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Journal of Optics B Quantum and Semiclassical Optics

Dynamical description of the creation and monitoring of a superposition state in a dissipative environment: the Paris experiment

J. G. Peixoto de Faria, Maria Carolina Nemes

Published Jul 24, 2002• 4 citations
Publisher

Abstract

Effects of dissipation during the interaction of two-level atoms with a single mode of the electromagnetic field are considered in the context of the dispersive Jaynes–Cummings model to which a damping mechanism is added. The results are applied to the analysis of the so-called Paris experiment (Brune M et al 1996 Phys. Rev. Lett. 77 4887). We obtain analytical expressions for the conditional probabilities measured in this experiment considering the dissipation during the atom–field interaction in both preparing and monitoring stages of the ‘Schrödinger cat’ state. We show that during the formation of the superposition state decoherence results from a competition between the atom–field (unitary) and field–cavity (dissipative) interactions. Moreover, it is quantitatively comparable to the purity loss expected for the field evolving freely during a time interval equal the interaction time. These effects are dominant at short time scales. For later times, the measured conditional probabilities reflect decoherence effects arising from field–cavity interactions.

DOI
10.1088/1464-4266/4/5/307

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Effects of dissipation during the interaction of two-level atoms with a single mode of the electromagnetic field are considered in the context of the dispersive Jaynes–Cummings model to which a damping mechanism is added. The results are applied to the analysis of the so-called Paris experiment (Brune M et al 1996 Phys. Rev. Lett. 77 4887). We obtain analytical expressions for the conditional probabilities measured in this experiment considering the dissipation during the atom–field interaction in both preparing and monitoring stages of the ‘Schrödinger cat’ state. We show that during the formation of the superposition state decoherence results from a competition between the atom–field (unitary) and field–cavity (dissipative) interactions. Moreover, it is quantitatively comparable to the purity loss expected for the field evolving freely during a time interval equal the interaction time. These effects are dominant at short time scales. For later times, the measured conditional probabilities reflect decoherence effects arising from field–cavity interactions.
An approximate solution is given for the Jaynes-Cummings model with cavity losses, i.e., the problem of a two-level atom interacting with a single mode of the quantized radiation field, in the rotating-wave approximation, when the field is damped by a reservoir at zero temperature. The approximate solution is derived for initial coherent field states with moderately large numbers of photons. It is simpler in form than earlier results derived by other authors and, over the appropriate parameter range, substantially more accurate than some of them, as shown by direct numerical integration of the master equation. In particular, it is found that an earlier treatment of this problem based on a secular approximation is seriously flawed, in that the conditions for its validity are much more restrictive than was previously believed. Among the results derived it is shown that, just as for the lossless case, when the atom is initially prepared in one of the semiclassical eigenstates the evolution is very simple, with the field and the atomic dipole drifting together in phase. For moderate losses this leads, as in the lossless case, to a ``state preparation''; i.e., to a good approximation, the state of the atom at a specific time can be made independent of its initial state. The effect of losses on the recently discovered ``Schr\"odinger cat'' state of the field is also analyzed. It is found that, although the dissipation destroys the coherence of the macroscopic superposition very rapidly, preparation and observation of the ``cat'' should be possible with the cavity quality factors reported in recent micromaser experiments.
We present the time evolution of a two-level atom interacting dispersively with an electromagnetic field in a dissipative cavity. We investigate the influence of dissipation on the entanglement of the two subsystems (atom+field).(\mathrm{atom}+\mathrm{field}).(atom+field). Simple but realistic, the model displays several nontrivial quantum features, which emerge when an environment is taken into account: the cavity is shown to have practically no influence in the coherence properties of the field from the qualitative point of view. On the other hand, although the atom is not directly coupled to the cavity modes, its coherent properties are strongly influenced by dissipation both qualitatively as well as quantitatively.
We give a fully description of the dynamics of an atom dispersively coupled to a field mode in a dissipative environment fed by an external source. The competition between the unitary atom-field (which leads to entanglement) and the dissipative field-environment couplings are investigated in detail. We find the time evolution of the global atom-field system for any initial state and we show that atom-field steady state is at most classically correlated. For an initial state chosen, we evaluate the purity loss of the global system and of atomic and field subsystems as a function of time. We find that the source will tend to compensate for the dissipation of the field intensity and to accelerate decoherence of the global and atomic states. Moreover, we show that the degree of entanglement of the atom-field state, for the particular initial state chosen, can be completely quantified by concurrence. Analytical expression for time evolution of the concurrence is given.
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.
ABSTRACT: The processes of quantum decoherence in QED cavities have been extensively studied in the last decade, both experimentally by Haroche, Raimond et. al., as theoretically by Nemes, Davidovich et. to the. We present here the dynamics of the Wigner function for a system consisting of a two-level atom and a cavity in a dissipative environment, using a numerical integration scheme that allows us to consider initial Squeezed and Schrodinger's Cat States. The interaction between the atom and the single-mode field is considered by a dispersive model, that is, the interaction in the Hamiltonian of Jaynes-Cummings appears as a small disturbance. The interest is focused both on the quantum characteristics of the dispersive approach (preparation of mesoscopic states) and on the aspects that characterize dynamics and dissipation. In particular, the gradual loss of quantum coherence is observed through the use of the Wigner function, where the disappearance of the interference regions of the initial quantum states is evidenced.