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International Journal of Quantum Chemistry

Interaction of a two‐level cyclic XY n‐spin model with a two‐mode cavity field in off‐resonant states

Horacio Grinberg

Published Aug 21, 2007• 3 citations
Publisher

Abstract

Abstract The interaction of the XY n‐spin cyclic model with a two‐mode cavity field in the rotating‐wave approximation is investigated in the framework of a generalized Jaynes–Cummings two‐level system consisting of the vacuum state and a thermally averaged manifold of excited sates. Computation of the energy of this manifold allows this interaction to be examined in off‐resonant states. Time evolution of the population inversion, photon distribution, and temperature distribution for an excited initial state are computed via second‐ and third‐order perturbation expansion of the time evolution operator matrix elements for the excited and ground states, respectively and for an ideal squeezed initial coherent state of the cavity field. It was assumed that the two modes have initially the same photon distribution. The pattern of the spin population inversion appears as a manifestation of multiple and complicated inerferences, which is mathematically reflected in a double discrete summation that appears in the calculation of the dynamics. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

DOI
10.1002/qua.21472

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Abstract The interaction of the XY n‐spin cyclic model with a two‐mode cavity field in the rotating‐wave approximation is investigated in the framework of a generalized Jaynes–Cummings two‐level system consisting of the vacuum state and a thermally averaged manifold of excited sates. Computation of the energy of this manifold allows this interaction to be examined in off‐resonant states. Time evolution of the population inversion, photon distribution, and temperature distribution for an excited initial state are computed via second‐ and third‐order perturbation expansion of the time evolution operator matrix elements for the excited and ground states, respectively and for an ideal squeezed initial coherent state of the cavity field. It was assumed that the two modes have initially the same photon distribution. The pattern of the spin population inversion appears as a manifestation of multiple and complicated inerferences, which is mathematically reflected in a double discrete summation that appears in the calculation of the dynamics. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008
The interaction of a two-level cyclic XY n-spin model with a two-mode cavity field involving two-photon transitions is investigated through a generalized Jaynes-Cummings model in the rotating-wave approximation. The two-photon interacting Hamiltonian becomes from the replacement of each single-mode field in the one-photon interacting Hamiltonian with the second-harmonic generation. It was assumed that initially the correlated field modes are in disentangled coherent states having the same photon distribution and that the spin system is in an excited state. At any time t > 0, the spin system and the field are in an entangled state, in this case, via a unitary time evolution operator. Thus, the spontaneous decay of a spin level was treated by considering the interaction of the two-level spin system with the modes of the universe in the vacuum state. The different cases of interest, characterized in terms of a detuning parameter for each mode, which emerge from nonvanishing commutation relations, were analytically implemented and numerically discussed for various values of the initial mean photon number and spin-photon coupling constants. Photon distribution, time evolution of the spin population inversion, as well as the statistical properties of the field leading to the possible production of nonclassical states, such as antibunched light, violations of the Cauchy-Schwartz inequality, and second- and fourth-order squeezing, are examined. The case of zero detuning of both modes was treated in terms of a linearization of the expansion of the time evolution operator, while in other three cases, the computations were conducted via second- and third-order Dyson perturbation expansion of the time evolution operator matrix elements for the excited and ground states of the spin system, respectively.
Abstract The quantum partition function and the emerging energy of a fermionic Ising ferromagnetic model involving all possible interactions (generalized Ising model) are obtained from an appropriate tracing of the analytic propagator path integral over Grassmann variable coherent nonorthogonal states in the imaginary time domain. The dynamics derived from the interaction of this system with a single‐mode cavity field in the rotating wave approximation is investigated for nonresonant states within the framework of the Jaynes–Cummings two‐level model consisting of the vacuum state and a thermally averaged manifold of excited states. Time evolution of the population inversion is computed in the nanosecond time scale, assuming that the initial coherent state of the field is given by a Poisson distribution. The limit of high temperatures characterizing the manifold of excited states becomes chaotic with rapid oscillations, whereas the ground state is described correctly in the thermodynamic limit by the vacuum state. A breakup is seen in the photon distribution into a series of peaks because of the detuning between the spin system and the field. However, this structure is smeared out, and the general shape is preserved in the computation emerging from the Laplace transform of the photon distribution. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006
The interaction of a two-level XYn-spin system with a two-mode cavity field is investigated through a generalized Jaynes-Cummings model in the rotating wave approximation. The spontaneous decay of a spin level was treated by considering the interaction of the two-level spin system with the modes of the universe in the vacuum state. The different cases of interest, characterized in terms of a detuning parameter for each mode, which emerge from the nonvanishing of certain commutation relations between interaction picture Hamiltonians associated with each mode, were analytically implemented and numerically discussed for various values of the initial mean photon number and spin-photon coupling constants. Photon distribution, time evolution of the spin population inversion, as well as the statistical properties of the field leading to the possible production of nonclassical states, such as antibunched light and violations of the Cauchy-Schwartz inequality are examined for an excited initial state. It was assumed that the two modes are initially in coherent states and have the same photon distribution. The case of zero detuning of both modes was treated in terms of a linearization of the expansion of the time evolution operator, while in other three cases, the computations were conducted via second- and third-order Dyson perturbation expansion of the time evolution operator matrix elements for the excited and ground states respectively.
The aim of this study is to investigate an effective two-level atom coupled to a twomode f-deformed cavity field with and without the rotating wave approximation.The first section discusses the theoretical model of the interaction between a two-mode cavity-field and an effective two-level atom within the framework of an f-DJCM without the rotating wave approximation.After that, we obtain the reduced density matrix of the atom with and without the rotating-wave approximation.Then, we have investigated the effect of the counterterm on temporal evolution of various nonclassical properties of the atom, i.e., atomic population inversion, atomic dipole squeezing and atom-field entanglement.Particularly, we compare the numerical result for three different values of the deformation parameter q (q=1, q=1.1, q=1) with and without the rotating wave approximation.
We present a general procedure to describe the dynamics of N degenerate quantized fields interacting resonantly with a two–level atom, all coupled with the same strength, within the rotating–wave approximation. Starting from the analysis of the two and three field cases, we generalize the method by identifying dynamical invariants that lead to a factorized form of the time–evolution operator. A unitary transformation reduces the problem to an effective Jaynes–Cummings Hamiltonian, where only one field interacts with the atom and the remaining modes contribute as free fields. Assuming initially coherent fields and an atomic superposition, we compute the atomic inversion and the mean photon number, revealing vacuum Rabi oscillations with a frequency determined by an effective coupling constant that exceeds the individual atom–field coupling, as well as the characteristic collapse-revival behavior.