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Journal of Experimental and Theoretical Physics

Crossing of quasilevels in the open Jaynes-Cummings model

Michael Z. Smirnov

Published Aug 1, 1998• 1 citation
Publisher

Abstract

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.

DOI
10.1134/1.558654

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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.
Here we study the open modification of the Jaynes-Cummings model that is the coupled system of the dressed atom and the quantized mode. The mode is initially in the coherent quantum state exhibiting the Poissonian photon statistics. When the quasienergy levels of the dressed atom cross the mean number of photons (n) in the mode undergoes high- amplitude oscillations. Numeric results show that each time the value of (n) falls the photon statistics becomes more regular. Instantaneously, the statistics can become sub- Poissonian with the Fano factor F equalsV (Delta) n2/(n) being many times as small as unity. The above observation provides the evidence that the photons undergo correlated absorption, i.e., they tend to disappear in twos, in threes, etc.
The Jaynes-Cummings model describes the interaction between a two-level atom and a single mode of the radiation field. This system has a conservation law which restricts its dynamics. On the basis of this conservation law alone one can make useful statements about the photon statistics of the fields which arise in the model. Two cases are considered. In the first the field is initially in a coherent state. Here it is found that the field statistics become less sub-Poissonian as the amplitude of the initial state increases. The case of an initial thermal state is also considered. In that situation, if the average number of photons present in the initial state is greater than 2.55, then the field statistics can never become sub-Poissonian.
The nonlinear dynamics of an open quantum system containing an arbitrary number of two-level atoms coupled with a classical polychromatic electromagnetic field and a quantised mode of the electromagnetic field is studied. Two particular cases of the elastic and inelastic interactions are considered. In the first case, the quantised mode is resonant with the transition between the quasi-energy levels corresponding to the same quasi-energy state, while in the second case, the levels involved in the interaction correspond to different quasi-energy states. For the elastic interaction, which can appear only in open quantum systems, an analytic solution of the Heisenberg equations is obtained. The time dependences of the population of quasi-energy states, the number of photons in the quantised mode, and photon statistics are numerically analysed for the inelastic interaction and at the crossing point of quasi-levels, when both types of the interaction are simultaneously present.
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.