Shedding Quantum Light on Strongly Correlated Materials

In this talk I will discuss recent progress in controlling and inducing materials properties with light [1]. Specifically I will discuss recent experiments showing light-induced superconductivity through phonon driving in an organic kappa salt [2] and its possible theoretical explanation via dynamical Hubbard U [3]. I will then highlight some recent theoretical and experimental progress in cavity quantum materials [4], where the classical laser as a driving field of light-induced properties is replaced by quantum fluctuations of light in confined geometries. Ideas and open questions for future work will be outlined. [1] Colloquium: Nonthermal pathways to ultrafast control in quantum materials, A. de la Torre, D. M. Kennes, M. Claassen, S. Gerber, J. W. McIver, M. A. Sentef, Rev. Mod. Phys. 93, 041002 (2021). [2] Photo-molecular high temperature superconductivity, M. Buzzi, D. Nicoletti, M. Fechner, N. Tancogne-Dejean, M. A. Sentef, A. Georges, M. Dressel, A. Henderson, T. Siegrist, J. A. Schlueter, K. Miyagawa, K. Kanoda, M.-S. Nam, A. Ardavan, J. Coulthard, J. Tindall, F. Schlawin, D. Jaksch, A. Cavalleri, Phys. Rev. X 10, 031028 (2020). [3] Dynamical Superconductivity in a Frustrated Many-Body System, J. Tindall, F. Schlawin, M. Buzzi, D. Nicoletti, J. R. Coulthard, H. Gao, A. Cavalleri, M. A. Sentef, D. Jaksch, Phys. Rev. Lett. 125, 137001 (2020). [4] Cavity Quantum Materials,
Frank Schlawin, Dante M. Kennes, Michael A. Sentef,
Applied Physics Reviews Reviews 9, 011312 (2022).
[OA] arXiv:2112.15018

In the first part, we discuss how dipole approximation is violated for itinerant electrons. Examples include integer quantum Hall and Josephson junctions, in the context of circuit-QED. The latter yields rich physics in form of a new type of built-in multi-qubit system with selective coupling to electromagnetic modes of the cavity. In the second part, we discuss how excitons can form in correlated materials. Specially, we discuss how excitons can emerge in Mott insulator systems, in terms of inter- and intra-band bound states, where spin physics plays a crucial role. The relevant physical systems include high-Tc cuprates, 2D materials, and ultracold fermions in optical lattices.

In this talk, we show that strong electron–electron interactions in quantum materials can give rise to electronic transitions that couple strongly to cavity fields, and collective enhancement of these interactions can result in ultrastrong effective coupling strengths. As a paradigmatic example we consider a one-dimensional Fermi–Hubbard model coupled to a single-mode cavity and find that resonant electron-cavity interactions result in the formation of a quasi-continuum of polariton branches. Quantum correlations in the electronic ground state as well as the microscopic nature of the light–matter interaction enhance the collective light–matter interaction compared to an ensemble of independent two-level atoms interacting with a cavity mode.

We have used transport to probe the ultra-strong light-matter coupling, and show now that the latter can induce a breakdown of the integer quantum Hall effect. The phenomenon is explained in terms of cavity-assisted hopping, an anti-resonant process where a an electron can scatter from one edge of the sample to the other by “borrowing” a photon from the cavity. Recent measurements are aiming at better understanding the microscopic nature of the process and the role of the sample geometry in its strength. [1] F. Appugliese et al., “Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect,” Science, vol. 375, no. 6584, pp. 1030–1034, Mar. 2022, doi: 10.1126/science.abl5818.

The quest for phases and phase transitions in general non-unitary quantum dynamics has been spotlighted by the recent discovery of measurement-induced phase transitions. They result from the competition of deterministic Schrödinger and random measurement dynamic, and surface in a qualitative change of the entanglement structure. Here we first introduce instances of entanglement transitions in fermion systems, between a regime of logarithmic entanglement growth, and a quantum Zeno regime obeying an area law. We identify the relevant degrees of freedom driving the phase transition in terms of an effective field theory. This yields a physical picture in terms of a depinning from the measurement operator eigenstates induced by unitary dynamics, and places it into the BKT universality class. In standard quantum mechanical observables however, these transitions are masked due to the degeneracy of measurement outcomes. We then point out a general route of gently breaking this degeneracy - pre-selection - which makes such transitions observable in state-of-the-art quantum platforms. It reveals an intriguing connection to quantum absorbing state transitions.

