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

Abstract

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.

Nonclassical effects in a highly nonlinear generalized homogeneous Dicke model

“…We now focus on the important quantum phenomenon of field squeezing. The initially coherent cavity field can be squeezed when it interacts with a single atom [36,42], and squeezing in the revivaltime regime can be very strong for large intensities of the field [43,44]. Fig.…”

“…. fail to commute, Dyson perturbation expansion of the time evolution operator matrix elements truncated to a finite order constitutes the ideal tool to deal with this manybody problem [36,37].…”

Динамічний Та Макроскопічний Описи Газу Взаємодіючих Атомів У Сильному Електромагнітному Полі Поблизу Резонансу

“…Бiльш глибокий аналiз такої ж системи з урахуванням неадiабатичних переходiв запропонований у [35]. Подiбний аналiтичний метод, процесами на узагальненiй моделi Джейнса-Камiнгса (Jaynes-Cummings model), описаний у [36]. У цiй роботi дослiджувались деякi характеристики свiтла у двомодовому резонаторi з можливiстю резонансних двофотонних переходiв для невзаємодiючих фермiонiв, але без урахування дисипативних процесiв у системi.…”

“…де усередненi величини P i;j (t, r i , r j ) i R i;j (t, r i , r j ) визначаються в (36). Тут було використано такi позначення:…”

Kinetics and Optical Properties of the Strongly Driven Gas Medium of Interacting Atoms

“…A deeper analysis of the same system adding non-adiabatic transitions was provided in [48]. In [49] a similar analytical method based on the generalized Jaynes-Cummings model was used. This work discussed some characteristics of light in two-mode cavity with the possibility of resonant two-photon transitions for non-interacting fermions, but did not include dissipative processes.…”