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arXiv:2004.13738

Cavity quantum electrodynamics of strongly correlated dipolar matter

Michael Schuler, Daniele De Bernardis, Andreas Martin Läuchli, Peter Rabl

Published Apr 28, 2020• 0 citations
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Abstract

The structure of solids and their phases is mainly determined by static Coulomb forces while the coupling of charges to the dynamical, i.e., quantized degrees of freedom of the electromagnetic field plays only a secondary role. Recently, it has been speculated that this general rule can be overcome in the context of cavity quantum electrodynamics (QED), where the coupling of dipoles to a single field mode can be dramatically enhanced. Here we present a first exact analysis of the ground states of a dipolar cavity QED system in the non-perturbative coupling regime, where electrostatic and dynamical interactions play an equally important role. Specifically, we show how strong and long-range vacuum fluctuations modify the states of dipolar matter and induce novel phases with unusual properties. Beyond a purely fundamental interest, these general mechanisms can be important for potential applications, ranging from cavity-assisted chemistry to quantum technologies based on ultrastrongly coupled circuit QED systems.

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The structure of solids and their phases is mainly determined by static Coulomb forces while the coupling of charges to the dynamical, i.e., quantized degrees of freedom of the electromagnetic field plays only a secondary role. Recently, it has been speculated that this general rule can be overcome in the context of cavity quantum electrodynamics (QED), where the coupling of dipoles to a single field mode can be dramatically enhanced. Here we present a first exact analysis of the ground states of a dipolar cavity QED system in the non-perturbative coupling regime, where electrostatic and dynamical interactions play an equally important role. Specifically, we show how strong and long-range vacuum fluctuations modify the states of dipolar matter and induce novel phases with unusual properties. Beyond a purely fundamental interest, these general mechanisms can be important for potential applications, ranging from cavity-assisted chemistry to quantum technologies based on ultrastrongly coupled circuit QED systems.
When in a quantum optical system the coupling between matter and cavity mode becomes comparable to the bare excitation frequency, we enter a non-perturbative coupling regime, as perturbation theory fails describing the system’s dynamics. While recent advances in Cavity Quantum Electrodynamics allowed to achieve very high values of the coupling strength, thanks to the resonators properties optimization and the employment of solid-state devices, an ever growing interest has been shown about the possibility of significantly modify materials’ properties. It has been demonstrated that the chemical structure of molecules strongly coupled to a photon mode can be altered, which opens the possibility to manipulate and control chemical reactions. The aim of this thesis is to explore non-perturbative regimes on several quantum systems, and to investigate the effects of the coupling upon their properties, such as internal degrees of freedom or electronic states structure. I first developed a novel theory to determine the polariton spectrum of a dipolar ensamble in which a Ising-like dipole-dipole interaction in the 2 non-perturbative regime is considered. A further important focus is the investigation of the saturation effects due to the inclusion of the inter-dipole interaction, and the interplay between the latter and light-matter coupling strength. I also explored specifically the influence of the coupling on the rotational degrees of freedom of an ensemble of two-dimensional freely rotating dipoles, all coupled to a single cavity mode, finding that they are driven by the collective light-matter coupling to undergo a crossover between an isotropic and an aligned phase. I then investigated the case of cavity-embedded doped quantum wells, demonstrating that not only it is possible to couple a discrete cavity mode and bound-to-continuum transitions, but also that a novel bound exciton state appears, induced by the coupling strength. This results shows how light–matter coupling can be used to tune both optical and electronic properties of semiconductor heterostructures beyond those permitted by mere crystal properties. Finally, I explored the physics of an array of THz metamaterial resonators coupled to cyclotron resonances of a two-dimensional electron gas, developing a multiple-mode theory that takes in account the interaction between multiple photon modes mediated by the electrons. My results show that this cross-interaction, due to the strong two-dimensional geometry of the optically active medium, leads to the hybridization of different uncoupled photon modes, and manifests as a visible change of the distribution of the coupled electromagnetic field.
We propose a generalized system of nonequilibrium cavity QED with interacting dipoles coupled to a single-mode of an electromagnetic field in strong-, ultrastrong-, and deep-strong-coupling regimes. To illustrate the applicability of the system, an extended Dicke model is developed for atoms undergoing Raman transitions between the ground states in the presence of laser fields and considering dipole-dipole interactions; the latter has been neglected in many previous works. We have studied the effect of a ferroelectric and an antiferroelectric arrangement on the phase transition for both a finite and an infinite number of dipoles. An additional superradiant phase is observed in the deep-strong-coupling regime due to influence of the dipole-dipole interaction term. A high degree of dipole-dipole entanglement occurs for the antiferroelectric arrangement in the deep-strong regime, whereas it gets disentangled quite rapidly for the ferroelectric arrangement. A sharp transition of system parameters is observed in the ultrastrong-coupling regime and beyond. The dipole-dipole interaction also influences the spectra of the system, inducing a significant shift in the peaks, and modifies the average number of photons emitted.
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.
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.
Interfacing materials with electromagnetic cavities offers a route to modify equilibrium properties through structured vacuum fluctuations. The coupling between light and correlated electrons lacks a characteristic energy scale, making vacuum induced ground state modifications of such systems inherently off-resonant and sensitive to the full photon mode structure. We develop a consistent cavity-QED formalism for dispersive electromagnetic environments in the Coulomb gauge, capturing both dynamical dressing via the vector potential and static screening by the dielectric. With this formalism, we perform a non-perturbative study of the cavity-induced modification of magnetism in the Hubbard model close to half-filling, including all cavity modes and with parameters determined from first principles. At half-filling, we show that the modification of the magnetic exchange interaction JJJ is controlled by a generalized Purcell factor, proportional to the frequency integrated photonic density of states relative to free space. This result identifies polaritonic surface cavities as promising platforms to modify correlated systems. For the surface cavity a competition between static screening and dynamical dressing via the vector potential leads to a net enhancement of JJJ, directly observable in two-magnon Raman spectroscopy. The inclusion of screening is essential to obtain even qualitatively correct results. At weak doping, a variational exact diagonalization of the cavity-coupled ttt-JJJ polaron reveals that a low-frequency surface cavity can reverse the nodal-antinodal dichotomy of the bare polaron dispersion. This effect lies beyond mean field theory and is observable via ARPES measurements. Our framework establishes a concrete design principle linking cavity geometry to material response in the off-resonant regime, which will guide future experimental and theoretical explorations.
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.