The time evolution of a quantum system can be strongly affected by dissipation. Although this mainly implies that the system relaxes to a steady state, in some cases it can lead to the appearance of new phases and trigger emergent dynamics. In our experiment, we study a Bose-Einstein Condensate dispersively coupled to a high finesse resonator. The cavity mode is populated via scattering off the atoms, such that the sum of the coupling field and the intracavity standing wave act as optical lattice potential. When the dissipative and the coherent timescales are comparable, we find a regime of persistent oscillations where the cavity field does not reach a steady state. In this regime the atoms experience an optical lattice that periodically deforms itself, without an external time dependent drive, leading to a pumping mechanism.

I will summarize our recent observations of discrete and continuous dissipative time crystals in a Bose-Einstein condensate strongly coupled to a single mode of a recoil resolving optical cavity.

The interplay of pairing with density wave order is one of the most prominent features of strongly correlated electronic systems, such as high-temperature superconductors. In our experiment, we realize a Fermi gas with short and long-range interactions, which can be independently and simultaneously controlled. We combine a quantum degenerate, unitary Fermi gas in a high-finesse optical cavity [1-4] with a pump laser beam, driving the atom-cavity system transversally to the cavity axis in the dispersive regime. This yields a tunable long-range photon-mediated interaction, which allows self-organization to a density wave ordered state above a critical strength. We show that this interaction is broadly tunable, and study the onset of density wave ordering in the BEC-BCS crossover. Our observations are compared with a mean-field theory. Our system offers a new way to study competing orders in strongly correlated matter. [1] K. Roux, H. Konishi, V. Helson, and J.-P. Brantut, “Strongly correlated Fermions strongly coupled to light,” Nat Commun, vol. 11, no. 1, p. 2974, Jun. 2020, doi: 10.1038/s41467-020-16767-8. [2] K. Roux, V. Helson, H. Konishi, and J. P. Brantut, “Cavity-assisted preparation and detection of a unitary Fermi gas,” New J. Phys., vol. 23, no. 4, p. 043029, Apr. 2021, doi: 10.1088/1367-2630/abeb91. [3] H. Konishi, K. Roux, V. Helson, and J.-P. Brantut, “Universal pair polaritons in a strongly interacting Fermi gas,” Nature, pp. 1–5, Aug. 2021, doi: 10.1038/s41586-021-03731-9. [4] V. Helson, T. Zwettler, K. Roux, H. Konishi, S. Uchino, and J.-P. Brantut, “Optomechanical Response of a Strongly Interacting Fermi Gas,” arXiv:2111.02931 [cond-mat, physics:physics, physics:quant-ph], Nov. 2021, [Online]. Available: http://arxiv.org/abs/2111.02931

We explore the many-body phases of a two-dimensional Bose-Einstein condensate with cavity-mediated dynamic spin-orbit coupling. With the help of two transverse noninterfering, counterpropagating pump lasers and a single standing-wave cavity mode, two degenerate Zeeman sub-levels of the quantum gas are Raman coupled in a double-Λ-configuration. Beyond a critical pump strength the cavity mode is populated via coherent superradiant Raman scattering from the two pump lasers, leading to the appearance of a dynamical spin-orbit coupling for the atoms. We identify three quantum phases with distinct atomic and photonic properties: the normal “homogeneous” phase, the superradiant “spin-helix” phase, and the superradiant “supersolid spin-density-wave” phase.

Exposing a many-body system to external drives and losses can transform the nature of its phases and opens perspectives for engineering new properties of matter. How such characteristics are related to the underlying microscopic processes of the driven and dissipative system is a fundamental question. I will discuss this point on a recent experiment (conducted at the Quantum Optics group at ETH) with a quantum gas that is strongly coupled to a lossy optical cavity mode using two independent Raman drives. The latter act on the spin and motional degrees of freedom of the atoms. This setting allows for control of the competition between coherent dynamics and dissipation by adjusting the imbalance between the drives. For strong enough coupling, the transition to a superradiant phase occurs, as is the case for a closed system. Yet, by imbalancing the drives, a dissipation-stabilized normal phase manifests alongside a region of multistability. Measuring the properties of excitations on top of the out-of-equilibrium phases reveals the microscopic elementary processes in the open system. Our findings provide prospects for studying squeezing in non-Hermitian systems, quantum jumps in superradiance, and dynamical spin-orbit coupling in a dissipative setting.

