Statistics of a Stokes‐Antistokes Interacting Boson System with Damping

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. Sunierical 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.

Quantum Statistical Properties of Photon and Phonon Fields in Brillouin Scattering with Intense Pumping

“…The present paper is a continuation of the work presented in [5], where a general description of the quantum statistics in Brillouin scattering were proposed based on the coherent-state technique . Recently, similar models for Raman scattering have been discussed in [6][7][8][9][10] . In [6], Peiina described the phonons as an infinite markoffian reservoir system whose variables have been eliminated in the process of calculation .…”

Quantum-statistical theory of Raman scattering processes

“…As a digression, let us mention that the same phenomenological Hamiltonians (2) have been used in the description of Brillouin scattering (see, for example, Refs. [105,180] and [23] and references therein). The main difference between Brillouin and Raman scattering lies in different kinds of the scatterers responsible for these effects: acoustic phonons in the Brillouin effect, and optical phonons in the Raman effect.…”

“…Refs. [23,105,145]), where optical phonons are included in the system, whereas other crystal excitation modes, such as acoustical phonons, electric excitations, and other species of molecular vibrations, serve as a thermal reservoir. The radiation fields are weakly coupled to the thermal reservoir.…”

“…Squeezing properties of Raman scattering have been studied by Peřinová and et al Peřina, Kárská and Peřina [56], Levenson et al and Peřina and Křepelka [67,68]. Sub-Poissonian photon-counting statistics and/or photon anticorrelations (in particular antibunching) have been investigated within various approaches to the standing-wave Raman effect by Loudon [30], Simaan [75], Agarwal and Jha [87], Trung and Schütte [104], Szlachetka and Kielich [61], Szlachetka et al [58][59][60], Gupta and Mohanty [78,79], Peřina [53,54], Tänzler and Schütte [63], Germey et al [105], Mohanty et al [80], Král [106], Gupta and Dash [90,107], Ritsch et al [92] and in papers already mentioned [55,56,[65][66][67][68] (see also Ref. [23]).…”

“…We shall concentrate on a statistical analysis within the master equation approach to the Raman effect proposed by Shen [26], Walls [122] and McNeil and Walls [73]. This approach has been studied by various authors, e.g., Simaan [75], Schenzle and Brand [31], Peřina [23,53,54], Germey et al [105], Gupta and Dash [107], Bogolubov et al [88], Grygiel [83], Miranowicz [84], and Kárská and Peřina [56]. Usually a master equation is converted to a classical differential equation.…”