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Physical Review A

Effect of dissipation on squeezed quantum fluctuations

Peter Schramm, Hermann Grabert

Published Nov 1, 1986• 20 citations
Publisher

Abstract

The decay of squeezed quantum fluctuations of a system coupled to a dissipative environment is discussed. For a model where the heat bath consists of an infinite set of harmonic oscillators, exact results for the time evolution of the mean-square fluctuations are obtained for arbitrary bath temperature and arbitrary damping strength.
DOI
10.1103/physreva.34.4515

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We study a quantum harmonic oscillator linearly coupled through the position operator to a first bath and through the momentum operator to a second bath yielding an Ohmic–Drude dissipation. We analyse the oscillator's fluctuations as a function of the ratio between the strength of the two couplings, focusing in particular on the situation in which the two dissipative interactions are comparable. Analytic formulas are derived in the relevant regimes corresponding to the low temperature limit and when the Drude high frequency cutoff is much larger than all other frequencies. At low temperature, each bath operates to suppress the oscillator's ground state quantum fluctuations or appearing in the corresponding interaction. When one of the two dissipative interactions dominates over the other, the fluctuations for the coupling operator are squeezed. When the two interactions are comparable, the two baths enter in competition as the two conjugate operators do not commute yielding quantum frustration . In this regime, remarkably, the fluctuations of both two quadratures can be enhanced by increasing the dissipative coupling.
Quantum dissipation in a thermal environment is investigated, using the path-integral approach. The reduced density matrix of the harmonic oscillator system coupled to a thermal bath of oscillators is derived for an arbitrary spectrum of bath oscillators. Time evolution and the end point of the two-body decay of unstable particles are then elucidated: After early transient times unstable particles undergo the exponential decay, followed by the power-law decay and finally ending in a mixed state of residual particles containing contributions from both on and off the mass shell, whose abundance does not suffer from the Boltzmann suppression.
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We study the quantum fluctuational properties of a parametric oscillator with and without coupling to an Ohmic environment. After considering the momentum and coordinate variances as a function of initial squeezing for the undamped dynamics, we invoke the functional integral method to derive the fully exact reduced density matrix for parametric dissipative quantum Brownian motion, covering the whole temperature regime from T=0 up to the classical limit at room temperatures. Moreover, we present the exact result for the quantum master equation for both the density matrix and the corresponding Wigner function. The time evolution of the covariance matrix elements of damped quantum fluctuations is studied numerically. These variances undergo within the regime of global stability asymptotic, periodic oscillations. As an interesting result, we find that the minima of these oscillations fall below the corresponding thermal equilibrium values.
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