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arXiv:1707.07056 · Journal of Physics A Mathematical and Theoretical

Microscopic approach to field dissipation in the Jaynes–Cummings model

Carlos A. González-Gutiérrez, D Solís-Valles, B. M. Rodríguez-Lara

Published Oct 16, 2017• 6 citations
arXivHTMLPDF

Abstract

Abstract We use the microscopic derivation of the Jaynes–Cummings model master equation under field losses to study the dynamics of initial field-qubit states in the single-excitation manifold and beyond. We show that field-qubit detuning, as well as finite temperature, modify the effective decay rate of the system using measures like field-qubit purity and concurrence for the case of one-excitation, and for initial Fock states for more excitations. For initial semi-classical states of the field, we show that the microscopic approach, in phase space, provides an evolution to thermal equilibrium that is smoother than the one provided by the standard phenomenological approach.

DOI
10.1088/1751-8121/aa93c3

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Abstract We use the microscopic derivation of the Jaynes–Cummings model master equation under field losses to study the dynamics of initial field-qubit states in the single-excitation manifold and beyond. We show that field-qubit detuning, as well as finite temperature, modify the effective decay rate of the system using measures like field-qubit purity and concurrence for the case of one-excitation, and for initial Fock states for more excitations. For initial semi-classical states of the field, we show that the microscopic approach, in phase space, provides an evolution to thermal equilibrium that is smoother than the one provided by the standard phenomenological approach.
An analytic approach to investigate the zero-temperature time evolution of the Jaynes-Cummings system with cavity losses is developed. With realistic coupling between the cavity and the environment assumed, a simple master equation is derived, leading to the explicit analytic solution for the resonant case. This solution is suitable for analyses not only on single-excitation states but also on many-excitation states, which enables us to investigate the photon coherent state and to observe sharp collapses and revivals under dissipation. For the off-resonant case, on the other hand, the present study presents an analytic, systematic method instead. We examine the small and large detuning limits and discuss the condition where the widely used phenomenological treatment is justified. Explicit evaluations of the time evolutions for various initial states with finite detuning are also presented.
A microscopic derivation of the master equation for the Jaynes–Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows us to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis (Scala et al 2007 Phys. Rev. A 75 013811 ), where a microscopic derivation was given in the framework of the rotating wave approximation.
Abstract. A microscopic derivation of the master equation for the Jaynes-Cummings model with cavity losses is given, taking into account the terms in the dissipator which vary with frequencies of the order of the vacuum Rabi frequency. Our approach allows to single out physical contexts wherein the usual phenomenological dissipator turns out to be fully justified and constitutes an extension of our previous analysis [Scala M. et al. 2007 Phys. Rev. A 75, 013811], where a microscopic derivation was given in the framework of the Rotating Wave Approximation. PACS numbers: 42.50.Lc, 03.65.Yz, 42.50.PqCavity losses for the dissipative Jaynes-Cummings Hamiltonian beyond RWA 2
Microscopic and phenomenological Microscopic master equations have been applied to Jaynes-Cummings model with the cavity losses when the initial state of composite system(atom+cavity) is Bell state or atomic excitation state and the field state is vacuum.The differences of the two kinds of master equations have been analyzed in different coupling regimes.We find that in strong coupling regime,the increase of the population of atomics ground state is linear using the microscopic master equation,but it is non-linear by the phenomenological master equation under large coupling constants.In small coupling constants the population of atomic ground state is similar to the situations in large coupling constants.Although the ground-state populations in the two equations increase rapidly in weak coupling region,this result by phenomenological master equation increases faster than that by microscopic master equation.The conclusion may be useful for cavity quantum electrodynamics(QED) in losses cavity to provide guidance for the realization of logical gate.
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.