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Annalen der Physik

Statistics in a Trilinear Interacting Stokes‐Antistokes Boson System

W. Tänzler, F.‐J. Schütte

Published Jan 1, 1981• 5 citations
Publisher

Abstract

Abstract The statistics of a system of four boson modes is treated with simultaneous Stokes‐Antistokes interaction taking place. The time evolution is calculated in full quantum manner but in short time approximation. Mean photon numbers and correlations of second order are calculated. Antibunching can be found in the laser mode and in the system of Stokes and Antistokes mode.

DOI
10.1002/andp.19814930109

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Abstract The statistics of a system of four boson modes is treated with simultaneous Stokes‐Antistokes interaction taking place. The time evolution is calculated in full quantum manner but in short time approximation. Mean photon numbers and correlations of second order are calculated. Antibunching can be found in the laser mode and in the system of Stokes and Antistokes mode.
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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.
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.
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.
We consider a cavity model in which the dynamics of photons and phonon modes, as well as their interaction with a boson reservoir, are taken into account. The second- and fourth-order quantum coherence functions are evaluated and examined under various conditions of coupling coefficients, phases, and noise. For the case when the laser–anti-Stokes coupling is larger than the laser–Stokes coupling, the quantum correlations between field operators are identified in the form of sum and ordinary squeezing. The reservoir can be noisy without severely degrading the sum squeezing.
In an earlier paper, we considered a Hamiltonian trilinear in boson operators, which described several physical systems of interest such as interaction of NNN two-level atoms with a single-mode resonant radiation field, parametric amplification, frequency conversion, Raman and Brillouin scattering, etc. We found that the dynamics of the system can almost exactly be determined if either one of the three modes is strong for all times or any two modes are separately strong in two complementary time domains. In the present paper, we determine the statistical behavior of the system in each case. We give explicit results for a number of initial states (e.g., coherent, chaotic, a mixture of coherent and chaotic, number state, etc.) of the modes 1, 2, and 3.