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

Abstract

The interaction of a two-level XY n-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.

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) .…”

“…This is probably the reason for no violation being observed in onephoton processes when the Gaussian distribution is used to represent the initial state of the field. 42 In fact, in the latter case, V(t) is always negative, indicating that the field statistics become more classical as a result of the interaction with this singlephoton generalized JCM. On the other hand, computations (not shown) reveal that when a photon distribution function for the field initially in a two-photon coherent state is used, the inequality in eq 101 is always violated in this case.…”

“…In the one-photon process, it was found that V(t) is strongly affected by the photon distribution used to represent the initial coherence of the field. 42 The dissimilar behavior in the nature of the time evolution of V(t) in one-photon and two-photon processes can be attributed to the fact that the Poisson distribution used in Figure 6 is more physical than the Gaussian distribution in the sense that this is the distribution followed by photons in a coherent state. This is probably the reason for no violation being observed in onephoton processes when the Gaussian distribution is used to represent the initial state of the field.…”

“…This result is perhaps a little surprising since the form of the interaction would seem to preserve the correlations. In the one-photon process, it was found that V ( t ) is strongly affected by the photon distribution used to represent the initial coherence of the field . The dissimilar behavior in the nature of the time evolution of V ( t ) in one-photon and two-photon processes can be attributed to the fact that the Poisson distribution used in Figure is more physical than the Gaussian distribution in the sense that this is the distribution followed by photons in a coherent state.…”

“…Moreover, since in this case the set of interaction picture Hamiltonians 𝒱( t 1 ), 𝒱( t 2 ),..., taken at different times t 1 , t 2 ,... fail to commute, Dyson perturbation expansion of the time evolution operator matrix elements truncated to a finite order has to be used. Although the presence of quadratic bosonic operators involved in the two-photon transitions of the cavity does not alter the general structure of the interaction picture Hamiltonian associated with the one-photon transitions, the system−cavity field interaction matrix elements and the resulting nonclassical properties are, however, quite different from those obtained in the case of one-photon transitions. , Thus, we give the accordingly modified equations to account for these two-photon transitions of the cavity field.…”