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Physical Review A

Properties of a deformed Jaynes-Cummings model

J. Črnugelj, M. Martinis, Vesna Mikuta-Martinis

Published Aug 1, 1994• 46 citations
Publisher

Abstract

It is shown that various variants of the deformed Jaynes-Cummings model (JCM) correspond to the JCM with an intensity-dependent coupling characterized by two additional phenomenological parameters (p,q). The standard JCM is obtained for p=q=1. The quantum collapse and revival effects and the squeezing properties of a particular variant of the (p,q)-deformed Jaynes-Cummings model are studied numerically. The model is based on the q-deformed oscillator algebra ${\mathit{AA}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$-${\mathit{qA}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$A=1 that interpolates between Fermi-Dirac and Bose-Einstein statistics. If the cavity field is prepared initially in a q-deformed coherent state, the quantum collapse and revival effects are observed only for q\ensuremath{\approxeq}1. For q>1, the atomic inversion 〈${\mathrm{\ensuremath{\sigma}}}_{3}$(t)〉 exhibits chaoticlike behavior, which is a feature observed also in other q-deformed JCM's. Strong squeezing is observed only for small positive and small negative q values. If q\ensuremath{\approxeq}1, the squeezing is very weak. In the limit q=1\ifmmode\pm\else\textpm\fi{}\ensuremath{\varepsilon} with \ensuremath{\varepsilon}\ensuremath{\ll}1, the algebra can be interpreted as describing a small violation of Bose-Einstein statistics in the JCM.

DOI
10.1103/physreva.50.1785

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It is shown that various variants of the deformed Jaynes-Cummings model (JCM) correspond to the JCM with an intensity-dependent coupling characterized by two additional phenomenological parameters (p,q). The standard JCM is obtained for p=q=1. The quantum collapse and revival effects and the squeezing properties of a particular variant of the (p,q)-deformed Jaynes-Cummings model are studied numerically. The model is based on the q-deformed oscillator algebra AA\ifmmode∘\else\textdegree\fi{\mathit{AA}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}AA\ifmmode∘\else\textdegree\fi-qA\ifmmode∘\else\textdegree\fi{\mathit{qA}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}qA\ifmmode∘\else\textdegree\fiA=1 that interpolates between Fermi-Dirac and Bose-Einstein statistics. If the cavity field is prepared initially in a q-deformed coherent state, the quantum collapse and revival effects are observed only for q\ensuremath{\approxeq}1. For q>1, the atomic inversion 〈\ensuremathσ3{\mathrm{\ensuremath{\sigma}}}_{3}\ensuremathσ3​(t)〉 exhibits chaoticlike behavior, which is a feature observed also in other q-deformed JCM's. Strong squeezing is observed only for small positive and small negative q values. If q\ensuremath{\approxeq}1, the squeezing is very weak. In the limit q=1\ifmmode\pm\else\textpm\fi{}\ensuremath{\varepsilon} with \ensuremath{\varepsilon}\ensuremath{\ll}1, the algebra can be interpreted as describing a small violation of Bose-Einstein statistics in the JCM.
Temporal evolution of atomic properties including the population inversion and quantum fluctuations of atomic dipole variables are discussed in three various variants of two-photon q-deformed Jaynes-Cummings model.With the the field initially being in three different types of q-deformed coherent states,the quantum collapse and revival effects as well as atomic diploe squeezing are studied for both on-and off-resonant atom-field interaction. Particularly, it is shown that for nonzero detuning the atomic inversion exhibits superstructures which are absent in the non-deformed Jaynes-Cummings model and the dipole squeezing may be enhanced.
Some nonclassical features, including photon antibunching, atomic squeezing and quantum collapse-revival phenomenon, were numerically studied in the vacuum field Jaynes–Cummings model (JCM). The influence of the initial atomic coherence on these features was discussed. It is shown that the squeezing can appear only if the atom is initially prepared in the coherent state, and photon antibunching can occur if the atom is initially in the excited state or the coherent one. The effect of the virtual-photon field was studied in JCM without the rotating-wave approximation (RWA). We have shown that even under the condition in which RWA is considered to be valid, there are significant effects on the nonc1assical features due to the interference between the virtual-photon processes and the real-photon processes. Quantum dynamics of JCM without RWA was also studied. We showed that regular dynamical behavior is exhibited in the cases rather close to the integrable limits, and irregular dynamical behavior is presented in the cases far from the integrable limits; in addition, all the nonclassical features disappear in the cases far from the integrable limits.
For multiphoton intensity-dependent Jaynes-Cummings model (JCM), which is described by two-level atom interacting with a radiation field, we prove that there is a relationship between the atomic inversion and the quadrature squeezing. We give the required condition to obtain best information from this relation. Also we show that this relation is only sensitive to large values of the detuning parameter. Furthermore, we discuss briefly such relation for the off-resonance standard JCM. PACS numbers: 42.50.Dv, 32.80.-t, 42.50.-p. I.
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.
We present a generalized Jaynes-Cummings model (JCM) with an intensity-dependent coupling interacting with a quantum group-theoretic coherent state. The field operators of the JCM Hamiltonian are identified as the elements of the suq{\mathrm{su}}_{\mathit{q}}suq​(1,1) quantum algebra in their Holstein-Primakoff realizations. We lay emphasis on the time evolution of field quadruatures and atomic population inversion of the generalized JCM. The revivals of radiation squeezing are obtained for any values of initial squeezing.