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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Unusual Rabi oscillations in the squeezed Jaynes - Cummings model: effects of the detuning and the Kerr nonlinearity

Si-de Du, Shangqing Gong, Zhizhan Xu, Chang-De Gong

Published Dec 1, 1997• 10 citations
Publisher

Abstract

Atomic Rabi oscillations are investigated in the interaction of quantized light with the Jaynes - Cummings model including the Kerr nonlinearity. When the cavity mode is initially prepared in a strongly squeezed state, the atomic dynamic response is extraordinary under the coexistence of the detuning and the Kerr nonlinearity. Due to the nonlinearity, the atomic Rabi oscillations exhibit various types of revivals as the detuning increases.

DOI
10.1088/1355-5111/9/6/007

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Journal of Modern Optics•Jun 1, 1991•1 citation
Atomic Rabi oscillations are investigated in the interaction of quantized light with the Jaynes - Cummings model including the Kerr nonlinearity. When the cavity mode is initially prepared in a strongly squeezed state, the atomic dynamic response is extraordinary under the coexistence of the detuning and the Kerr nonlinearity. Due to the nonlinearity, the atomic Rabi oscillations exhibit various types of revivals as the detuning increases.
The dynamics of the Jaynes–Cummings (JCM) model with a nonlinear Kerr medium at initially thermal and squeezed vacuum fields is discussed. At a special choice of the detuning the Rabi frequency can have a minimum at the initial mean photon number [nbar]. Then the situation becomes especially interesting and instead of the first-order ‘usual’ revivals resembling those manifested by the standard coherent JCM, the nonlinear JCM exhibits second-order revivals, also for initially thermal and squeezed vacuum fields, at least for not too large [nbar]. The revival times are highly sensitive to the nature of [nbar]. In the first case the revival period of the oscillations is dependent on whether [nbar] is integer or non-integer (situation similar to an initially coherent field) while in the latter case it depends additionally on the parity of the integer [nbar]. Moreover, for the squeezed vacuum model appearance of the revivals at an integer [nbar] is accelerated when compared to coherent and thermal models.
Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.
In this work, the authors investigated the dynamics of entanglement of two identical two-level atoms (qubits) in the framework of the two-photon double Jaynes–Cummings model, taking into account the detuning between atoms and the double frequency of the field modes of the resonators, as well as the Kerr medium in both resonators. The authors derived the time dependence of the negativity parameter for the Bell initial states of the atoms and the vacuum states of the resonator fields. The results showed that detuning and Kerr nonlinearity leads to stabilization of the entanglement for all initial Bell-type atomic states. For some initial atomic entanglement states, the detuning and Kerr environment in the resonators can prevent the effect of sudden death of the atom-atom entanglement.
Dynamical evolution of atomic squeezing is studied in a generalized multiphoton Jaynes–Cummings model. The influence of some nonlinear interactions and the counter-rotating wave term on the squeezing is discussed in detail. These nonlinear interactions influence the squeeze duration and its revival period. In a multiphoton transition, switching on the counter-rotating wave term has a much more destructive effect on the squeezing, but this destructive effect is weakened due to the presence of a nonlinear Kerr-like medium.
An electromagnetic field state is found which maintains the population inversion of the atom stationary during the interaction with the field through a Jaynes-Cummings model (JCM) with a Kerr type nonlinearity in the cavity. The condition of stationarity of the population inversion includes the phase coupling of atomic dipole with the field. We have shown that the Kerr nonlinearity in the cavity field significantly modifies the photon statistics of the trapped field state through an intensity dependent detuning in the field compared to the normal JCM trapping state. We have also demonstrated the novel features of sub-Poissonian character and the squeezing of the trapped field state. The dynamics of the initial trapped field is studied in terms of squeezing and the Q-function.