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Interaction of Interpolating Number-Coherent States with Atomic Systems

Yinqi Feng, Hong‐Chen Fu, A. I. Solomon

Published Sep 17, 1999• 0 citations
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Abstract

Interpolating number-coherent states are new states of the radiation field which interpolate between number and coherent states, to which they reduce in appropriate limits. We study some fundamental features of the interaction of these new states with a atomic system in the framework of the Jaynes-Cummings model(JCM). The dynamical evolution of atomic population inversion, field entropy, the Q-function and photon number distribution properties are investigated in detail. 1

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The Effect of Number-State Filtration on the Collapse and Revival Features of the Jaynes–Cummings Model

S. Hashmitha, Nilakantha Meher

A two-level atom interacting with a cavity field initialized in a coherent state exhibits the collapse and revival features in its population inversion dynamics under the Jaynes–Cummings interaction. When the cavity field is prepared in a number-state filtered coherent state, obtained by filtering the number state | m 〉 from a coherent state | α 〉 , we observe micro-Rabi oscillations in the collapse region instead of a perfect collapse. We find that the Rabi frequency of these micro oscillations depends only on the filtered photo-number m, whereas the amplitude depends on both m and α . This dependence enables one to infer the filtered number state from the coherent-state distribution by analyzing the time evolution of the atomic population inversion. Conversely, the amplitude and frequency of the micro-Rabi oscillations can be tuned by filtering an appropriate number state. Furthermore, we investigate the effect of filtering multiple number states from a coherent state on the atomic population inversion dynamics.

•Jun 17, 2026•0 citations
Interpolating number-coherent states are new states of the radiation field which interpolate between number and coherent states, to which they reduce in appropriate limits. We study some fundamental features of the interaction of these new states with a atomic system in the framework of the Jaynes-Cummings model(JCM). The dynamical evolution of atomic population inversion, field entropy, the Q-function and photon number distribution properties are investigated in detail. 1
Using the eigenvalue definition of binomial states we construct new intermediate number-coherent states which reduce to number and coherent states in two different limits. We reveal the connection of these intermediate states with photon-added coherent states and investigate their non-classical properties and quasiprobability distributions in detail. It is of interest to note that these new states, which interpolate between coherent states and number states, neither of which exhibit squeezing, are nevertheless squeezed states. A scheme to produce these states is proposed. We also study the interaction of these states with atomic systems in the framework of the two-photon Jaynes-Cummings model, and describe the response of the atomic system as it varies between the pure Rabi oscillation and the collapse-revival mode and investigate field observables such as photon number distribution, entropy and the Q -function.
We investigate the influence of superposition of coherent states of light on population inversion and the evolution of the field entropy for two-level atoms in the framework of the Jaynes–Cummings model. We compare the behavior of the system in the case of having a coherent superposition state and a statistical mixture of coherent states as an initial field. Our results show that the superposition of coherent states plays an important role in the evolution of the field entropy in the intensity-dependent Jaynes–Cummings model (JCM).
We investigate some of the basic features of the interaction of superpositions of coherent states of light with two-level atoms in the framework of the Jaynes-Cummings model. We compare the behaviour of the system in the case of having a coherent superposition state and a statistical mixture of coherent states as an initial field. We investigate the collapses and revivals of the atomic inversion by studying the evolution of the Q function of the cavity field. We also establish the connection between the purity of the field and the collapses and revivals of the atomic inversion.
We investigate some of the fundamental features of the interaction of squeezed light with two-level atoms in the framework of the Jaynes-Cummings model. We start our analysis by calculating the collapses and revivals of the atomic inversion. We discuss the degree of purity of the field (given by the entropy) and its disentanglement from the atomic source. The connection with the evolution of the Q-function is also made. We notice that contrary to the coherent state case, the field turns into a nearly pure (squeezed) state at the revival time as if the field was prepared in a coherent state. The field also becomes a superposition of squeezed states at half of the revival time, and this is confirmed by investigating the photon number distribution. The phase properties of the field are discussed using the Pegg-Barnett formalism.
Recently, we introduced a new version of the Jaynes–Cummings model in which the interaction Hamiltonian is independent of the excitation number, or field intensity. Exact solution for this model was found allowing the study of nonclassical effects exhibited by the atom and the field, the latter initially in a coherent state. Here, we extend this study to the case of a field initially in the binomial state to investigate those nonclassical effects, as population trapping and sub-Poissonian statistics as function of the interpolating parameters of this state. The previous results are obtained from the present treatment, in the limit of a coherent state allowed by the binomial state.
A two-level atom interacting with a cavity field initialized in a coherent state exhibits the collapse and revival features in its population inversion dynamics under the Jaynes–Cummings interaction. When the cavity field is prepared in a number-state filtered coherent state, obtained by filtering the number state | m 〉 from a coherent state | α 〉 , we observe micro-Rabi oscillations in the collapse region instead of a perfect collapse. We find that the Rabi frequency of these micro oscillations depends only on the filtered photo-number m, whereas the amplitude depends on both m and α . This dependence enables one to infer the filtered number state from the coherent-state distribution by analyzing the time evolution of the atomic population inversion. Conversely, the amplitude and frequency of the micro-Rabi oscillations can be tuned by filtering an appropriate number state. Furthermore, we investigate the effect of filtering multiple number states from a coherent state on the atomic population inversion dynamics.