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Journal of Shanxi University

Coherent Transients from Three-level Λ System with Local Field: Analytical Results

Yan Wei-Xian

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

Using a perturbation theory based on the Liouville equation of motion,we analyze the nonlinear response of a three-level model system,after considering the Lorentz local field effect.In the nonlinear optical response,two consecutive coherent pulses with the wave vector k_1 and k_2 generate new light waves in the new directions.The expression for the four-wave mixing signal,a third response,is given by accounting of the Lorentz local field.It is found that an four-wave mixing signal still persists in the direction 2k_2-k_1 for the negative time delay,and the frequency of the four-wave mixing signal has a shift related to the Lorentz local field factor l.

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Using a perturbation theory based on the Liouville equation of motion,we analyze the nonlinear response of a three-level model system,after considering the Lorentz local field effect.In the nonlinear optical response,two consecutive coherent pulses with the wave vector k_1 and k_2 generate new light waves in the new directions.The expression for the four-wave mixing signal,a third response,is given by accounting of the Lorentz local field.It is found that an four-wave mixing signal still persists in the direction 2k_2-k_1 for the negative time delay,and the frequency of the four-wave mixing signal has a shift related to the Lorentz local field factor l.
Using a perturbation theory based on the density-matrix formulation, we study the nonlinear optical responses of a noninteracting three-level model system to consecutive coherent pulsed excitations, as realized in several recent experiments involving excitonic transitions in quantum wells. The terahertz emission, which is a second-order response, and the four-wave mixing signal, a third-order response, are calculated within the rotating-wave approximation, in the presence of detuning, dephasing, and inhomogeneous broadening. We study the quantum beats in the photon echo from transient four-wave mixing experiments of a three-level system. We find that the temporal profile of the photon echo signal in the four-wave mixing experiments depends very strongly on the amount of inhomogeneous broadening of the energy levels involved. Both the position and the intensity of the peaks exhibit a smooth evolution from strong quantum beats to a conventional photon echo as the inhomogeneous broadening increases. These features from our noninteracting model system are compared with a recent experiment, and found to account for a number of experimental observations.
A systematic theoretical and computational investigation of the microscopic factors which determine the phase of the signal field in time-resolved quasidegenerate three-pulse scattering experiments is presented. The third-order phase-matched response is obtained by density-matrix perturbation theory using a Green-function formalism for a system composed of two well-separated sets of closely spaced energy levels. Equations for calculating the electric field of four-wave-mixing signals generated by path-length delayed pulses are given. It is found that the phase of the signal field is determined by the excitation pulse phases, the dynamics of the nonlinear polarization decay, the product of four transition dipole matrix elements, and by a pulse-delay-dependent phase modulation at the frequency of the first dipole oscillation in the four-wave-mixing process. Analytic results for a two-level Bloch model show the phase shift from rapid nonlinear polarization decay. The product of dipole matrix elements is real and positive for three-level processes (bleached ground-state absorption and excited-state emission), but can be real and negative for some four-level Raman processes. The pulse-delay-dependent phase modulation treated here is closely related to the interferometric pulse-delay-dependent amplitude modulation observed in some collinear experiments, and plays a role in producing photon echos in inhomogeneously broadened samples. Numerical calculations of phase-resolved electric fields for finite duration pulses using a Brownian oscillator model appropriate for condensed-phase dynamics are presented. The ability of pulse-delay-dependent phase modulation to encode the frequency of the initially excited dipole onto the phase of the signal field can be exploited to examine energy-level connectivity, reveal correlations hidden under the inhomogeneous lineshape, and probe relaxation pathways in multilevel systems.
It was studied the solvent influence over a two level system in the four wave mixing spectroscopy. the solvente effect was incorporated to the model in a stochastic form, through the broadening of the upper molecular level. Two intense waves of the same frequency, ω1, and another wave with minor intensity and ω2 frequency, were considered coupled to the nonlinear system, generating a new signal whose frequency is ω3, and where the wave-vectors follow the relation vector k1 + vector k1 = vector k2 + vector k3. Using the dipolar-electric and the rotating wave approximations, it was calculated the average of the coherence at the ω1, ω2 and ω3 frequencies. From that results, analytical expressions to the susceptibilities at the studied frequencies were obtained. Linear, coherent and coupled processes were identified.
We have measured electromagnetically induced transparency (EIT) and four wave mixing (FWM) signals in a three level atomic system to enhance nonlinearity for a weak field due to quantum coherence with standing fields. We were able to observe quite different EIT signals according to a traveling or standing coupling field. (1) We obtained EIT and FWM signals depending on detunings, polarization, (2) and power of the coupling field. Our results will be analyzed theoretically in viewpoint of a photonic band gap model.