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The European Physical Journal B

Influence of coloured noise on the diffusion of a quantum particle. Part I: General results

Klaus Kassner, P. Reineker

Published Sep 1, 1985• 23 citations
Publisher
DOI
10.1007/bf01307442

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By means of the unified coloured noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser cubic model driven by coloured pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λ q between the real and imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviours of the mean intensity ⟨ I ⟩ and variance λ 2 (0) for both below and above the threshold operation and many new phenomena are discovered. When the laser is operated above the threshold, increasing the cross-correlation intensity λ q makes the ⟨ I ⟩–τ curves exhibit a ``re-entrant phase transition''. Whether the laser is above or below the threshold, the whole ⟨ I ⟩–τ curve moves down as λ q increases; however, when λ q = 1 (perfect cross-correlation), the curve abruptly runs up. A nonzero value of cross-correlation time τ (τ≠0) leads to the entire λ 2 (0)– p ′ curve being suppressed (here p ′ is the pump noise intensity). This indicates the increasing precision of the laser beam due to the existence of the self-correlation time τ. The behaviour of the λ 2 (0)– p ′ curve as a function of λ q is similar to that of the ⟨ I ⟩–τ curve against λ q : that is, whether the laser is above or below the threshold, the λ 2 (0)– p ′ curve moves up as λ q increases; however, when λ q = 1, the curve suddenly moves down. Through the study in this paper, we can find a way to optimize for output laser intensity.

Chinese Physics•Feb 23, 2004•8 citations
We use Feynman's influence-functional theory to study the quantum dynamics of a heavy particle moving in a free Fermi gas with arbitrary average velocity. A semiclassical expansion yields a nonlinear Langevin equation with the exact friction coefficient as derived in an earlier publication. The fluctuations around a steady state far from equilibrium are due to a nonclassical state-dependent noise term and can be described by a diffusion constant. In the limit of zero average velocity, the Einstein relation is fulfilled for arbitrary temperatures. For finite velocities the diffusion around the steady state is different in longitudinal and transverse directions and can be expressed in terms of the transport cross section and a ``diffusion'' cross section. In the case where the frictional force exhibits a maximum as a function of velocity and thus an unstable branch for v>vc{\mathit{v}}_{\mathit{c}}vc​, the longitudinal diffusion constant diverges on approaching vc{\mathit{v}}_{\mathit{c}}vc​ from below. Numerical results for the noise spectrum and the temperature and velocity dependence of the diffusion constants are presented for simple repulsive interaction potentials in one and three dimensions.
By means of the unified coloured noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser cubic model driven by coloured pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λ q between the real and imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviours of the mean intensity ⟨ I ⟩ and variance λ 2 (0) for both below and above the threshold operation and many new phenomena are discovered. When the laser is operated above the threshold, increasing the cross-correlation intensity λ q makes the ⟨ I ⟩–τ curves exhibit a ``re-entrant phase transition''. Whether the laser is above or below the threshold, the whole ⟨ I ⟩–τ curve moves down as λ q increases; however, when λ q = 1 (perfect cross-correlation), the curve abruptly runs up. A nonzero value of cross-correlation time τ (τ≠0) leads to the entire λ 2 (0)– p ′ curve being suppressed (here p ′ is the pump noise intensity). This indicates the increasing precision of the laser beam due to the existence of the self-correlation time τ. The behaviour of the λ 2 (0)– p ′ curve as a function of λ q is similar to that of the ⟨ I ⟩–τ curve against λ q : that is, whether the laser is above or below the threshold, the λ 2 (0)– p ′ curve moves up as λ q increases; however, when λ q = 1, the curve suddenly moves down. Through the study in this paper, we can find a way to optimize for output laser intensity.