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arXiv:2207.06444 · Physical review. B./Physical review. B

Critical light-matter entanglement at cavity mediated phase transitions

Giuliano Chiriacò, Marcello Dalmonte, Titas Chanda

Published Oct 6, 2022• 19 citations
arXivHTMLPDF

Abstract

We consider a model of a light-matter system, in which a system of fermions (or bosons) is coupled to a photonic mode that drives phase transitions in the matter degrees of freedom. Starting from a simplified analytical model, we show that the entanglement between light and matter vanishes at small and large coupling strength and shows a peak in the proximity of the transition. We perform numerical simulations for a specific model (relevant to both solid state and cold atom platforms) and show that the entanglement displays critical behavior at the transition and features maximum susceptibility, as demonstrated by a maximal entanglement capacity. Remarkably, light-matter entanglement provides direct access to critical exponents, suggesting another approach to measure universal properties without direct matter probes.

DOI
10.1103/physrevb.106.155113

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We consider a model of a light-matter system, in which a system of fermions (or bosons) is coupled to a photonic mode that drives phase transitions in the matter degrees of freedom. Starting from a simplified analytical model, we show that the entanglement between light and matter vanishes at small and large coupling strength and shows a peak in the proximity of the transition. We perform numerical simulations for a specific model (relevant to both solid state and cold atom platforms) and show that the entanglement displays critical behavior at the transition and features maximum susceptibility, as demonstrated by a maximal entanglement capacity. Remarkably, light-matter entanglement provides direct access to critical exponents, suggesting another approach to measure universal properties without direct matter probes.
A quantum critical point develops when matter undergoes a continuous transformation between distinct ground states at absolute zero. It hosts pronounced quantum fluctuations, which render the system highly susceptible to external perturbations. While light-matter coupling has rapidly moved forward as a means to probe and control quantum materials, the capacity of quantum critical fluctuations in the photon-mediated responses has been largely unexplored. Here we advance the notion that directly coupling a quantum critical mode to a quantized cavity field dramatically facilitates the realization of the elusive superradiant phase transition in equilibrium, circumventing at once the key obstacles that have prevented its attainment in spite of decades of pursuit. The superradiant phase transition develops far below the ultrastrong regime of light-matter couplings, and the transition is accompanied by the light-matter hybrid system showing strongly enhanced intrinsic squeezing and amplified quantum Fisher information. We also identify candidate cavity quantum materials platforms for validating the proposed effect. Our findings suggest a general principle by which quantum criticality amplifies the response to cavity photons. They also demonstrate that cavity coupling accesses the elevated quantum entanglement of the underlying matter at quantum criticality, thereby pointing to a pathway towards realizing the potential of highly collective quantum materials to expand the capacities of quantum information science. Quantum critical systems host strong fluctuations that can enhance their response to external fields. Here the authors show that directly coupling cavity-bound photons to a quantum critical material produces highly correlated light-matter states at modest light-matter couplings that access the matter’s enhanced quantum entanglement.
The hybridization between light and matter forms the basis to achieve cavity control over quantum materials. In this Letter we investigate a cavity coupled to a quantum chain of interacting spinless fermions by numerically exact solutions and perturbative analytical expansions. We draw two important conclusions about such systems: (i) Specific quantum fluctuations of the matter system play a pivotal role in achieving entanglement between light and matter; and (ii) in turn, light-matter entanglement is a key ingredient to modify electronic properties by the cavity. We hypothesize that quantum fluctuations of those matter operators to which the cavity modes couple are a general prerequisite for light-matter entanglement in the ground state. Implications of our findings for light-matter-entangled phases, cavity-modified phase transitions in correlated systems, and measurement of light-matter entanglement through Kubo response functions are discussed.
