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Physical Review A

Nonperturbative effects of deep strong light-matter interaction in a mesoscopic cavity-QED system

Andrey Kudlis, D. Novokreschenov, Ivan V. Iorsh, I. V. Tokatly

Published Nov 13, 2023• 1 citation
Publisher

Abstract

The authors quantitatively describe the nonperturbative correlations in finite- size cavity quantum electrodynamics (cavity QED) systems. They track the onset of these correlations as the system departs from the thermodynamic limit. They propose an experimental setup, where these correlations can be directly probed.
DOI
10.1103/physreva.108.l051701

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We present a systematic study of the properties of systems composed of NNN two-level quantum emitters coupled to a single cavity mode, for light-matter interaction strengths ranging from the weak to the ultrastrong and deep-strong coupling regimes. Beginning with an analysis of the energy spectrum as a function of the light-matter coupling strength, we examine systems with varying numbers of emitters, from a pair to large collections, approaching the thermodynamic limit $(N\ensuremath{\rightarrow}\ensuremath{\infty})$. Additionally, we explore the emission properties of these systems under incoherent excitation of the emitters, employing a general theoretical framework for open cavity-QED systems, which is valid across all light-matter interaction regimes and preserves gauge invariance within truncated Hilbert spaces. Furthermore, we study the influence of the emitter-environment interaction on the spectral properties of the system. Specifically, when each emitter interacts independently with its own reservoir, we observe the emergence of an emission peak at the cavity's resonant frequency for even values of NNN. Our analysis also clarifies the evolution of the system as the number of emitters increases, ultimately converging toward an equivalent system composed of two interacting single-mode bosonic fields.
Quantum light-matter systems at strong coupling are notoriously challenging to analyze due to the need to include states with many excitations in every coupled mode. We propose a nonperturbative approach to analyze light-matter correlations at all interaction strengths. The key element of our approach is a unitary transformation that achieves asymptotic decoupling of light and matter degrees of freedom in the limit where light-matter interaction becomes the dominant energy scale. In the transformed frame, truncation of the matter or photon Hilbert space is increasingly well justified at larger coupling, enabling one to systematically derive low-energy effective models, such as tight-binding Hamiltonians. We demonstrate the versatility of our approach by applying it to concrete models relevant to electrons in crystal potential and electric dipoles interacting with a cavity mode. A generalization to the case of spatially varying electromagnetic modes is also discussed.
We address the fundamental question of whether or not it is possible to achieve conditions under which the coupling of a single dipole to a strongly confined electromagnetic vacuum can result in nonperturbative corrections to the dipole's ground state. To do so we consider two simplified, but otherwise rather generic cavity QED setups, which allow us to derive analytic expressions for the total ground-state energy and to distinguish explicitly between purely electrostatic and genuine vacuum-induced contributions. Importantly, this derivation takes the full electromagnetic spectrum into account while avoiding any ambiguities arising from an ad hoc mode truncation. Our findings show that while the effect of confinement per se is not enough to result in substantial vacuum-induced corrections, the presence of high-impedance modes, such as plasmons or engineered LC resonances, can drastically increase these effects. Therefore, we conclude that with appropriately designed experiments it is at least in principle possible to access a regime where light-matter interactions become nonperturbative.
We study a generic cavity-QED system where a set of (artificial) two-level dipoles is coupled to the electric field of a single-mode LCLCLC resonator. This setup is used to derive a minimal quantum mechanical model for cavity QED, which accounts for both dipole-field and direct dipole-dipole interactions. The model is applicable for arbitrary coupling strengths and allows us to extend the usual Dicke model into the nonperturbative regime of QED, where the dipole-field interaction can be associated with an effective fine-structure constant of order unity. In this regime, we identify three distinct classes of normal, superradiant, and subradiant vacuum states and discuss their characteristic properties and the transitions between them. Our findings reconcile many of the previous, often contradictory predictions in this field and establish a common theoretical framework to describe ultrastrong-coupling phenomena in a diverse range of cavity-QED platforms.