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Physical Review A

Motion-quantized Jaynes-Cummings models with an arbitrary intensity-dependent medium

Jiaren Liu, Yuzhu Wang

Published Sep 1, 1996• 27 citations
Publisher

Abstract

The exact time dependence of the density operator and various physical quantities for the motion-quantized Jaynes-Cummings models (MQJCMs) is given using the operator transformation under which it is shown that the MQJCMs have the same dynamics as the ordinary JCMs in the Kerr medium. The quantum collapses and revivals of the atomic motion due to the quantum properties of light fields and the quantization of atomic position and momentum, are predicted. The effects of the initial atomic momentum distribution and the arbitrary intensity-dependent medium on the collapse and revival phenomena of the population inversion, atomic momentum and radiation are formulated in detail. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.2326

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Journal of the Optical Society of America B•May 1, 1985•6 citations
The exact time dependence of the density operator and various physical quantities for the motion-quantized Jaynes-Cummings models (MQJCMs) is given using the operator transformation under which it is shown that the MQJCMs have the same dynamics as the ordinary JCMs in the Kerr medium. The quantum collapses and revivals of the atomic motion due to the quantum properties of light fields and the quantization of atomic position and momentum, are predicted. The effects of the initial atomic momentum distribution and the arbitrary intensity-dependent medium on the collapse and revival phenomena of the population inversion, atomic momentum and radiation are formulated in detail. \textcopyright{} 1996 The American Physical Society.
An extension of the standard Raman-coupled Jaynes-Cummings model has been made to include atomic external effects due to quantization of atomic motion. The collapse-and-revival phenomena in population inversion and in atomic motion, the velocity-selective population and their relation for a motion-quantized atom are given on the basis of a fundamental constant characterizing the interaction strength between the field modes and the atomic internal and external states. This study reveals how the initial statistics of atomic momentum affect the atomic internal dynamics and how those of the fields affect the atomic external dynamics through the atomic internal states. An exact expression for the time evolution of the density operator has been given for two fields and the center-of-mass motion initially in coherent states and in an arbitrary superposition of atomic momentum eigenstates. The statistics of atomic external and internal quantities such as the radiation force and the atomic momentum are given. \textcopyright{} 1996 The American Physical Society.
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.
The collapse-and-revival phenomenon in the population inversion and the time evolution of the quasiprobability Q function of an atom undergoing a two-photon process are investigated when the cavity is supposed to be filled with a Kerr-like medium. An exact expression for the atomic population inversion has been given for a field initially in the coherent state. The closed form of this expression as well as that of the Q function are obtained under the high-field approximation. Also, the tendency toward inhibited decay of the excited state has been explicitly shown. This study reveals how the simultaneous occurrence of two nonlinear processes affects the atomic dynamics.
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.
The Jaynes–Cummings model (JCM) is used to give a detailed analysis of the long-time behavior of a two-level atom interacting with a (Glauber) coherent-state field. This work is based on the earlier work of J. H. Eberly and collaborators, who drew attention to the collapse and revival of the Rabi oscillations of the atomic inversion. We use the three components S1, S2, and S3 of the pseudospin vector S to analyze the dynamics of the atom within the rotating-wave approximation and exact resonance. We show that, at the times when the revivals peak, the variables σ = |S| and η = S3/σ become independent of (1) the transition dipole moment of the atom, (2) the intensity of the coherent-state field, and (3) the (common) frequency of the atom and the field. Thus these special values of σ and η are a universal feature of the JCM that should be observed in experiments with any two-level atom in an arbitrarily intense (but resonant) coherent-state field. The derivation of the above results was facilitated by transforming into a rotating coordinate frame in which S1 = 0 so that S2 and S3 are the only dynamical variables. The two-dimensional nature of S in this frame makes it easy to visualize the dynamical changes in the atom. The dynamics of the JCM is clarified by comparison with the closely related Buck–Sukumar model. The relationship of the phenomena discussed here to photon echoes and to quench echoes (in condensed media) is pointed out.