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

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.

Nonclassical Effects of a Two-Level Spin System Interacting with a Two-Mode Cavity Field via Two-Photon Transition

“…Although there has been a lot of previous work dealing with both the response of two-level atoms to dual-frequency semiclassical excitation in the steady-state regime , and the transient regime with a quantum probe field, ,,,,,, a systematic analysis concerning the degenerate and nondegenerate two-mode nonclassical states associated with the resonant and off-resonant states of the cavity field with a spin system is not completely documented so far, and this motivates us to introduce in this paper a generalized JCM in which two-photon transitions are mediated by two modes of photons in resonant and off-resonant states. Thus, this paper extends earlier studies of the transient dynamics of a two-level n -spin model interacting with a quantized cavity field via superposition of single- and two-mode coherent states. − This is an important issue in view of the possibility of observing a variety of typical nonlinear phenomena such as entanglement propagation through spin chains in the presence of a staggered magnetic field, entangled light via nonlinear vacuum−multiparticle inteactions, as well as quantum phase transitions in photonic cavities . In the present paper, the quantum dynamics of a cyclic spin system interacting with initial correlated two-mode field states is investigated through a generalized JCM, in which the spin cyclic system is that described in the classical paper by Lieb, Schultz, and Mattis (LSM) .…”

Dynamics and Nonclassical Photon Statistics in the Interaction of Two-Level Spin Systems With a Two-Mode Cavity Field: A Generalized Jaynes-Cummings Model

“…(92) was performed with the time dependent coefficients given by Eqs. (44) and (48), assuming a Gaussian distribution with Γ = 4. If the coupling constant of one mode (in this case the first mode) is large (solid line), as the time increases, the neighboring revivals increasingly overlap.…”

“…In this case, the dynamics is governed by the coefficients given in Eqs. (44) and (48), assuming in both cases that the initial coherent field is given by a Poisson distribution. We notice that both modes are bunched and antibunched.…”

“…43 In a recent paper, some preliminary results were reported in off-resonant states of the twomode cavity field with this spin system. 44 In the present work, the interaction of this spin model with a two-mode cavity field in the quantum regime is investigated in the rotating wave approximation through a linearization of the expansion of the time evolution operator in the case of exact simultaneous resonance of both modes of the cavity field with the spin transition frequency. In off-resonant states, on the other hand, the interaction picture non-phenomenological Hamiltonian of the model becomes time-dependent.…”

“…(71) in the picosecond time scale t = 3.2 ps in the case of exact simultaneous resonance of both modes, i.e., the trace over the spin states in Eq. (71) is calculated from Eqs (44). and(48).…”