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arXiv:2005.09088 · Physical review. B./Physical review. B

Theory of photon condensation in a spatially varying electromagnetic field

Gian Marcello Andolina, F. M. D. Pellegrino, Vittorio Giovannetti, Allan H. MacDonald, Marco Polini

Published Sep 21, 2020• 108 citations
arXivHTMLPDF

Abstract

Whether or not superradiant phase transitions (photon condensates) can occur in equilibrium systems is a long-debated open question. The realization of photon condensation in a spatially uniform cavity field is forbidden by a ``no-go'' theorem stemming from gauge invariance. Here, bypassing the theorem by considering a spatially varying electromagnetic field, the authors derive a series of criteria for the occurrence of photon condensation. The cases of both three-dimensional and two-dimensional electronic systems are analyzed. This work paves the way for the realization of equilibrium photon condensation in solid-state systems.

DOI
10.1103/physrevb.102.125137

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Whether or not superradiant phase transitions (photon condensates) can occur in equilibrium systems is a long-debated open question. The realization of photon condensation in a spatially uniform cavity field is forbidden by a ``no-go'' theorem stemming from gauge invariance. Here, bypassing the theorem by considering a spatially varying electromagnetic field, the authors derive a series of criteria for the occurrence of photon condensation. The cases of both three-dimensional and two-dimensional electronic systems are analyzed. This work paves the way for the realization of equilibrium photon condensation in solid-state systems.
Equilibrium phase transitions between a normal and a photon condensate state (also known as superradiant phase transitions) are a highly debated research topic, where proposals for their occurrence and no-go theorems have chased each other for the past four decades. Previous no-go theorems have demonstrated that gauge invariance forbids second-order phase transitions to a photon condensate state when the cavity-photon mode is assumed to be spatially uniform. First-order phase transitions were previously considered as possible paths to bypass the no-go theorem. In particular, it has been theoretically predicted that a collection of three-level systems coupled to light can display a first-order phase transition to a photon condensate state. Here, we lay down a general no-go theorem, which forbids first-order as well as second-order superradiant phase transitions in a spatially-uniform cavity field. By using the tools of lattice gauge theory, we then derive a fully gauge-invariant model for three-level systems coupled to light. In agreement with the general theorem, our model does not display photon condensation.
In spite of decades of work it has remained unclear whether or not superradiant quantum phases, referred to here as photon condensates, can occur in equilibrium. In this Rapid Communication, we first show that when a nonrelativistic quantum many-body system is coupled to a cavity field, gauge invariance forbids photon condensation. We then present a microscopic theory of the cavity quantum electrodynamics of an extended Falicov-Kimball model, showing that, in agreement with the general theorem, its insulating ferroelectric and exciton condensate phases are not altered by the cavity and do not support photon condensation.
We introduce a gauge-invariant model of planar, square molecules coupled to a quantized spatially varying cavity electromagnetic vector potential Â(r) . Specifically, we choose a temporally cavity hosting a uniform magnetic field B̂ , as this is the simplest instance in which a transverse spatially varying Â(r) is at play. We show that when the molecules are in the Van Vleck paramagnetic regime, an equilibrium quantum phase transition to a photon condensate state occurs. Published by the American Physical Society 2024
The possibility of a superradiant phase transition in light-matter systems is the subject of much debate, due to numerous apparently conflicting no-go and counter no-go theorems. Using an arbitrary-gauge approach we show that a unique phase transition does occur in archetypal many-dipole cavity QED systems, and that it manifests unambiguously via a macroscopic gauge-invariant polarization. We find that the gauge choice controls the extent to which this polarization is included as part of the radiative quantum subsystem and thereby determines the degree to which the abnormal phase is classed as superradiant. This resolves the long-standing paradox of no-go and counter no-go theorems for superradiance, which are shown to refer to different definitions of radiation.
Abstract We investigate the ground state of two physically motivated modifications of the Dicke model. The first modification corresponds to particles whose phase space contains only two states, for example, artificially created qubits. The second modification describes two-level systems that arise as a result of truncating the full Hilbert space of atoms to two levels that are in resonance with the electromagnetic field and are described by the gauge-invariant Dicke model. We demonstrate that the behavior of these systems is qualitatively distinct in both cases. In particular, in the first scenario, a superradiant phase transition (SPT) into a state with a non-zero amplitude of the classical field is possible, while in the second case, the so-called order parameter η = 〈 a ˆ 〉 which would indicate condensation into a coherent state remains zero, meaning that the SPT is forbidden. It resolves the long-standing discussion about the SPT in the Dicke model. At the same time, the average number of photons n ¯ = 〈 a ˆ † a ˆ 〉 ≠ 0 , and the collective excitation in the system manifests as a non-classical ‘squeezed’ state of the field. We analyze the observable characteristics of both systems in a wide range of variation of their parameters.
The superradiant quantum phase transition (QPT) is of fundamental interest, and has potential applications in modern quantum technology. The existence of an equilibrium superradiant QPT in cavity and circuit QED systems is still debated, though, considering the no-go theorem. Combining cavity QED and optomechanics, the authors predict at thermal equilibrium a single-photon-triggered superradiant QPT that is immune to the no-go theorem. Being able to manipulate a QPT in this manner is expected to inspire both the creation of innovative photonic quantum devices and the exploration of single-photon quantum-criticality physics.