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Journal of Modern Optics

Dissipation and Amplification of Jaynes-Cummings Superposition States

M.S. Kim

Published Jul 1, 1993• 31 citations
Publisher

Abstract

There have recently been several proposals for generation of optical superposition states in the resonant atom-field interaction and more practically in microwave cavities. In the present paper we study the influence of the vacuum reservoir on properties of the near-superposition state of the cavity field which is described by the Jaynes-Cummings model at one-half of the revival time. Instead of introducing the cavity loss from the first instance of the atom-field interaction we consider the cavity loss only after the near-superposition state is produced and after the atom leaves the cavity. We solve the corresponding master equation with the initial condition being the Jaynes-Cummings field at one-half of the revival time. We find that under the influence of the vacuum reservoir the photon number distribution of the superposition state we study exhibits certain asymmetry around the mean photon induced by the decay process. We show that an analogous effect can be seen when the Jaynes-Cummings superposition state is amplified. For a basic test of our approach we study the dissipation and amplification of Fock states.

DOI
10.1080/09500349314551391

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There have recently been several proposals for generation of optical superposition states in the resonant atom-field interaction and more practically in microwave cavities. In the present paper we study the influence of the vacuum reservoir on properties of the near-superposition state of the cavity field which is described by the Jaynes-Cummings model at one-half of the revival time. Instead of introducing the cavity loss from the first instance of the atom-field interaction we consider the cavity loss only after the near-superposition state is produced and after the atom leaves the cavity. We solve the corresponding master equation with the initial condition being the Jaynes-Cummings field at one-half of the revival time. We find that under the influence of the vacuum reservoir the photon number distribution of the superposition state we study exhibits certain asymmetry around the mean photon induced by the decay process. We show that an analogous effect can be seen when the Jaynes-Cummings superposition state is amplified. For a basic test of our approach we study the dissipation and amplification of Fock states.
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.
It is well-known that the field in the Jaynes-Cummings model shows second-order and fourth-order quadrature squeezing. We study the influence of a heat bath reservoir on the squeezing properties of the Jaynes-Cummings field. The experimental realization of the Jaynes-Cummings model is the one-atom maser. Instead of introducing the cavity loss from the first instance of the atom-field interaction we consider the cavity loss only after the atom leaves the cavity under the assumption of strong coupling of the atom with the cavity field as in micromaser theory. In this way we can suggest an optimum span of time to preserve the squeezing properties of the Jaynes-Cummings field. We first investigate the thermal decay of the Fock state and with use of this analytical result we study the evolution of squeezing properties of the cavity field surrounded by the heat bath. Unlike the monotonic decay of second-order squeezing, we find an interesting result of enhancement of fourth-order squeezing during the dissipation process. We extensively analyse the enhancement of fourth-order squeezing through the dissipation process so as to apply the analysis to the case of decay of an arbitrary field state into the vacuum.
The field squeezing and the atomic dipole squeezing of a two-level atom in a dissipative cavity initially in vacuum are investigated.By means of exact solution of the master equation,the matrix elements of the density operator of the compound atom-field system are obtained.It is found that the cavity dissipation has an obvious influence on the atomic squeezing and the field squeezing under the resonant atom-field interaction.But the effects of the cavity dissipation on both squeezing will decrease under the off-resonance interaction condition.
Collapse and revivals in the Jaynes-Cummings model are studied within the context of the Mollow transformation for a single-mode coherent-state cavity field. The Mollow-transformed Jaynes-Cummings Hamiltonian has two atom-field terms, one corresponding to a classical field and the other to a quantized field driving the atomic transition. As such it maps onto the complementary problem of an atom in an optical cavity, whose field is initially in the vacuum state, driven by an external classical field. Both problems have the same atomic-state dynamics. It is shown that the revivals can be associated with two distinct properties of the quantized field of the transformed Hamiltonian. Revivals occurring at even (odd) multiples of the revival time are correlated with field states that are close to the initial field state and for which the average energy in the field is a minimum (maximum). Using semiclassical dressed states, we are able to map the problem for the field states onto one involving two uncoupled oscillators driven by off-resonant fields, provided effects related to dispersion are neglected. Analytic expressions for the photon number distribution of the transformed cavity field, including dispersion, are obtained for the even revival times.
The dissipation of the field in the two-photon Jaynes-Cummings model (JCM) with degenerate atomic levels was studied. The initial degenerate atomic state affects the field coherence loss. When the degenerate atom is initially in an equal probability superposition state, the field coherence loss is smallest. It is found that the degeneracy of the atomic level increases the period of entanglement between the atom and the field. When the degeneracy was considered, the coherence properties of the field could be affected by the reservoir qualitatively, if a nonlinear two-photon process is involved. This is different from the dissipation of one-photon JCM with degenerate atomic levels.