Transient Coherence Four-and Six-wave Mixing Spectroscopy With Phase-conjugation Geometry

Polarization beats with phase-conjugation geometry originate from the polarization interference between four- or six-wave mixing processes. This coherence effect is qualitatively different from quantum beats, which originate from interference between wave-function amplitudes. We have employed a second-order coherence function theory to study the effect of laser coherence on polarization beats in quasi-two-level, cascade three-level and four-level system. It is found that, the temporal behavior of the beat signal depends on the stochastic properties of the lasers and transverse relaxation rate of the transition. The cases that pump beams have either narrow band or broadband linewidth are considered and it has been found that the beat signal oscillates not only temporally but also spatially. If polarization beats with phase-conjugation geometry is employed for the energy-level difference measurement, the advantages are that the energy-level difference between states can be widely separated and a Doppler-free precision in the measurement can be achieved. We have investigated the relationship between polarization beats with phase-conjugation geometry and other Doppler-free techniques in frequency and in time domains. It is found that polarization beats with phase-conjugation geometry is closely related to the Doppler-free saturated absorption spectroscopy (or two-photon absorption spectroscopy with a resonant intermediate state) and the three-pulse stimulated photon echo (or sum-frequency trilevel photon-echo) when the pump beams are narrow band and broadband linewidth, respectively. However, it possesses the main advantages of these techniques in the frequency domain and in the time domain.Based on the second-order coherence function theory, we have studied the asymmetric behavior of the polarization beats in Doppler-broadened system, and attributed this asymmetry to the shift of the zero time delay, which is due to the dispersion of the optical components. It is worth mentioning that the asymmetric behavior of the polarization beat signal do not affect the overall accuracy of using polarization beats with phase-conjugation geometry to measure the energy-level difference. We have also employed second-order coherence function theory to study the nonlinear effects of third- and fifth-order on polarization beats in quasi-two-level, cascade three-level and four-level Doppler-broadened system. It is found that the phase-conjugate fifth-order polarization beat is due to the interference between fifth- and fifth-order optical polarizations, the beat signal oscillates not only temporally but also spatially, and the measurement accuracy for laser absolute frequency could reach the same order of magnitude as the laser linewidth.The correlation effects of fourth-order on polarization beats in a Doppler-broadened system are investigated using chaotic, phase-diffusion and real Gaussian field models. It has been found that the temporal behavior of the beat signal depends on the stochastic properties of the lasers and transverse relaxation rate of the transitions, and the modulation terms of the beat signal depend on the second-order coherence function, which is determined by the laser line shape. Since different stochastic models of the laser field affect only the fourth-order coherence function, they have little influence on the general temporal modulation behavior of the beat signal. The different roles of the phase fluctuation and amplitude fluctuation have been pointed out in the time domain. The fourth-order coherence function theory of chaotic field is of vital importance in polarization beats with phase-conjugation geometry. The difference between the polarization beats with phase-conjugation geometry and the DeBeer's ultrafast modulation spectroscopy is discussed as well from a physical viewpoint.Finally, we have employed phase-diffusion model to study the effects of laser field correlation on the Raman-enhanced nondegenerate four-wave mixing. The different roles of the field fluctuations have been pointed out. A time-delayed method has been proposed to suppress the thermal background. An enhancement of the ratio between the resonant and nonresonant Raman-enhanced nondegenerate four-wave mixing signal intensities was found as the time delay is increased when the laser has broadband linewidth. This enhancement can be explained by considering that the field fluctuations have different effects on the Raman resonance and on the laser-induced molecular-reorientational grating. When the lasers have Gaussian line shape, we present a second-order coherence function theory to elucidate the temporal asymmetry behavior of the Raman-enhanced nondegenerate four-wave mixing signal. The correlation effects of sixth-order on the Raman-enhanced polarization beats with phase-conjugation geometry in carbon disulfide are also investigated using chaotic and phase-diffusion models. Based on two types of models, the cases that the pump beams have either narrow band or broadband linewidth are considered and it is found that the beat signal oscillates not only temporally but also spatially. The overall accuracy of using Raman-enhanced polarization beats to measure the resonant frequency of Raman-active vibrational mode is determined by the relaxation rates of the Raman mode and the molecular-reorientational grating. Moreover, the temporal behavior of the beat signal depends on the stochastic properties of the lasers and the decay rates of the Raman mode and the molecular-reorientational grating. Different stochastic models of the laser field only affect the sixth- and fourth-order coherence function. Furthermore, the different roles of the phase fluctuation and amplitude fluctuation have been pointed out in the time domain. The difference between the Raman-enhanced polarization beats and the fourth-order coherence on polarization beats in Doppler-broadened system has been discussed as well from a physical viewpoint. Therefore, the sixth-order coherence function theory of chaotic field is of vital importance in Raman-enhanced polarization beats.