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Journal of Experimental and Theoretical Physics

Spatial and temporal characteristics of signals representing transient Raman scattering and photon echo under two-photon excitation conditions

Sergey M. Zakharov, Edward A. Manykin

Published Nov 1, 1987• 0 citations
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A quantum theory of stimulated Raman scattering is established that takes into account the time-dependence of pump laser pulse, two-photon detuning and atomic populations, allowing the general transient and spatial propagation study of Raman memory. Heisenberg–Langevin and Maxwell equations for the collective atomic operators are solved analytically under adiabatic condition , where the electric field envelopes and the collective atomic operators vary slowly. The analytical solution of Stokes/anti-Stokes signal electric field operator is obtained. The spatial–temporal intensity of quantum signal field is studied numerically and analytically for different two-photon detunings and initial populations.
A theoretical analysis is made of the problem of parallel amplification of the Stokes signal in a nonmonochromatic spatially inhomogeneous pump field in stimulated Raman scattering. Expressions are obtained for the spatial and temporal characteristics of the process of amplification of the Stokes signal. It is shown that in the course of amplification the slowly varying amplitude of the Stokes signal field becomes similar to the slowly varying amplitude of the pump field. The relationships obtained apply also, subject to certain restrictions, to other types of scattering.
We study the dynamics of coherent emission of a semiconductor within the framework of the semiconductor Bloch equations, both in the time domain and in real space for various excitation conditions. We find that the spatial properties of the four-wave-mixing (FWM) response reflect the well-known temporal dynamics. For excitation high above the band edge, the FWM signal is emitted as a photon echo. This photon echo from continuum states of a semiconductor has the same dynamical properties as a photon echo from inhomogeneously broadened uncoupled two-level systems. However, unlike the case of two-level atoms, the polarization of the photon echo from the semiconductor continuum extends over macroscopic distances in real space. The implications of the large spatial extent of the photon echo polarization are discussed. In particular, we show that, in spite of the macroscopic size of the photon echo polarization, the wavelength of the exciting light can still be neglected.