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Physical Review A

Singular points, squeezing, and nonadiabatic transitions in the dressed-atom Jaynes-Cummings model

Georgii P. Miroshnichenko, Michael Z. Smirnov

Published Sep 27, 2001• 5 citations
Publisher

Abstract

We study the quasienergy spectrum and the nonadiabatic time dynamics of the open quantum system, which incorporates the two-level atom dipole coupled to both the quantized mode and the polychromatic classical field. Both the numeric calculations and the original perturbation technique are applied to track the quasilevel positions against the strength of the classical field. The first-order perturbation theory predicts the singular behavior of the system including the infinitely large squeezing of the quantized mode quadratures at certain values of the field strength. The singularity is removed here by allowing for the nonadiabatic transitions among the quasienergy states and the higher perturbations as well.

DOI
10.1103/physreva.64.053801

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We study the quasienergy spectrum and the nonadiabatic time dynamics of the open quantum system, which incorporates the two-level atom dipole coupled to both the quantized mode and the polychromatic classical field. Both the numeric calculations and the original perturbation technique are applied to track the quasilevel positions against the strength of the classical field. The first-order perturbation theory predicts the singular behavior of the system including the infinitely large squeezing of the quantized mode quadratures at certain values of the field strength. The singularity is removed here by allowing for the nonadiabatic transitions among the quasienergy states and the higher perturbations as well.
A perturbation theory is developed for constructing the quasi-energy operator Q of the Tavis-Cummings Hamiltonian, which includes the interaction of atoms with a classical quasi-monochromatic field. The operator Q of the first order in the interaction δ of an atom with a resonator mode has a form of the generalized Tavis-Cummings Hamiltonian (in the interaction representation) to which the oppositely rotating terms with a changed interaction constant are added. Such a Hamiltonian has a singularity in the dimensionless amplitude σ of a classical field. In the vicinity of this singularity, the Hamiltonian spectrum tends to a continuous one, while the degree of squeezing of field quadratures (in its eigenstates) increases infinitely. In the case of one atom and the biharmonic perturbation, the operator Q is obtained up to the third order of the perturbation theory. The spectral problem for Q is studied. The features of the dependence of the quasi-energy spectrum on σ are explained by the presence of an efficient barrier between the regions of the “coordinate” space. It is found that the above-mentioned singularity corresponds to the beginning of the parametric resonance zone. Analytic expressions for the top and bottom of this zone in the δσ plane are presented.
We calculate the quasienergies and steady states of a coupled two-level atom and quantized electromagnetic cavity mode with the cavity mode driven by a periodic classical field. The atom, the cavity mode, and the classical field are all on resonance. The quasienergies give shifted Jaynes-Cummings level splittings. These splittings are reduced by the interaction with the driving field and vanish at a threshold value of the driving field strength. Above the threshold, discrete quasienergies and normalizable steady states do not exist. Below the threshold, for weak driving fields, the steady states are squeezed and displaced Jaynes-Cummings eigenstates. We discuss the relevance of these results to work in cavity quantum electrodynamics.
The nonlinear dynamics of an open quantum system consisting of a “dressed” atom, i.e., an atom coupled with an external multifrequency electromagnetic field, and a single quantized mode of an electromagnetic field is studied. At different crossing points of the quasilevels of the dressed atom, the average number of photons in the quantized mode may either increase without limit with the passage of time or oscillate within finite limits. In the latter case a decrease of the number of photons is accompanied by regularization of their statistics, which may become sub-Poissonian.
We study the coupled system of the dressed atom and the quantized mode of the electromagnetic field (an open modification of the Jaynes-Cummings model). The mode is initially excited to the coherent quantum state and exhibits Poissonian photon statistics. When the quasienergy levels of the dressed atom cross, the mean number of photons in the mode oscillates at high amplitude. Numerical results show that the photon statistics in the mode regularizes, correlating as the value of falls. Near the local minima of , the statistics can become sub-Poissonian with Fano factor many times smaller than unity.
The quasienergies and the steady states of a two-level atom coupled to a quantized cavity mode and driven by a classical periodic field are solved in the case that the detunings among the atom, the cavity mode and the field are small. We also constitute two sets of orthonormal wavefunctions based on the steady states we obtained from the system and present a unitary evolution operator. Finally, the specific calculations show that the approximate solution is a useful tool for the further investigation of the properties of the driven Jaynes–Cummings model with small detunings.