Theoretical Methods for Ultrastrong Light–Matter Interactions

Abstract

This article reviews theoretical methods developed in the last decade to understand cavity quantum electrodynamics in the ultrastrong-coupling regime, where the strength of the light-matter interaction becomes comparable to the photon frequency. Along with profound modifications of fundamental quantum optical effects giving rise to a rich phenomenology, this regime introduces significant theoretical challenges. One of the most important is the break-down of the rotating-wave approximation which neglects all non-resonant terms in lightmatter interaction Hamiltonians. Consequently, a large part of the quantum optical theoretical framework has to be revisited in order to accurately account for all interaction terms in this regime. We give in this article a broad overview of the recent progress, ranging from analytical estimates of ground-state properties to proper derivations of master equations and computation of photodetection signals. For each aspect of the theory, the basic principles of the methods are illustrated on paradigmatic models such as quantum Rabi and spin-boson models. In this spirit, most of the article is devoted to effective models, relevant for the various experimental platforms in which the ultrastrong coupling has been reached, such as semiconductor microcavities and superconducting circuits. The validity of these models is discussed in the last part of the article, where we address recent debates on fundamental issues related to gauge invariance in the ultrastrong-coupling regime.

Thermodynamics of ultrastrongly coupled light-matter systems

“…However, even in this special case our exact numerical calculations confirm that the bound f g < 1 still holds. [60,61,62]. In this frame the cavity QED Hamiltonian can be written as [32,33,38,63]…”

Multiple photon antibunching-to-bunching transitions in the dissipative anisotropic quantum Rabi model

“…Under the assumption that the system-bath interaction is weak, we can separately perturb both V c and V q to obtain the DME by including Born-Markov approxi-mation. Finally, the DME is described as [50,53]…”

“…Two-photon correlation function is widely considered as the main observable to characterize the nonclassicality of output photons, which is originally introduced by Glauber to investigate the optical coherence of quantum theory [49]. However, due to the realizations of ultrastrong qubit-photon coupling [5,6], the system-bath interaction should be properly treated in the eigenstate framework of the whole hybrid quantum systems [50][51][52][53]. In particular, Ridolfo et al recently proposed a modified definition of the two-photon correlation function to characterize steady-state photon statistics in the dissipative QRM [54][55][56][57], based the quantum dressed master equation (DME) [50].…”

Approximating the two-mode two-photon Rabi model

“…Interest in the model and its extensions to multilevel systems and multiple modes continues, as such systems have presented many exciting experimental opportunities to explore rich physical phenomena [16][17][18][19][20][21][22][23][24][25][26][27][28]. In particular, cavity and circuit QED experiments have proposed constructions of quantum switches [29][30][31][32][33], single-photon transistors [34], and various two-qubit gates [35,36].…”