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arXiv:cond-mat/9809014

Classical behavior of a macroscopic Schroedinger cat

Carlo Presilla A

Published Sep 1, 1998• 1 citation
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Abstract

We study the dynamics of classical and quantum systems linearly interacting with a classical environment represented by an infinite set of harmonic oscillators. The environment induces a dynamical localization of the quantum state into a generalized coherent state for which the $\hbar \to 0$ limit always exists and reproduces the classical motion. We describe the consequences of this localization on the behavior of a macroscopic system by considering the example of a Schroedinger cat.

DOI
10.48550/arxiv.cond-mat/9809014

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We study the dynamics of classical and quantum systems linearly interacting with a classical environment represented by an infinite set of harmonic oscillators. The environment induces a dynamical localization of the quantum state into a generalized coherent state for which the ℏ→0\hbar \to 0ℏ→0 limit always exists and reproduces the classical motion. We describe the consequences of this localization on the behavior of a macroscopic system by considering the example of a Schroedinger cat.
"As a rule, the coupling of a quantum system to an uncontrollable thermal reservoir (a “bath”) gives rise to the system’s decoherence, i.e., the destruction of its unitary coherent evolution [1]. Not less common is the rule that the more complex the quantum system, the more detrimental are the bath effects [2]. Here we point out that the coupling of a complex quantum system to a bath may actually induce advantageous coherent dynamics. Namely, an exact solution for a quantum many-body system characterized by large angular momentum (or spin) that is coupled to a thermal bath reveals a hitherto unexplored general effect: bath-induced effectively nonlinear evolution. This evolution can drive the large-spin system into a macroscopic quantum-superposition (“Schroedinger-cat”) state [3, 4]. Such counter-intuitive bath-induced effects should be observable in various setups on long (Markovian) time scales. They change our perspective of non-classicality in open many-body quantum systems. Namely, the bath may cause rather than impede the formation of distinctly non-classical Schroedinger-cat states, despite their fragility in the presence of a bath [2, 5]."
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the measured system. Selective and nonselective measurement processes are then introduced according to a selection of or an average over all possible initial configurations of the measurement apparatus. At quantum level, the selective processes are described by a nonlinear stochastic Schrödinger equation whose solutions evolve into properly defined coherent states in the case of linear systems. For arbitrary measured systems, classical behavior is always recovered in the macroscopic limit.
There has been a lot of interest recently in what are referred to as Schrodinger cat states. No precise formulation of the concepts of Schrodinger cat states and classical distinguishability appears to exist. This paper aims to explore these concepts. A number of illustrative examples are presented, including a perturbed harmonic oscillator admitting coherent states with time-dependent amplitude modulation. One can convert the results on harmonic oscillators to single-mode optical systems in the standard manner. It would be interesting to see an experimental realization of these amplitude-modulated coherent states.
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the measured system. Selective and non-selective measurement processes are then introduced according to a selection of or an average over all possible initial configurations of the measurement apparatus. At quantum level, the selective processes are described by a nonlinear stochastic Schrödinger equation whose solutions evolve into properly defined coherent states in the case of linear systems. For arbitrary measured systems, classical behaviour is always recovered in the macroscopic limit.