Erratum to: “Interaction of a two-level XY n-spin model with a cavity field” [Phys. Lett. A 344 (2005) 170]

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

“…In a previous paper, 40,41 it was shown that the two-level n-spin system is characterized by the ground state |0 ≡ |a and a thermally averaged manifold of excited states |b . By using the completeness relation |a a| + |b b| ≡ σ aa + σ bb = 1, the Hamiltonian (1) can be written as…”

“…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.…”

“…It is further shown that the number of configurations of a given multiplicity is perfectly consistent with the dimension of the trace of the unit operator in a basis of Grassmann generators. 40,41 This is an important issue because all the states derived from the totality of spin adapted configurations have to be included in the computation of the spin transition frequency in off-resonant states of both modes. Finally, the temperature distribution in off-resonant states and in the isotropic limit of the spin system is briefly discussed in the limit of high and low temperatures.…”