When light and matter are weakly coupled, they can be described as two distinctive systems exchanging quanta of energy. By contrast, for very large coupling strength, the systems hybridize and form compounds that cannot be described in terms of light or matter only. In this Thesis, we study some exotic properties which arise in this regime. In particular, we are interested in the possibility to engineer quantum phase transitions in these systems. One direction we explore is the study of two-photon coupling, a mechanism in which matter creates or absorb photons by pairs. This mechanism creates a rich phase diagram containing both phase transitions and instabilities. A second topic is the use of these transitions for sensing applications. Indeed, near the critical point, the system becomes extremely sensitive to external perturbations. We study a setup in which a single qubit is coupled to a bosonic field. We show that even this finite-size system displays a phase transition, which can be used to measure the frequency of the qubit and the field with improved accuracy. This protocol could be used to develop small-scale sensors. Finally, we study how the ability of a system to perform certain metrological tasks could be used to characterize and quantify nonclassicality, by using the formalism of resource theories. The first three chapters present the main concepts and key results in the fields of ultrastrong light-matter coupling, superradiant phase transitions, and quantum metrology. I have strived to write these chapters pedagogically; they can be used by non-specialists or students as an introduction to these domains. The three other chapters present my own research contributions. Although most of those have already been published elsewhere, this manuscript contains additional results, remarks, and perspectives, and should be considered as an improved version of the original papers.
Systems of strongly interacting atoms and photons, which can be realized wiring up individual cavity QED systems into lattices, are perceived as a new platform for quantum simulation. While sharing important properties with other systems of interacting quantum particles, here we argue that the nature of light-matter interaction gives rise to unique features with no analogs in condensed matter or atomic physics setups. By discussing the physics of a lattice model of delocalized photons coupled locally with two-level systems through the elementary light-matter interaction described by the Rabi model, we argue that the inclusion of counterrotating terms, so far neglected, is crucial to stabilize finite-density quantum phases of correlated photons out of the vacuum, with no need for an artificially engineered chemical potential. We show that the competition between photon delocalization and Rabi nonlinearity drives the system across a novel Z(2) parity symmetry-breaking quantum criticality between two gapped phases that share similarities with the Dicke transition of quantum optics and the Ising critical point of quantum magnetism. We discuss the phase diagram as well as the low-energy excitation spectrum and present analytic estimates for critical quantities.
The Hubbard model on the honeycomb lattice is a pristine realisation of a semimetal-to-insulator Mott transition belonging to the O(3) Gross-Neveu universality class. We couple this system to a single linearly polarised, uniform cavity photon mode. For this interacting light-matter model, we formulate a negative-sign-free fermion quantum Monte Carlo algorithm that allows for unbiased results on finite system sizes. Our numerical results show that the coupling to the cavity is irrelevant at criticality, even at strong electron-photon coupling. On the other hand, we observe, and show analytically, that the photon spectrum acquires finite corrections in the form of the optical conductivity. In the semimetal phase, gapless particle-hole excitations produce a low-energy polaritonic mode, which is suppressed in the Mott insulator phase. Furthermore, we show that the photon spectra can be used to detect universal information about the quantum critical point. Thereby, our results establish that a single, uniform cavity photon mode acts as a contact-free non-invasive probe for Mott criticality. Our results can be generalised to any cavity where an intensive number of uniform linearly polarised photon modes couple to the electronic system.
Recent experiments have demonstrated an open system realization of the Dicke quantum phase transition in the motional degrees of freedom of an optically driven Bose–Einstein condensate in a cavity. Relevant collective excitations of this light–matter system are polaritonic in nature, allowing access to the quantum critical behavior of the Dicke model through light leaking out of the cavity. This opens the path to using photodetection-based quantum optical techniques to study the dynamics and excitations of this elementary quantum critical system. We first discuss the photon flux observed at the cavity face and find that it displays a different scaling law near criticality than that obtained from the mean-field theory for the equivalent closed system. Next, we study the second-order correlation measurements of photons leaking out of the cavity. Finally, we discuss a modulation technique that directly captures the softening of polaritonic excitations. Our analysis takes into account the effect of the finite size of the system, which may result in an effective symmetry-breaking term.