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arXiv:quant-ph/0702054 · Physical Review A

Strongly driven one-atom laser and decoherence monitoring

Pavel Lougovski, Federico Casagrande, ALFREDO LULLI, E. Solano

Published Sep 7, 2007• 38 citations
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Abstract

We propose the implementation of a strongly driven one-atom laser, based on the off-resonant interaction of a three-level atom in $\ensuremath{\Lambda}$ configuration with a single cavity mode and three laser fields. We show that the system can be described equivalently by a two-level atom resonantly coupled to the cavity and driven by a strong effective coherent field. The effective dynamics can be solved exactly, including a thermal field bath, allowing an analytical description of field statistics and entanglement properties. We also show the possible generation of quantum superposition (Schr\"odinger cat) states for the whole atom-field system and for the field alone after atomic measurement. We propose a way to monitor the system decoherence by measuring atomic populations. Finally, we confirm the validity of our model through numerical solutions.

DOI
10.1103/physreva.76.033802

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arXiv:0711.1314•Physical Review A•Mar 20, 2008•24 citations
We propose the implementation of a strongly driven one-atom laser, based on the off-resonant interaction of a three-level atom in \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ configuration with a single cavity mode and three laser fields. We show that the system can be described equivalently by a two-level atom resonantly coupled to the cavity and driven by a strong effective coherent field. The effective dynamics can be solved exactly, including a thermal field bath, allowing an analytical description of field statistics and entanglement properties. We also show the possible generation of quantum superposition (Schr"odinger cat) states for the whole atom-field system and for the field alone after atomic measurement. We propose a way to monitor the system decoherence by measuring atomic populations. Finally, we confirm the validity of our model through numerical solutions.
We propose the implementation of a strongly-driven one-atom laser, based on the off-resonant interaction of a three-level atom in Lambda\\LambdaLambda-configuration with a single cavity mode and three laser fields. We show that the system can be described equivalently by a two-level atom coupled to the cavity and driven by a strong effective coherent field, yielding Schr\\"odinger cat states. The effective dynamics can be solved exactly, including a thermal field bath, allowing an analytical description of field statistics and entanglement properties, as well as of the environment-induced decoherence of atom-field pure states. Finally, we propose a way to monitor the decoherence of these states by measuring atomic populations and confirm the validity of our model through full numerical solutions.
We present the exact solution of the dynamics of N two-level atoms strongly driven by an external coherent field and equally coupled on resonance to a cavity mode, in the presence of both cavity dissipation and atomic decay. Analytical results are presented for system and subsystem dynamics, showing how environment-induced decoherence leads the system from pure to mixed states. In the limit of negligible atomic decay, where the system is known to exhibit decoherence-free subspaces, we present a detailed discussion of the decoherence function that can be monitored by atomic population measurements.
We consider the resonant interaction of a cavity mode with a two-level atom that is driven by a coherent field while it crosses the cavity. Starting from the cavity field in a coherent state, we show that the state of the system can reach the maximum entanglement after a unitary evolution for long enough interaction times. Also we illustrate how the generation of cavity field superposition states can allow, in the open system dynamics, the observation of their decoherence in atomic correlation measurements, for any initial cavity field state, and even under the combined effects of dissipation, thermal noise, and atomic pumping.
The models of a strongly-driven micromaser and a one-atom laser are developed. Their analytical solutions are obtained by means of phase space techniques. It is shown how to exploit the model of a one-atom laser for simultaneous generation and monitoring of the decoherence of the atom-field "Schrödinger cat" states. The similar machinery applied to the problem of the generation of the maximally-entangled states of two atoms placed inside an optical cavity permits its analytical solution. The steady-state solution of the problem exhibits a structure in which the two-atom maximally-entangled state correlates with the vacuum state of the cavity. As a consequence, it is demonstrated that the atomic maximally-entangled state, depending on a coupling regime, can be produced via a single or a sequence of no-photon measurements. The question of the implementation of a quantum memory device using a dispersive interaction between the collective internal ground state of an atomic ensemble and two orthogonal modes of a cavity is addressed. The problem of quantum state reconstruction in the context of cavity quantum electrodynamics is considered. The optimal operational definition of the Wigner function of a cavity field is worked out. It is based on the Fresnel transform of the atomic invertion of a probe atom. The general integral transformation for the Wigner function reconstruction of a particle in an arbitrary symmetric potential is derived.
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.
We present a fully analytical solution of the dynamics of two strongly driven atoms resonantly coupled to a dissipative cavity field mode. We show that an initial atom-atom entanglement cannot be increased. In fact, the atomic Hilbert space divides into two subspaces, one of which is decoherence free so that the initial atomic entanglement remains available for applications, even in presence of a low enough atomic decay rate. In the other subspace a measure of entanglement, decoherence, and also purity, are described by a similar functional behavior that can be monitored by joint atomic measurements. Furthermore, we show the possible generation of Schr\"odinger-cat-like states for the whole system in the transient regime, as well as of entanglement for the cavity field and the atom-atom subsystems conditioned by measurements on the complementary subsystem.