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arXiv:2007.07844 · Physical Review A

Two-photon-interaction effects in the bad-cavity limit

Nicolò Piccione, Simone Felicetti, Bruno Bellomo

Published Jan 26, 2022• 18 citations
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Abstract

Taking advantage of recently developed adiabatic elimination techniques, the authors investigate two-photon light-matter interactions in a system comprised of an oscillator and a collection of qubits operating in the ``bad-cavity'' regime. They derive a general master equation which unveils some unexpected effects of two-photon couplings, like a richer dependence on temperature of the collective quantum phenomena with respect to the one-photon-coupling case.

DOI
10.1103/physreva.105.l011702

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Taking advantage of recently developed adiabatic elimination techniques, the authors investigate two-photon light-matter interactions in a system comprised of an oscillator and a collection of qubits operating in the ``bad-cavity'' regime. They derive a general master equation which unveils some unexpected effects of two-photon couplings, like a richer dependence on temperature of the collective quantum phenomena with respect to the one-photon-coupling case.
The interaction of a two-level atom with a single mode of the radiation field is examined. The cavity mode is damped by coupling to a reservoir in a squeezed state, and the atom is also driven by an external laser field. A master equation for the atomic density operator in the bad-cavity limit is derived. The effect of the squeezing in the stationary population inversion and in the resonance spectrum of the light emitted by the atom into the background modes is studied. The results are compared with the numerical solution of the full master equation for the atom-plus-cavity mode-density operator.
We model the evolution of a single atom in a cavity interacting with two lasers, one far off resonance which creates an optical potential lattice and one near resonance, which can interact with the atom. The atom may tunnel between sites in the lattice. We find the photon counting statistic g(2)(τ)g^{(2)}(τ)g(2)(τ) depends on the tunneling rate. Additionally we derive methods to work with a Bose-Einstein Condensate in the same situation, in ther Josephson junction regime. It is shown that oscillations in g(2)(τ)g^{(2)}(τ)g(2)(τ) are directly proportional to the tunneling coefficient. We work in the bad-cavity limit and give an example of the use of adiabatic elimination in quantum trajectory theory
We study the extracavity quantum vacuum radiation generated by a sudden switch on and off of the vacuum Rabi frequency of a single two-level system coupled to a single cavity mode in the strong and ultrastrong coupling regime. Dissipation is described by including the qubit-resonator coupling in the derivation of the master equation. The output stream of photons and their second-order correlation functions are calculated by exploiting a recently developed input-output formulation of resonators valid for arbitrary light-matter couplings. The obtained output photon correlations provide direct information on the quantum correlations among the virtual excitations of the dressed vacuum.
We explore the validity of adiabatic elimination in the derivation of an essential-states representation of the time-dependent Schr\"odinger equation in the presence of a strong laser field. We consider the elimination of off-resonant states in generating an effective two-level description of the light-matter interaction, where the initial and final states are two-photon resonant. The treatment is nonperturbative and can be generalized to NNN-photon absorption.
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We present a theory of dressed-state lasers, i.e., lasers that operate on an inverted transition between dressed states of a coupled atom-field system, in the bad-cavity limit. We discuss the validity of the effective Hamiltonian approach in such a case and generalize the theory beyond secular and effective Hamiltonian approximations. We demonstrate that higher-order instabilities that lead to self-pulsing and optical chaos may occur in experiments on dressed-state lasers. With the help of the generalized theory we study the competition between the resonant one-photon and two-photon processes and try to understand it physically by looking at the spectrum of the emitted radiation.