Population inversion, temperature, and photon distributions of the generalized fermionic Ising ferromagnetic model: Path‐integral representation of the spin system

Abstract

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.

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

“…This paper extends earlier studies 1–4 of the transient dynamics of a two‐level n ‐spin model interacting with a single mode quantized cavity field. Here it is explored the situation in which the spin model is coupled to a two‐mode cavity field which is allowed to evolve dynamically in the quantum regime.…”

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

“…2 to obtain the energy of the spin system restores the discrete translational invariance of the infinite lattice in the finite sample needed for the simulations. [40][41][42]49 The size of the spin chain is n = 14, and thus the manifold of excited states was thermally averaged over the 16383 configurations out of the vacuum state. In fact, the number of independent spin states of a given multiplicity, which exist for a system of n spins, denoted by f (n, S), can be derived in an analogical fashion.…”

“…43 Complete analytical details on the thermally averaged procedure involving non-orthogonal Grassmann coherent states to generate a manifold of excited states, by allowing one to treat the model as a Jaynes-Cummings two-level system, and thus opening the possibility of exploring the dynamics in off-resonant states, are described in previous papers. [40][41][42] In Sec. 3, the interaction of this spin system with a quantized cavity field is analyzed in the interaction picture representation, which is a competent scenario to generate explicit expressions of dynamical properties.…”

“…This paper extends earlier studies of the transient dynamics of a two-level n-spin model interacting with a single mode quantized cavity field. [40][41][42] Here, the quantum dynamics of this system interacting with 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). 43 In a recent paper, some preliminary results were reported in off-resonant states of the twomode cavity field with this spin system.…”

“…Another important aspect of the present model is the possibility of exploring the temperature dependence on the detuning parameters through the explicit incorporation of a thermal photon state for each mode. [40][41][42] The superposition states from several two-mode coherent states were reported, and it was shown that under certain conditions, the superposition states may exhibit nonclassical effects, such as photon antibunching, sub-Poissonian photon statistics, squeezing, and violation of the Cauchy-Schwartz inequality. 35,[46][47][48] Thus, the main focus of attention in this paper is not only on the the photon distribution and population dynamics (actually the spin inversion), but some aspects of the dynamics of the field statistics exhibiting nonclassical properties, such as the possible production of antibunched states and violations of the Cauchy-Schwartz inequality, will also be investigated in some detail.…”