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arXiv:1306.4896 · Physical Review A

Two-level system with broken inversion symmetry coupled to a quantum harmonic oscillator

H. K. Avetissian, G. F. Mkrtchian

Published Oct 9, 2013• 7 citations
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Abstract

We study the generalized Jaynes-Cummings model of quantum optics at the inversion-symmetry breaking and in the ultrastrong coupling regime. With the help of a generalized multiphoton rotating-wave approximation, we study the stationary solutions of the Schr\"odinger equation. It is shown that the problem is reduced to resonant interaction of two position-displaced harmonic oscillators. Explicit expressions for the eigenstates and eigenvalues of generalized Jaynes-Cummings Hamiltonian are presented. We exemplify our physical model with analytical and numerical considerations regarding Rabi oscillations, collapse and revivals of the initial population of a two-level system, and photon distribution function at the direct multiphoton resonant coupling.

DOI
10.1103/physreva.88.043811

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We present a general procedure to describe the dynamics of N degenerate quantized fields interacting resonantly with a two–level atom, all coupled with the same strength, within the rotating–wave approximation. Starting from the analysis of the two and three field cases, we generalize the method by identifying dynamical invariants that lead to a factorized form of the time–evolution operator. A unitary transformation reduces the problem to an effective Jaynes–Cummings Hamiltonian, where only one field interacts with the atom and the remaining modes contribute as free fields. Assuming initially coherent fields and an atomic superposition, we compute the atomic inversion and the mean photon number, revealing vacuum Rabi oscillations with a frequency determined by an effective coupling constant that exceeds the individual atom–field coupling, as well as the characteristic collapse-revival behavior.
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