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Journal of Modern Optics

Collapse-revival Phenomenon in the Jaynes-Cummings Model Interacting with the Multiphoton Holstein-Primakoff SU(2) Coherent State

V. Buek, Igor Jex

Published Nov 1, 1989• 9 citations
Publisher

Abstract

We have analysed the behaviour of the atomic population inversion of the two-level atom interacting with a single-mode field initially prepared in the multiphoton Holstein-Primakoff SU(2) coherent state. It is shown that the behaviour of the atomic inversion depends on the parameters characterizing the initial state of the field. In particular, the atomic inversion can exhibit periodical oscillations as well as the collapse-revival phenomenon.

DOI
10.1080/09500348914551511

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We have analysed the behaviour of the atomic population inversion of the two-level atom interacting with a single-mode field initially prepared in the multiphoton Holstein-Primakoff SU(2) coherent state. It is shown that the behaviour of the atomic inversion depends on the parameters characterizing the initial state of the field. In particular, the atomic inversion can exhibit periodical oscillations as well as the collapse-revival phenomenon.
When single mode coherent light field interacts with two-level atomic mixed-state,the properties of the atomic population inversion is studied by means of the multi-photon anti-Jaynes-Cummings model.The influence for the parameters of average photon number of the coherent light field,transition photon number and mixing extent of the atomic initial state on the atomic population inversion has been discussed.The results show that the collapse and revival phenomena of periodicity will also appear in the two-level atomic population inversion.With the increasing of the average photon number of the coherent light field and the transition photon number,the revival period and attenuation time of collapse will change.With the increase of the average photon number of the coherent light field,the oscillation frequency of the atomic population inversion increases correspondingly.The revival period and attenuation time of collapse will not change,but the oscillation amplitude of the atomic population inversion will be increase as the decreasing of mixing extent of the atomic initial state.
In this paper we study the interaction between two-level atom and quantized single-mode field, namely, Jaynes-Cummings model (JCM). The field and the atom are initially prepared in the binomial state and the excited atomic state, respectively. For this system we prove that the revival-collapse phenomenon exhibited in the atomic inversion of the standard JCM can be numerically (naturally) manifested in the evolution of the squeezing factor of the three-photon (standard) JCM provided that the initial photon-number distribution of the radiation has a smooth envelope.
For a system of multiphoton Jaynes–Cummings model, which represents the interaction of a two-level atom with the radiation field, we study the connection between the atomic inversion, in particular the occurrence of revival–collapse phenomenon (RCP), and the higher-order fluctuation factors. We assume that the atom and the field are initially prepared in the excited and the k -photon coherent states, respectively. We show that there is a class of states for which the higher-order fluctuation factor can provide RCP similar to that involved in the corresponding atomic inversion. Moreover, for initial coherent light we prove that the higher-order fluctuation factor of the three-photon transition can provide RCP similar to that occurring in the atomic inversion of the one-photon transition. As an example we discuss the fourth-order fluctuation in detail.
Abstract In the photon-atom interaction, one of the most interesting phenomena can be collapse-revival effect in population inversion of atomic levels. Since a single-photon-transition Jaynes–Cummings model can be generalized to a multiphoton-transition Jaynes–Cummings model, of which the Hamiltonian can exhibit a supersymmetric Lie algebra structure, in this paper, quantum collapse and revival in atomic population inversion, which is a collaborative effect of a variety of quantum Rabi oscillations with various quantum Rabi frequencies, is studied for the supersymmetric multiphoton-transition Jaynes–Cummings model. In the literature, it has been pointed out that quantum collapse and revival might find an application in qubit design. We expect that a supersymmetric two-level system might serve as such a kind of qubits. Compared with ordinary two-level qubits, more information could be stored in the basis vectors of supersymmetric qubits, and this could increase the degrees of freedom of tensor product (multi-component extension) of basis vectors of this multiphoton-atom interacting system. For this reason, some characteristics of the collapse-revival effect driven by ordinary coherent states and Yurke–Stoler coherent states will be addressed in this paper. The influence of various characteristic parameters of this supersymmetric Jaynes–Cummings model and the quantized optical fields on the quantum collapse and revival in the population inversion will be indicated in some numerical illustrative examples.
In this paper we consider a system consisting of a two-level atom, initially prepared in a coherent superposition of upper and lower levels, interacting with a radiation field prepared in generalized quantum states in the framework of multiphoton Jaynes–Cummings model. For this system, we show that there is a class of states for which the fluctuation factors can exhibit the revival-collapse phenomenon (RCP) similar to that exhibited in the corresponding atomic inversion. This is shown not only for normal fluctuations but also for amplitude-squared fluctuations. Furthermore, apart from this class of states we generally demonstrate that the fluctuation factors associated with three-photon transition can provide the RCP similar to that occurring in the atomic inversion of the one-photon transition. These are novel results and their consequence is that the RCP occurring in the atomic inversion can be measured via a homodyne detector. Furthermore, we discuss the influence of the atomic relative phases on such phenomenon.