Two-Level Atom (The Matrix Approach, a Quantized Field)

Perry R. Rice

Perry R. Rice

Anubhav Paul, Arnab Laha, Somnath Ghosh

Abstract We report an analytical model to investigate an atom-cavity interaction phenomenon with the consideration of a two-level atom and a quantized mode of the cavity field in the form of harmonic oscillation. Accordingly, we consider the matrix form of a special type of two-level Hamiltonian consisting of three units, explaining a two-level atom, a quantum harmonic oscillator to be equivalent to a quantized cavity-mode field, and an interaction matrix between them, which are connected by some iteration parameters. The iteration parameters of the proposed Hamiltonian have judiciously been modulated to encounter an exceptional point (EP). A specific closed parameter space encircling the embedded EP has been considered to study the dynamics of the coupled states in the context of a flip-of-state phenomenon. We also incorporate a deliberate phase difference between the two unperturbed levels associated with the atomic system and study the phase induced interaction between them in the context of state-flipping around the identified EP. The proposed analytical model indeed opens up a fertile platform to explore a range of interesting applications associated with the atom-cavity interaction.

S. M. Chumakov, A. B. Klimov, C. Saavedra

We study the dynamics of a collection of two-level atoms interacting with a single mode of a quantized field in a dissipative cavity in the dispersive regime. The quantized mode is driven by a classical driving field. The steady-state density matrix is obtained. The influence of the driving field on the quantized driven field and on atomic properties in both the dissipative and the lossless cases is studied. The atomic decoherence time in the dissipative-driven case is obtained. We show that the external driving field strongly suppresses the atomic coherence (in comparison with the dissipative cavity without the driving field).

V. I. Koroli

The interaction between the laser cooled and trapped equidistant three-level atom (ion) and the quantized cavity field is investigated. The dipole moment matrix transition elements between the adjacent atomic energy levels d12 and d23 are assumed to be different. This model generalizes the problem of the pair of indistinguishable two-level atoms interacting with the squeezed vacuum which is equivalent to the equidistant three-level atom with equal dipole moment matrix transition elements. The exact analytical solution for the atom-field state-vector is found in the case in which at the initial moment t = 0, the single-mode cavity field is supposed to be in the squeezed vacuum state. With the help of this solution, the quantum-statistical and squeezing properties of the radiation field are studied. The obtained results are compared with those for the single two-level atom model. It should be noted that in the proposed model, the exact periodicity of the squeezing revivals is violated by the analogy with the single two-level atom one. The two limiting cases are analyzed. In the first limiting case in which d12 → d23 the quantum-statistical properties of the single-mode cavity field resemble those for the pair of indistinguishable two-level atoms. In the second one d12 → 0 the quantum-statistical and squeezing features of the proposed model are similar with those for the single two-level atom model.

Dipankar Bhattacharyya, Jyotirmoy Guha