Interaction of a para-Bose state with two two-level atoms: control of dissipation by a local classical field

Abstract

We consider a parity-deformed Jaynes–Cummings model (JCM) consisting of two identical two-level atoms interacting with a single-mode para-Bose field in a cavity. Compared to the standard JCM, this model introduces the action of a specific local classical field as an external control which can be simulated through an intensity-dependent two-atom JCM with a particular intensity-dependent function. The conservation of the total excitation number and overall parity provides a complete number parity basis for the Hilbert space of the system. In this basis, the matrix representation of the system’s Hamiltonian becomes block diagonal. The corresponding eigenvalues and eigenstates of the system are then analytically calculated by diagonalizing the block matrices. In continuum, we investigate the dynamical evolution of some physical properties such as entanglement, atomic inversion, photon statistics and atomic squeezing in the parity representation, with emphasis on the control role of the local external classical fields. In addition, in the presence of the cavity decay, we study the effect of cavity dissipation on the quantum dynamics of the system. In the ideal case (without the cavity dissipation), we show that the initial states of the system with even–odd parity manifest qualitatively distinct control role of the local external classical fields on the dynamical behavior of the physical properties. In the dissipation regime, we show that the control of local classical fields has the general effect to improve the stabilization of the quantum properties of the system generated during the time evolution.