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arXiv:quant-ph/9804033 · Physical Review A

Decoherence of mesoscopic states of cavity fields

K. M. Fonseca-Romero, Maria Carolina Nemes, J. G. Peixoto de Faria, A. N. Salgueiro, A. F. R. de Toledo Piza

Published Oct 1, 1998• 17 citations
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Abstract

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.

DOI
10.1103/physreva.58.3205

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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-QQQ 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.
We present several schemes for preparing and detecting coherent superpositions of classically distinct states of the electromagnetic field in one or two high-Q cavities. These proposals are based on two-atom correlation measurements, to be performed on circular Rydberg atoms interacting dispersively with the cavity fields. Changing the time interval between the two detected atoms allows a monitoring of the decay of quantum coherence due to dissipation. \textcopyright{} 1996 The American Physical Society.
A single circular Rydberg atom is used to prepare in a high quality superconducting cavity a “Schrödinger cat” state, quantum superposition of two coherent fields with different classical phases. A second atom probes the cavity state after a tunable delay. The decay of the quantum correlations between the two atoms reveals the evolution of the field state from an initial quantum superposition into a mere statistical mixture. The time scale of this decay decreases when the separation between the two components increases. This is the first experimental observation of the dynamics of decoherence, lying at the heart of the quantum measurement process.
Decoherence is an extremely fast and efficient environment-induced process transforming macroscopic quantum superpositions into statistical mixtures. It is an essential step in quantum measurement and a formidable obstacle for a practical use of quantum superpositions (quantum computing for instance). For large objects, decoherence is so fast that its dynamics is unobservable. Mesoscopic fields stored in a high-quality superconducting millimeter-wave cavity, a modern equivalent to Einstein’s ‘photon box’, are ideal tools to reveal the dynamics of the decoherence process. Their interaction with a single circular Rydberg atom prepares them in a quantum superposition of fields, containing a few photons, with different classical phases. The evolution of this ‘Schrödinger cat’ state can be later probed with a ‘quantum mouse’, another atom, assessing its coherence. We describe here the experiments performed along these lines at ENS, and stress the deep links between decoherence and complementarity. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The two-atom correlation scheme originally proposed by Davidovich, Brune, Raimond, and Haroche for measuring the decoherence of a mesoscopic superposition of coherent states of a QED cavity field is shown to be equivalent to a quantum computer solving Deutsch's problem. Using the existing analysis of decoherence in the Master equation formalism, and other important losses in this system, the final probability for obtaining the correct result for the computation is found in terms of the time period between atom traversals, the number of photons in the cavity, and the precision of the atomic velocity. The error due to decoherence in this system amounts to a phase error, and in the Master equation approach is a linear effect at small time scales. By explicitly considering the dynamics of the decoherence process when the system is coupled to a bath of oscillators with finite mode cutoff the error due to decoherence is found to decrease significantly and becomes a quadratic effect at short-time scales.
In a micromaser where a classical field strongly drives the atoms while they cross the cavity, remarkable atom–atom correlations show up at steady state, which vanish much faster than dissipative decay. Hence we consider atom pair correlation measurements in which the detection of the first probe atom prepares a mesoscopic superposition state of the cavity field, that entangles with a second probe atom. The conditional probabilities for the latter atomic detection provide a description of the decoherence of the superposition state, occurring in an open system in the presence of pumping, driving, dissipative, and thermal effects. The decoherence rate scales as the squared interaction time, that sets the separation in phase space between the superposition components, whereas the quantum coherence is unaffected by the atomic pumping. Hence we further investigate the system when the cavity is not pumped. Starting the correlation measurements from a thermal state, we can describe the effect of temperature on decoherence. Starting from a vacuum state, the superposition states are maximally separated Schrodinger cat states, whose decoherence can thus be monitored.
The preparation of mesoscopic states of radiation and matter fields through atom-field interactions has been achieved in recent years and employed for a range of striking applications in quantum optics. Here we present a technique for the preparation and control of a cavity mode which, in addition to interacting with a two-level atom, is simultaneously submitted to linear and parametric amplification processes. The role of the amplification-controlling fields in the achievement of real mesoscopic states is to produce highly squeezed field states and, consequently, to increase both (i) the distance in phase space between the components of the prepared superpositions and (ii) the mean photon number of such superpositions. When the squeezed superposition states are submitted to the action of similarly squeezed reservoirs, we demonstrate that under specific conditions the decoherence time of the states becomes independent of both the distance in phase space between their components and their mean photon number. An explanation is presented to support this remarkable result, together with a discussion of the experimental implementation of our proposal. We also show how to produce number states with fidelities higher than those derived as circular states.