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arXiv:2309.15788 · Optica Quantum

Reconciling quantum and classical spectral theories of ultrastrong coupling: role of cavity bath coupling and gauge corrections

Stephen Hughes, Chris Gustin, Franco Nori

Published Mar 8, 2024• 13 citations
arXivHTMLPDF

Abstract

Cavity quantum-electrodynamics (QED) is a rich area of optical physics, where extreme light–matter coupling can give rise to ultrastrong coupling. The ultrastrong coupling regime presents some fascinating uniquely quantum mechanical effects, such as ground state virtual photons and vacuum squeezing. Focusing on the widely adopted Hopfield model with cavity dissipation, we show how the linear spectrum of an ultrastrong coupled cavity and a dipole can be described either classically or quantum mechanically, but only when the quantum model includes (i) corrections to maintain gauge invariance, and (ii) a specific type of cavity bath coupling, which has so far not been identified. We also show the impact of this bath model on the quantum Rabi model, which has no classical analog in ultrastrong coupling. These results can be used to guide emerging experiments and significantly impact current models and interpretations of ultrastrong coupling between light and matter.

DOI
10.1364/opticaq.519395

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Cavity quantum-electrodynamics (QED) is a rich area of optical physics, where extreme light–matter coupling can give rise to ultrastrong coupling. The ultrastrong coupling regime presents some fascinating uniquely quantum mechanical effects, such as ground state virtual photons and vacuum squeezing. Focusing on the widely adopted Hopfield model with cavity dissipation, we show how the linear spectrum of an ultrastrong coupled cavity and a dipole can be described either classically or quantum mechanically, but only when the quantum model includes (i) corrections to maintain gauge invariance, and (ii) a specific type of cavity bath coupling, which has so far not been identified. We also show the impact of this bath model on the quantum Rabi model, which has no classical analog in ultrastrong coupling. These results can be used to guide emerging experiments and significantly impact current models and interpretations of ultrastrong coupling between light and matter.
Phenomenological approaches to photon loss have long been the workhorse of cavity-QED, but prove inadequate in the presence of sufficiently broadband light-matter interactions. We present a rigorous and ab initio derivation of a quantum master equation for a quantized optical cavity mode coupled to a dipole, using a quasinormal mode (QNM) quantization procedure for plasmonic and dielectric open-system cavity-QED, which is valid in broadband light-matter interaction regimes, including ultrastrong coupling (USC). The theory supports general three-dimensional resonators with arbitrary dispersion and loss, and thus can be applied to a wide range of realistic open cavities. Our ab initio and gauge-invariant approach fully recovers a recent result for the spectral density of a quantized cavity with a single dipole and reveals important departures from previous heuristic assumptions about system-reservoir coupling. We identify a new criterion for what we term the "broadband dissipative" regime of cavity-QED, where phenomenological models require corrections in accordance with the intrinsic and spatially-dependent complex phase of the QNM, and also shed light on fundamental limits to single-mode models in extreme coupling regimes. Using experimentally motivated plasmonic and dielectric cavity examples, we show validity ranges of our QNM master equation and spectral USC calculations, and discuss prospects for near-term experimental observation of the broadband dissipative effects.
The interaction between quantized electromagnetic fields in cavities and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interactions and quantum technologies.Recently, new regimes beyond the weak and strong light-matter coupling of cavity-QED have been explored in several settings, wherein the light-matter coupling rate becomes comparable to (ultrastrong coupling) or even exceeds (deep-strong coupling) the photon frequency.These ultrastrong coupling regimes can give rise to new physical effects and applications, and they challenge our understanding of cavity QED; fundamental issues like the proper definition of subsystems, their quantum measurements, the structure of light-matter ground states, and the analysis of time-dependent interactions are subject to gauge ambiguities that lead to even qualitatively distinct predictions.The resolution of these ambiguities is important for understanding and designing next-generation quantum devices that can operate in extreme coupling regimes.Here we discuss and provide solutions to these ambiguities by adopting an approach based on operational procedures involving measurements on the individual light and matter components of the interacting system.
We revisit the derivation of Rabi- and Dicke-type models, which are commonly used for the study of quantum light-matter interactions in cavity and circuit QED. We demonstrate that the validity of the two-level approximation, which is an essential step in this derivation, depends explicitly on the choice of gauge once the system enters the ultrastrong-coupling regime. In particular, while in the electric dipole gauge the two-level approximation can be performed as long as the Rabi frequency remains much smaller than the energies of all higher-lying levels, it can dramatically fail in the Coulomb gauge, even for systems with an extremely anharmonic spectrum. We extensively investigate this phenomenon both in the single-dipole (Rabi) and multidipole (Dicke) case, and consider the specific examples of dipoles confined by double-well and square-well potentials, and of circuit QED systems with flux qubits coupled to an LC resonator.
A quantum dipole interacting with an optical cavity is one of the key models in cavity quantum electrodynamics (cavity-QED). To treat this system theoretically, the typical approach is to truncate the dipole to two levels. However, it has been shown that in the ultrastrong-coupling regime, this truncation naively destroys gauge invariance. By truncating in a manner consistent with the gauge principle, we introduce master equations to compute gauge-invariant emission spectra and quantum correlation functions which show significant disagreement with previous results obtained using the standard quantum Rabi model, with quantitative differences already present in the strong coupling regime. Explicit examples are shown using both the dipole gauge and the Coulomb gauge.
Ultrastrong-coupling between an effective two-level system and radiation offers immense potential for advancing both fundamental and applied quantum electrodynamics (QED). Such regimes cannot be treated using the rotating-wave approximation, which applied to the quantum Rabi model yields the apparently less fundamental Jaynes-Cummings model. However, the implications of gauge-freedom for ultrastrong-coupling QED are yet to be recognised. Here we show that when truncating the material system to only two levels, each gauge gives a different effective description whose predictions can vary significantly for ultrastrong-coupling. Rabi models are obtained through specific gauge choices, but so too is a Jaynes-Cummings model without needing the rotating-wave approximation. Analysing a circuit QED setup, we find that this Jaynes-Cummings model is not only valid well beyond the rotating-wave approximation, it is often more accurate than the Rabi model. Among the many implications of this finding is that the system's ground state is not necessarily highly entangled, which is usually considered a hallmark of ultrastrong-coupling light-matter physics.
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 light–matter 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. In this article, a broad overview of the recent progress is given, 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. The validity of effective Hamiltonians for the different experimental platforms is discussed in the last part of the article, addressing recent debates on fundamental issues related to gauge invariance in the ultrastrong‐coupling regime.