While there is currently a considerable interest in vacuum-modifications of material properties, such as chemical reactivity, conductivity or phase transitions, theoretical predictions of such effects usually rely on effective single- or few-mode models. These models ignore the coupling to the infinite number of electromagnetic modes that the vacuum is actually comprised of and are therefore fundamentally incapable of making reliable predictions about the magnitude or even the sign of vacuum energy shifts. In this talk I will present a first-principle derivation of the ground state energy shift of a single molecular dipole in ultrastrong coupling cavity QED. This analysis provides a clear distinction between purely electrostatic and genuine vacuum effects and allows us to study both contributions as a function of the relevant system parameters. Finally, I will address the implications of these findings for experimental and theoretical research in this field.

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 phase transitions to a photon condensate state when the cavity-photon mode is assumed to be {\it spatially uniform}. However, 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. It has also been recently shown that truncation of the Hilbert space of the matter system can affect the gauge invariance of the theory. However, it is always possible to obtain approximate Hamiltonians obeying the gauge principle in the truncated Hilbert space. Here, we demonstrate a general no-go theorem for truncated, gauge-invariant models, which forbids first-order {\it as well} as second-order superradiant phase transitions in the absence of a magnetic field, in agreement with the general theory. Finally, we show that the no-go theorem does not apply to {\it spatially-varying} quantum cavity fields. We find a criterion for the occurrence of photon condensation that depends solely on the static, non-local orbital magnetic susceptibility $\chi_{\rm orb}(q)$, of the electronic system (ES) evaluated at a cavity photon momentum $\hbar q$. Only 3D ESs satisfying the Condon inequality $\chi_{\rm orb}(q)>1/(4\pi)$ can harbor photon condensation. For the experimentally relevant case of two-dimensional (2D) ESs embedded in quasi-2D cavities the criterion again involves $\chi_{\rm orb}(q)$ but also the vertical size of the cavity. We use these considerations to identify electronic properties that are ideal for photon condensation. Our theory is non-perturbative in the strength of electron-electron interaction and therefore applicable to strongly correlated ESs.

We derive an arbitrary gauge criterion under which condensed matter within an electromagnetic field may transition to a photon condensed phase. Previous results are recovered by selecting the Coulomb gauge wherein photon condensation can only occur for a spatially-varying field and can be interpreted as a magnetic instability. We demonstrate the gauge-invariance of our description directly, but since matter and photons are gauge-relative concepts we find more generally that photon condensation can occur within a spatially uniform field, and that the relative extent to which the instability is both magnetic and electric versus purely magnetic depends on the gauge.

In this talk I will present a theory for the out-of-equilibrium dynamics of many-body cavity QED which is systematically derived starting from the master equation of a quantum gas of scatterers strongly coupled to a high-finesse resonator. I will then discuss the relaxation dynamics after slow and sudden quenches and compare the predictions with experimental measurements.

We investigate the full quantum evolution of ultracold interacting bosonic atoms on a chain and coupled to an optical cavity. Extending the time-dependent matrix product state techniques and the many-body adiabatic elimination techniques to capture the global coupling to the cavity mode and the open nature of the cavity, we examine the long time behavior of the system beyond the mean-field elimination of the cavity field. We show that the fluctuations beyond the mean-field state change the nature of the dissipative phase transition, giving a mixed state character to the self-organized steady states. In the case of ideal bosons coupled to the cavity, the open system exhibits a strong symmetry which leads to the existence of conservation laws and multiple steady states. In each symmetry sector a dissipative phase transition occurs at a different critical point, implying a coexistence of phases of very different natures. We find that the introduction of a weak breaking of the strong symmetry by a small interaction term leads to a direct transition from multiple steady states to a unique steady state.

