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Physical Review A

Generalized Jaynes-Cummings model with an intensity-dependent coupling interacting with a quantum group-theoretic coherent state

Zhe Chang

Published Jun 1, 1993• 32 citations
Publisher

Abstract

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 ${\mathrm{su}}_{\mathit{q}}$(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.

DOI
10.1103/physreva.47.5017

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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.
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.
We present a general qubit-boson interaction Hamiltonian that describes the Jaynes-Cummings model and its extensions as a single Hamiltonian class. Our model includes non-linear processes for both the free qubit and boson field as well as non-linear, multi-boson excitation exchange between them. It shows an underlying algebra with supersymmetric quantum mechanics features allowing an operator based diagonalization that simplifies the calculations of observables. As a practical example, we show the evolution of the population inversion and the boson quadratures for an initial state consisting of the qubit in the ground state interacting with a coherent field for a selection of cases covering the standard Jaynes-Cummings model and some of its extensions including Stark shift, Kerr-like, intensity dependent coupling, multi-boson exchange and algebraic deformations.
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.