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Physica Scripta

Generation and Preservation of Coherence in Dissipative Quantum Optical Environments

B. M. Garraway, P. L. Knight, Martin Bodo Plenio

Published Jan 1, 1998• 13 citations
Publisher

Abstract

We discuss the decay and decoherence of nonclassical states in quantum optics coupled to zero-temperature heat baths, and contrast ensemble behaviour with that of individual realizations. We show how nonclassical states are highly sensitive to dissipation in a number of cases, but present an example of how dissipation can be used to generate nonclassical states.

DOI
10.1238/physica.topical.076a00152

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We discuss the decay and decoherence of nonclassical states in quantum optics coupled to zero-temperature heat baths, and contrast ensemble behaviour with that of individual realizations. We show how nonclassical states are highly sensitive to dissipation in a number of cases, but present an example of how dissipation can be used to generate nonclassical states.
We show how nonclassical states can be constructed by interference amongst constituents in a superposition of basis states (chosen either from a Fock or coherent state basis). Such superpositions are fragile and highly susceptible to dissipation. We discuss the connection between ensemble averages and the evolution of individual realizations using quantum jump and quantum state diffusion models of conditioned measurements, each realization reflecting a particular measurement record. This allows us to distinguish between decoherence, localization and the deconstruction of superpositions into their components.
This chapter describes how the nonclassical states are peculiarly sensitive to dissipation when the coupling of the field modes to their larger environment is taken into account. Well before the field energy is significantly dissipated, the coherences responsible for the nonclassical behaviour will decay, at a ‘decoherence rate’ determined by the square of the separation of the constituent components of the nonclassical superpositions in phase-space. The Wigner functions for each Fock state component are given by Laguerre polynomials. These interfere to generate the superposition of interest. Coherences are destroyed at a rate which is proportional to the degree of excitation of the system as the system relaxes to a statistical mixture of relevant ‘pointer bases’. The chapter shows how the dissipative environment ‘deconstructs’ the field into its appropriate constituent parts. The chapter examines the Jaynes-Cummings system governed by the Milburn equation and shows how the intrinsic decoherence modifies the time evolution of the atomic inversion.
We suggest that propagation of nonclassical light in lattices of optical waveguides can provide a laboratory tool to simulate quantum decoherence phenomena with high non-Markovian features. As examples, we study decoherence of optical Schrödinger cats in a lattice that mimics a dissipative quantum harmonic oscillator coupled to a quantum bath, showing fractional decoherence in the strong coupling regime, and Bloch oscillations of optical Schrödinger cats, where damped revivals of the coherence can be observed.
We suggest that propagation of nonclassical light in lattices of optical waveguides can provide a laboratory tool to simulate quantum decoherence phenomena with high non-Markovian features. As examples, we study decoherence of optical Schrödinger cats in a lattice that mimics a dissipative quantum harmonic oscillator coupled to a quantum bath, showing fractional decoherence in the strong coupling regime, and Bloch oscillations of optical Schrödinger cats, where damped revivals of the coherence can be observed.
We study open quantum systems where the coupling between the system and its environment is of a quantum nondmolition (QND) type. Such a system undergoes decoherence without dissipation of energy. We obtain the master equation for the evolution of such a system under the influence of a squeezed thermal bath. From the master equation it can be seen explicitly that the process involves decoherence without any dissipation. We work out the decoherence causing term in the high and zero temperature limits and show that they match with known results in the different temperature regimes for the case of a thermal bath. We also make a comparison between the quantum statistical properties of QND and non-QND (i.e., involving decoherence as well as dissipation) types of evolution.
Applying the recently developed semiclassical hybrid dynamics [Grossmann, J. Chem. Phys. 125, 014111 (2006)], we study the decay of interference patterns in the reduced density as well as of the purity in a Morse oscillator test system due to the interaction with a finite harmonic bath at zero temperature. In the case that the bath mimics a continuous Ohmic spectral density, in addition to the quantum classical transition induced by the interaction with the environment, we corroborate the existence of a blueshift due to the bath coupling, predicted by Pollak [Phys. Rev. A 33, 4244 (1986)]. Furthermore, the decoherence dynamics of cat states is confirmed to be faster than that of single coherent states and we show that for a resonant bath the dissipation leads to an increase in the decoherence rate as compared to the low frequency bath.