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arXiv:quant-ph/0106044 · Physical Review A

Modeling the reversible decoherence of mesoscopic superpositions in dissipative environments

S. G. Mokarzel, A. N. Salgueiro, Maria Carolina Nemes

Published Mar 22, 2002• 20 citations

Abstract

A model is presented to describe the recently proposed experiment [J. Raimond, M. Brune, and S. Haroche, Phys. Rev. Lett 79, 1964 (1997)] in which a mesoscopic superposition of radiation states is prepared in a high-Q cavity that is coupled to a similar resonator. The dynamical coherence loss of such a state in the absence of dissipation is reversible and can be observed in principle. We show how this picture is modified due to the presence of the environmental couplings. Analytical expressions for the experimental conditional probabilities and the linear entropy are given. We conclude that the phenomenon can still be observed provided the ratio between the damping constant and the intercavities coupling does not exceed about a few percent. This observation is favored for superpositions of states with a large overlap.

DOI: 10.1103/physreva.65.044101

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A model is presented to describe the recently proposed experiment [J. Raimond, M. Brune, and S. Haroche, Phys. Rev. Lett 79, 1964 (1997)] in which a mesoscopic superposition of radiation states is prepared in a high-Q cavity that is coupled to a similar resonator. The dynamical coherence loss of such a state in the absence of dissipation is reversible and can be observed in principle. We show how this picture is modified due to the presence of the environmental couplings. Analytical expressions for the experimental conditional probabilities and the linear entropy are given. We conclude that the phenomenon can still be observed provided the ratio between the damping constant and the intercavities coupling does not exceed about a few percent. This observation is favored for superpositions of states with a large overlap.

We describe the blueprint of an experiment in which the decoherence of a mesoscopic superposition of radiation states (``Schr\"odinger cat'') becomes a reversible process. When the high

Q

cavity containing the Schr\"odinger cat is coupled to another resonator, the mesoscopic quantum coherence first decays rapidly, then exhibits sharp revivals with the period of the energy exchange between the two cavities. The interpretation of this experiment emphasizes the link between decoherence and complementarity and leads to an illuminating quantitative interpretation of the usual irreversible decoherence phenomenon.

We show that two-atom correlation measurements of the type involved in a recent experimental study of the evolution of a mesoscopic superposition state prepared in a definite mode of a high-

Q

cavity can be used to determine the eigenvalues of the reduced density matrix of the field, provided the assumed dynamical conditions are actually fulfilled to experimental accuracy. These conditions involve (i) a purely dispersive coupling of the field to the Rydberg atoms used to manipulate and to monitor the cavity field, and (ii) the effective absence of correlations in the ground state of the system consisting of the cavity coupled to the ``reservoir'' which accounts for the decoherence and damping processes. A microscopic calculation at zero temperature is performed and compared to master equation results.

Quite recently quantum features exhibited by a mesoscopic field interacting with a single Rydberg atom in a microwave cavity has been observed [A. Auffeves et al., Phys. Rev. Lett. 91, 230405 (2003)]. In this paper we theoretically analyze all the phases of this articulated experiment considering from the very beginning cavity losses. Fully applying the theory of quantum open systems, our modelization succeeds in predicting fine aspects of the measured quantity, reaching qualitative and quantitative good agreement with the experimental results. This fact validates our theoretical approach based on the fundamental atom-cavity interaction model and simple mathematical structure of dissipative superoperators.

Using resonant interaction between atoms and the field in a high-quality cavity, we show how to generate a superposition of many mesoscopic states of the field. We study the quasiprobability distributions and demonstrate the nonclassicality of the superposition in terms of the zeros of the

Q

function as well as the negativity of the Wigner function. We discuss the decoherence of the generated superposition state. We propose homodyne techniques of the type developed by [Auffeves et al., Phys. Rev. Lett. 91, 230405 (2003)] to monitor the superposition of many mesoscopic states.