The interplay of light and matter can give rise to intriguing cooperative effects in quantum many-body systems. At strong light-matter coupling, phase transitions in condensed matter may be modified even by the vacuum fluctuations of the electromagnetic field, because collective modes of a solid get dressed by virtual photons. A sizeable effect of the light-matter coupling can be achieved in two cases: (i) For a small system which strongly couples to few modes, or even a single mode of the electromagnetic field [1], and (ii), for a macroscopic solid, if the electromagnetic field can be engineered such that it couples to momenta in a large portion of the Brillouin zone. In this project, we focus on the second situation. The light-mediated interactions are treated using bosonic dynamical mean-field theory (DMFT). We consider a model of a two-dimensional material that couples to a surface plasmon polariton (SPP) mode of a metal-dielectric interface. In mean-field approximation, the system exhibits a ferroelectric phase transition that is not modified by the light- matter coupling. Bosonic DMFT allows to go beyond this simplified description and reveals that the photon-mediated interactions enhance the ferroelectric order and stabilize the ferroelectric phase over a larger range of parameters. [1] K. Lenk, J. Li, P. Werner, and M. Eckstein, arXiv:2205.05559.

In this talk, I will introduce the notion of frustrated superradiant phases of coupled light and matter [1]. Frustration occurs when a system cannot find the lowest-energy configuration due to conflicting constraints. I will show that a lattice of interacting bosons can be frustrated when the ground-state coherence of bosonic modes due to the strong local qubit-boson interaction cannot simultaneously minimize the positive hopping energies. The emergent frustrated superradiant phase exhibits exotic properties such as the coexistence of two diverging time scales at the critical point and site-dependent critical exponents. Moreover, we demonstrate that, by introducing a synthetic magnetic field to the lattice of bosons through the engineering of complex hopping energies, a plethora of exotic frustrated phases emerge as one varies the total flux due to the interplay between the time-reversal symmetry breaking and frustration of lights. We will discuss potential experimental realizations using quantum optical systems. [1] J. Zhao and M. -J. Hwang, Physical Review Letters 128 163601 (2022)

One very successful approach to photonic system engineering consists in controlling ensembles of coupled nonlinear photonic resonators. Fascinating properties emerge at the confluence between condensed matter physics and nonlinear optics: light can undergo Bose-Einstein condensation, behave as a superfluid, or propagate along edge channels in topological lattices. One ingredient at the heart of the system is the driving field, which enables maintaining a non-equilibrium steady-state. Drive and dissipation thus provide two important control parameters, that govern the physics of the system. In this talk, I will focus on two situations where the driven-dissipative nature of the system plays a key role in the physics of polariton lattices. I will start with a general introduction to polariton physics and polariton lattices [1]. I will then present two recent experiments realized at C2N in 1D lattices. In the first experiment, we investigated the non-linear optical properties of a 1D topological lattice under resonant excitation, and found pumping conditions where the nonlinear steady-state triggers the emergence of an edge state in the Bogoliubov excitation spectrum [2]. In the second experiment, we explored the physics of out-of-equilibrium Bose-Einstein condensates and evidenced universal scaling laws related to the Kardar–Parisi–Zhang universality class [3]. References: [1] C. Ciuti and I. Carusotto, Quantum fluids of light, Rev. Mod. Phys. 85, 299 (2013). [2] N. Pernet et al., Gap solitons in a one-dimensional driven-dissipative topological lattice, Nature Physics 18, 678 (2022). [3] Q. Fontaine et al., Observation of KPZ universal scaling in a one-dimensional polariton condensate, arXiv:2112.09550 (2021).

Driven-dissipative quantum fluids of light, experimentally realised in for example semiconductor microcavities, circuit or cavity QED systems, provide a unique testbed to explore new non-equilibrium quantum phenomena. I will review recent progress in this field. In particular, we show that polariton quantum fluid can exhibit a non-equilibrium order, where superfluidity is accompanied by stretched exponential decay of correlations. This celebrated Kardar-Parisi-Zhang (KPZ) phase has not been achieved before in any system in 2D and even 1D realisations are not conclusive. I will then discuss how these systems can undergo other unconventional phase transitions and orders, and display flow properties connected but distinct from conventional superfluidity. Finally, when placed in strained honeycomb lattice potentials, polariton fluids can condense into a rotating state, the lowest Landau level, forming a vortex array and spontaneously breaking time reversal symmetry.

