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Modern Physics Letters B

JAYNES-CUMMINGS MODEL WITH INTENSITY-INDEPENDENT INTERACTION VIA THE PHASE OPERATORS

B. Baseia, Gil C. Marques, A. N. Chaba, A. L. De Brito, S. B. Duarte

Published Aug 20, 1995• 1 citation
Publisher

Abstract

We introduce a new version of the JC-Model using the (non-Hermitian) phase operators [Formula: see text] in the interaction Hamiltonian, which becomes independent of the excitation number or the field intensity, thus being able to describe properties of the atom in the saturation regime. We employ the “dressed-states” formalism to find an exact solution for our system. As applications we investigate the occurrence of nonclassical effects in the field (squeezing and sub-Poissonian statistics) and in the atom (collapses and revivals of Rabi oscillations and population trapping).

DOI
10.1142/s0217984995001194

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We introduce a new version of the JC-Model using the (non-Hermitian) phase operators [Formula: see text] in the interaction Hamiltonian, which becomes independent of the excitation number or the field intensity, thus being able to describe properties of the atom in the saturation regime. We employ the “dressed-states” formalism to find an exact solution for our system. As applications we investigate the occurrence of nonclassical effects in the field (squeezing and sub-Poissonian statistics) and in the atom (collapses and revivals of Rabi oscillations and population trapping).
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.
In the representation of dressed states, which diagonalizes the Hamiltonian in the Jaynes-Cummings model, the Bose operator for excitation annihilation Â, the spin operator Σ^_\hat \Sigma \_Σ^_ , and the corresponding Hermitian-conjugate operators are found. Using these operators, correlated coherent states were constructed and statistical properties of a field mode and an atom in these states are studied. Nonclassical field properties, such as the deviation of the probability distribution for the number of photons from the Poissonian distribution, its time dependence, and the squeezing of quadrature field components are found. For small interaction coefficients k, all these characteristics of the model vary weakly in time in the resonance case.
We have shown that the Jaynes-Cummings model (JCM) with an environment-induced pure decoherence is an exactly solvable problem. Rabi oscillation of atomic population inversion and oscillation in the field population get trapped due to decoherence. But the decay of the coherence properties of the atom as well as of the field is comparatively slower than that of the population terms. It is also shown that although the fast oscillation in nonclassical properties are suppressed due to decoherence but an initial Poissonian field acquires a sub-Poissonian character in the steady state. So unlike the ordinary spontaneous emission all the nonclassical properties of the system are not erased.
An alternative approach to the Jaynes-Cummings model (JCM) with dissipation at a finite enviromental temperature is presented in terms of a new master equation under Born-Markovian approximations. An analytic solution of the dissipation JCM is obtained. A variety of physical quantities of interest are calculated analytically. Dynamical properties of the atom and the field are investigated in some detail. It is shown that both cavity damping and environmental temperature strongly affect nonclassical effects in the JCM, such as collapse and revivals of the atomic inversion, oscillations of the photon-number distribution, quadrature squeezing of the field and sub-Poissonian photon statistics.
. The Jaynes-Cummings Model (JCM), a soluble fully quantum mechanical model of an atom in a field, was first used (in 1963) to examine the classical aspects of spontaneous emission and to reveal the existence of Rabi oscillations in atomic excitation probability for fields with sharply defined energy (or photon number). For fields having a statistical distribution of photon numbers the oscillations collapse to an expected steady value. In 1980 it was discovered that with appropriate initial conditions (e.g. a near-classical field), the Rabi oscillations would eventually revive – only to collapse and revive repeatedly in a complicated pattern. The existence of these revivals, present in the analytic solutions of the JCM, provided direct evidence for discreteness of field excitation (photons) and hence for the truly quantum nature of radiation. Subsequent study revealed further nonclassical properties of the JCM field, such as a tendency of the photons to antibunch. Within the last two years it has been found that during the quiescent intervals of collapsed Rabi oscillations the atom and field exist in a macroscopic superposition state (a Schrödinger cat). This discovery offers the opportunity to use the JCM to elucidate the basic properties of quantum correlation (entanglement) and to explore still further the relationship between classical and quantum physics.
In this paper, we investigate various dynamical properties of the Jaynes–Cummings (JC) model beyond the rotating wave approximation (RWA). We first show that in the absence of the RWA, the JC Hamiltonian can be transformed into an intensity-dependent Hamiltonian. Corrections produced by the counter-rotating terms (CRTs) appear in the first order as the intensity-dependent detuning, i.e. the dynamical Stark shift and in the second order as the intensity-dependent atom–field coupling. Then, by determining the atom–field wavefunction evolution, we study the effects of CRTs on various dynamical properties of the JC model, including the atomic population inversion, atomic dipole squeezing, atomic entropy squeezing, photon counting statistics, quadrature field squeezing, field entropy squeezing and quantum phase properties of the cavity field.