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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Rapid decoherence in integrable systems: A border effect

R. M. Angelo, K. Furuya, Maria Carolina Nemes, G. Q. Pellegrino

Published Nov 1, 1999• 34 citations
Publisher

Abstract

We show that rapid decoherence, usually associated with chaotic dynamics, is not necessarily a hallmark of nonintegrability: border effects in integrable systems may produce similarly drastic decoherence rates. These can be found when the subsystem under observation possesses an energy limitation as, e.g., in the N-atom Jaynes-Cummings model. We show for this model that special initial coherent wave packets exhibit entropy production rates strikingly similar to the chaotic case. Also, a (de)localization phenomenon is found to be a function of the proximity to the phase-space border.

DOI
10.1103/physreve.60.5407

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We show that rapid decoherence, usually associated with chaotic dynamics, is not necessarily a hallmark of nonintegrability: border effects in integrable systems may produce similarly drastic decoherence rates. These can be found when the subsystem under observation possesses an energy limitation as, e.g., in the N-atom Jaynes-Cummings model. We show for this model that special initial coherent wave packets exhibit entropy production rates strikingly similar to the chaotic case. Also, a (de)localization phenomenon is found to be a function of the proximity to the phase-space border.
Manifestation of chaotic behavior is found in an intrinsically quantum property. The entanglement process, quantitatively expressed in terms of the reduced density linear entropy, is studied for the NNN-atom Jaynes-Cummings model. For a given energy, initial conditions are prepared as minimum uncertainty wave packets centered at regular and chaotic regions of the classical phase space. We find for short times a faster increase in decoherence for the chaotic initial conditions as compared to regular ones, which have oscillatory increase.
Quantum wave function of a chaotic system spreads rapidly over distances on which the potential is significantly nonlinear. As a result, the effective force is no longer just a gradient of the potential, and predictions of classical and quantum dynamics begin to differ. We show how the interaction with the environment limits distances over which quantum coherence can persist, and therefore reconciles quantum dynamics with classical Hamiltonian chaos. The entropy production rate for such open chaotic systems exhibits a sharp transition between reversible and dissipative regimes, where it is set by the chaotic dynamics.
Open quantum systems undergo decoherence, which is responsible for the transition from quantum to classical behavior. The time scale in which decoherence takes place can be analyzed using upper limits to its rate. We examine the dynamics of open chaotic quantum systems governed by random Lindblad operators sourced from Gaussian and Ginibre ensembles with Wigner-Dyson symmetry classes. In these systems, the ensemble-averaged purity decays monotonically as a function of time. This decay is governed by the decoherence rate, which is upper-bounded by the dimension of their Hilbert space and is independent of the ensemble symmetry. These findings hold upon mixing different ensembles, indicating the universal character of the decoherence rate limit. Moreover, our findings reveal that open chaotic quantum systems governed by random Lindbladians tend to exhibit the most rapid decoherence, regardless of the initial state. This phenomenon is associated with the concentration of the decoherence rate near its upper bound. Our work identifies primary features of decoherence in dissipative quantum chaos, with applications ranging from quantum foundations to high-energy physics and quantum technologies. Published by the American Physical Society 2024
The rise in linear entropy of a subsystem in the N-atom Jaynes-Cummings model is shown to be strongly influenced by the shape of the classical orbits of the underlying classical phase space: we find a one-to-one correspondence between maxima (minima) of the linear entropy and maxima (minima) of the expectation value of atomic excitation Jz.{J}_{z}.Jz​. Since the expectation value of this operator can be viewed as related to the orbit radius in the classical phase-space projection associated with the atomic degree of freedom, the proximity of the quantum wave packet to this atomic phase-space borderline produces a maximum rate of entanglement. The consequence of this fact for initial conditions centered at periodic orbits in regular regions is a clear periodic recoherence. For chaotic situations the same phenomenon (proximity of the atomic phase-space borderline) is, in general, responsible for oscillations in the entanglement properties.
We study the open system dynamics of a circuit QED model operating in the ultrastrong coupling regime. If the resonator is pumped periodically in time the underlying classical system is chaotic. Indeed, the periodically driven Jaynes-Cummings model in the Born-Oppenheimer approximation resembles a Duffing oscillator which in the classical limit is a well-known example of a chaotic system. Detection of the field quadrature of the output field acts as an effective position measurement of the oscillator. We address how such detection affects the quantum chaotic evolution in this bipartite system. We differentiate between single measurement realizations and ensembles of repeated measurements. In the former case a measurement/decoherence induced localization effect is encountered, while in the latter this localization is almost completely absent. This is in marked contrast to numerous earlier works discussing the quantum-classical correspondence in measured chaotic systems. This lack of a classical correspondence under relatively strong measurement induced decoherence is attributed to the inherent quantum nature of the qubit subsystem and in particular to the quantum correlations between the qubit and the field which persist despite the decoherence.