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Annalen der Physik

Statistics of a Stokes‐Antistokes Interacting Boson System with Damping

Kurt Germey, F.‐J. Schütte, R. Tiebel

Published Jan 1, 1981• 6 citations
Publisher

Abstract

Abstract The statistics of a system of four boson modes in Stokes‐Antistokes interaction is considered with respect to the influence of damping in one mode. The time evolution of the system is calculated. The mean particle numbers and the factorial moments of photon number distribution are calculated. Numerical results show strong dependence on bath temperature but only weak influence of the bath coupling strength. In the combined Stokes‐Antistokes system Antibunching appears if the bath temperature is low.

DOI
10.1002/andp.19814930110

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Abstract The statistics of a system of four boson modes in Stokes‐Antistokes interaction is considered with respect to the influence of damping in one mode. The time evolution of the system is calculated. The mean particle numbers and the factorial moments of photon number distribution are calculated. Numerical results show strong dependence on bath temperature but only weak influence of the bath coupling strength. In the combined Stokes‐Antistokes system Antibunching appears if the bath temperature is low.
The many-time Green's-function theory for a damped boson system subjected to an external time-dependent excitation is presented. The damping is properly taken into account by means of a generalized form of the Senitzky-Haken theory of a boson system interacting with a heat bath. The theory leads to a hierarchy of equations for the Green's functions of the system, which are averaged over the heat-bath variables and which take into account the damping of the various boson modes. Two examples for a ferromagnetic magnon system coupled by an anharmonic interaction are given.
Abstract The time variation of the density matrix for a system of three interacting boson field modes is described in the Schrödinger picture with the help of the unitary time development operator in coherent state basis. The nonlinear c‐number equation for this operator is solved using a perturbation expansion in powers of the coupling constant. The explicit time dependence is obtained for the matrix elements of the total density matrix and of the particular density matrices of the individual modes. Photon number distributions and second order correlations are calculated for several initial situations.
The quantum theory of the stimulated Raman and Brillouin effects, the parametric amplifier, and the frequency converter is developed, starting with a simple Hamiltonian for a system of three coupled field modes. The intense incident beam is treated classically. The evolution in time of the statistical properties of the quantized Stokes and anti-Stokes waves are analyzed by means of appropriate time-dependent phasespace distributions under various assumptions for the initial fields. Expansions of the field variables in terms of complete sets of orthogonal operators are discussed. Several regimes of operation are considered. It is shown that an initially coherent state develops, in general, into a superposition of a coherent state and a chaotic state. The amplitudes of the coherent components follow the same equations of motion as the mode operators. The chaotic components stem from the amplification of the vacuum fluctuations.
This paper aims to study the photons antibunching in the fundamental, Stokes and signal modes of CAHRS (coherent anti-Stokes hyper Raman scattering). The generalized interaction Hamiltonian was calculated for different conditions in the Heisenberg picture under short time approximation to observe photons antibunching in the fundamental, Stokes and signal modes of CAHRS. It has been found that antibunching in the fundamental field is dependent upon interaction time, photons number, and coupling strength of field. Third order photon antibunching is found to be nonclassical to a greater extent than second- and first-order photon antibunching for the identical pump photons count. It has been also observed that the effect of photon antibunching in Stokes and signal modes is less prominent than in the fundamental- mode. Furthermore, it is also found that antibunching will increase at short interaction timeswith the increase of depth of nonclassical behavior. Finally, the extent of photons antibunching peaks precisely where the second correlation function is lowest.
We investigate the quantum statistics of three time-dependent coupled oscillators in the presence of multiphoton processes. The system is connected with the two-atom multiphoton Tavis-Cummings model. The solution of the Heisenberg equations of the motion is obtained in a compact form. We assume that the modes are initially prepared in coherent states, and we discuss nonclassical phenomena (squeezing and sub-Poissonian behavior). Further, we examine the joint quasi-distribution functions as well as photon-number distribution and its factorial moments. The system has shown that the nonclassical effect is apparent in compound modes (1,3) and (2,3). Moreover, the superstructure phenomenon is observed when the photon transition is increased.