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Journal of Modern Optics

Jaynes-Cummings Model with Damping Involving Nonlinear Interaction with Reservoir

Amitabh Joshi, S. V. Lawande

Published Jun 1, 1991• 1 citation
Publisher

Abstract

We have presented the exact solution of the density matrix equation under the dressed-atom approximation for an isolated atom interacting with a single mode of cavity which has non-zero damping via a nonlinear interaction with reservoir. These solutions are then used to study the phenomenon of collapses and revivals of Rabi oscillations in the atom.

DOI
10.1080/09500349114551171

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We have presented the exact solution of the density matrix equation under the dressed-atom approximation for an isolated atom interacting with a single mode of cavity which has non-zero damping via a nonlinear interaction with reservoir. These solutions are then used to study the phenomenon of collapses and revivals of Rabi oscillations in the atom.
A study of multiatom effects, i.e., dipole-dipole interactions and phase-interrupting collisions between atoms in the Jaynes-Cummings model, is presented here. For this purpose we consider two identical two-level atoms interacting with a single-mode field in a lossless cavity and study the effect of the dipole-dipole interaction between these two atoms on the collapse-and-revival phenomenon of Rabi oscillations by calculating the analytical expression of the excitation probability in the coherent field. We also consider another situation in which a single atom interacting with a single-mode field in a damped cavity undergoes phase-interrupting collisions. The effect of phase-interrupting collisions along with the usual cavity damping on the collapse-and-revival phenomenon has been explicitly calculated using the dressed-atom approach under the secular approximation.
We study the two-photon interaction of a two-level atom with a quantized bimodal field of a loss-free cavity. We assume that both the coupling strength and the atom-field detuning may depend on the populations of the two modes. We show that this general nonlinear model is exactly solvable in terms of a dressing unitary operator. Exact expressions for the eigenstates as well as for the Rabi frequencies of the coupled system are given as explicit functions of the nonlinearity terms present in the model. Exploiting the flexibility of these results, we investigate the atomic inversion supposing that at t=0 one mode is coherent, the other is in a Fock state and the atom is excited. We compare the dynamical behaviour of various particular nonlinear models. A common feature is the presence of collapses and revivals of the Rabi oscillations. We find that the atomic inversion manifests exact periodicity when only one specific type of intensity-dependent term (coupling strength or detuning) is present. Such behaviour is physically interpreted in the framework of the dressed atom representation. The simulataneous presence of both nonlinear contributions in the model breaks such regular behaviour in the long-time atomic evolution, in which case competition effects occur which qualitatively modify the quantum dynamics of the system. Other quantum manifestations are brought to light. Their relevance, in connection with the possibility of preparing a cavity mode in an arbitrary Fock state, is briefly discussed.
The master equation currently used to describe a two level atom interacting with a single mode field damped by contact with a thermal reservoir (the damped Jaynes-Cummings model) is shown not to have, as its steady state solution, the expected canonical density operator prescribed by the general principles of statistical mechanics for a system in thermal equilibrium. A modified master equation is derived here which satisfies this requirement. Except for a reservoir at zero temperature, this master equation differs from that which is currently used in that the damping terms contain contributions due to the atom-field interaction.