and scatters from the atomic coherence leading to efficient generation of a signal field.So far, most reports on STIRAP and F-STIRAP are in atomic vapor. For many potential applications, a solid-state medium is preferred. However, most solid materials have relatively broad optical linewidths and short relaxation times, which limits the achievable atom coherent effects. A notable exception to this general rule is Pr3+:Y2SiO5(Pr:YSO), which has narrow spectrum structure and long relaxation times. So far, electromagnetically induced transparency (EIT), four-wave mixing (FWM), and light storage based on EIT have been realized with these crystals. To our knowledge, however, F-STIRAP has not been investigated with these crystals.In this thesis, we report theoretically and experimentally F-STIRAP in a Pr:YSO crystal. We consider a closed there-level system of Pr3+ irons shown in Fig 1.3 H 4(±3/2),3 H 4(±1/2) and1 D2 (±3/2) are regarded as b , c and a , respectively. The coupling fields ofω1 andω2( with Rabi frequenciesΩ1 andΩ2) interacts with the transitions c ? a , b ? a , respectively.Δ1 is the one-photon detuning from the b ? a transition, andΔ2is the two-photon detuning from the c ? a transition. The repump fieldωRis on resonance with the transiton of3 H 4(±5/2)? 1 D2 (±1/2). The repump field refills the holes burned by the coupling fields, and changes the large inhomogeneous broadening.The ionic state is initialized to b which can be achieved by optical pumping with these fields. We use the coupling pulseω1 initially couples the two empty states, c and a , and next another coupling pulseω2 couples b and a . It can create maximal coherence between levels b and c when the pulses satisfy F-STIRAP with the same back edge. After some time, (less than the lifetime of the lower level coherence) the probe pulseω3 (with Rabi frequencyΩ3) arrives and scatters from the atomic coherenceρbcleading to efficient generation of a signal fieldω4( with Rabi frequencyΩ4).The interaction Hamiltonian in the rotating wave and dipole moment approximations for the three-level system isThe elements of the density matrix are given by the Liouville equation:The propagation of optical pulse fields in a medium is described by whereηac =ω1 Nμa2c/nε0c andηab =ω2 Nμa2b/nε0c are the coupling constants. We use coordinatesξandτ, which are related to the laboratory coordinates byξ= z,τ= t ? cz. The equation (2) and the equation (3) form a self-consistent system of equations.We performed numerical simulations of the above self-consistent equations for the case of maximal atomic coherence between hyperfine levels in Pr3+ irons. Fig. 2(a) shows the pulses at the entrance of the crystal. Fig. 2(b) shows the pulses at the exit of the crystal. We can see that the coupling pulseω2becomes weaken by stimulated scattering when the coupling pulses interact with the crystal, and the end edge of coupling pulseω1 is larger. The probe pulseω3 scatters the coherence leads to the generation of a signal pulseω4.Fig 3 shows the population distributing and the coherence between the lower levels as a function of time. At the beginning the population is in the state b , when the coupling pulses arrives, the population tranfer from b to c . The coherence termρbc, as illustrated in dashed curve, reaches its maximum value and the states b and c are half/half populated when the coupling pulses end.The next part is our experiment on F-STIRAP. The experimental arrangement is illustrated in Fig 4. We use a Coherent dye laser 899. The dye laser is continuous wave, and its linewidth is 0.5MHz, and its maximal output power is about 700mW in the wavelength of 605.977nm. We use acousto-optic modulators (AO) to make three different coherent laser fields as shown. The three fieldsω1 ,ω2, andωRare upshifted 167.9, 178.1, and 200 MHZ from the laser frequency, respectively. The continuous power of the fieldsω1 ,ω2, andωRare 10mW, 14mW, and 2mW, respectively.Fig 5, 6, and 7 shows the experimental results. Fig 5 shows the experimental curve of F-STIRAP. We can see a probe pulseω3 arrives 15μslater, and a Raman signalω4generated. The pinnacle in the end ofω2is produced by stimulated scattering in the two-photon interaction process. Fig 6 shows the amplitudes of generated signalω4as a function of mutual delay between coupling pulses. Zero delay was selected for the conditon where the tails of the pulses coincide. At this condition, the amplitude was maximal.We also study the amplitudes of generated signalω4as a function of the interval between the coupling pulse and the probe pulse as in Fig 7. The amplitude is smaller when the interval increases. The curve owns a slope which is decided by the decoherent speed between the hyperfine states 3 H 4(±1/2)and 3 H 4(±3/2). In our experiment, when the interval is longer than 40μs, we can not observe the generation of Raman signal.In summary, we have experimentally demonstrated the enhancement of coherent Raman scattering in Pr:YSO. We create spin coherence between the two states in ground state of Pr3+ via F-STIRAP. After some time, a probe arrives and scatters from the atomic coherence leading to efficient generation of a signal field. The intensity of the signal field depends on the magnitude of the atomic coherence. It becomes smaller when the interval of the probe pulse and the coupling pulse increases. When the interval is 40μs, the signal is very small, approximate to zero. The experimental results are in good agreement with numerical simulations. The results support the possibility of increasing the sensitivity of coherent anti-Stokes Raman spectroscopy by preparing maximal atomic or molecular coherence using short pulses.