Exciton-polaritons, mixed states of confined photons and electron-hole pairs in semiconductors, are attracting increasing interest for the study of non-Hermitian macroscopic quantum phenomena, further appealed by their relatively easy way of being created, controlled and observed in solid state devices. Here we will discuss recent observations of some intriguing effects in polariton condensates exploiting their relatively strong nonlinearities, their peculiar dispersion and the possibility of controlling, their out-of-equilibrium character. In particular, we will show how such quantum fluids can be a perfect platform for studying quantum turbulence related phenomena with simultaneous mapping of the flow velocity and thousands of vortex states under their ultrafast dynamics. Moreover, tailoring their dispersion we will observe how the realisation of ad hoc photonic structures can lead to interesting combination of quantum fluid dynamics in specific topological bands realised in semiconductor microcavities or patterning polariton waveguides. Eventually we will also speculate on the possibility to work in the genuine quantum regime of single polaritons for the implementation of correlated quantum systems.

I will discuss three different aspects of the interaction between strong matter-light coupling and electrically charged (doped) systems. 1. Considering electrical doping in an inorganic semiconductor affects the nature of excitonic and polaritonic pairing. By considering a two-dimensional charge-imbalanced electron-hole systems in an optical microcavity, we found that strong coupling to photons favors states with pairing at zero or small center-of-mass momentum, leading to a condensed state with spontaneously broken time-reversal and rotational symmetry and unpaired carriers that occupy an anisotropic crescent-shaped sliver of momentum space. I will discuss the phase diagram of this system, and some open questions raised by this work. 2. Considering again an inorganic semiconductor, in the few excitation limt, I will discuss dressing of excitons by excitations of the Fermi surface, and the nature of polaron formation due to this dressing. I will discuss the difference between cases where the carriers forming the exciton are distinguishable or indistinguishable from those doping the system. 3. Considering organic polariton systems, I will discuss how the presence of a polariton condensate affects the incoherent hopping of charges. [1] Artem Strashko, Francesca M. Marchetti, Allan H. MacDonald, and Jonathan Keeling. Phys. Rev. Lett. 125, 067405 (2020) [2] Antonio Tiene, Jesper Levinsen, Jonathan Keeling, Meera M. Parish, and Francesca M. Marchetti Phys. Rev. B 105, 125404 (2022) [3] M. Ahsan Zeb, Peter G. Kirton, Jonathan Keeling. arXiv: 2004.09790

Recent advances in the strong coupling of solid state materials to photons and the quantitative experimental study of the arising hybrid system have made it necessary to develop new theoretical tools, required for a systematic explanation of the observed phenomena. In this talk I will specifically address the time-evolution of polaron-polaritons in a two-dimensional semiconductor irradiated by an intense light pulse to explain the fundamental challenges these experiments pose to the development of theoretical models. Taking these into account, I will present a newly developed approach based on non-equilibrium Green's functions and highlight our recent advances towards the quantitative description of the dynamics of highly excited many-body systems.

In this talk, I will propose that a prompt quench from a metal into a transient superconducting state induces large Higgs fluctuations of the order parameter. I will demonstrate that these fluctuations give rise to the amplification of light at frequencies below the superconducting gap. I will show recent measurements on K$_3$C$_{60}$, in which these predictions are verified experimentally.

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 a 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 a novel approach to measure universal properties without direct matter probes.

Intense laser-matter interactions are at the center of interest in research and technology since the development of high power lasers. They have been widely used for fundamental studies in atomic, molecular, and optical physics, and they are at the core of attosecond physics and ultrafast opto-electronics. Although the majority of these studies have been successfully described using classical electromagnetic fields, recent investigations based on fully quantized approaches have shown that intense laser-atom interactions can be used for the generation of controllable high-photon-number entangled coherent states and coherent state superposition. We provide a comprehensive fully quantized description of intense laser-atom interactions. We elaborate on the processes of high-harmonic generation, above-threshold-ionization, and we discuss new phenomena that cannot be revealed within the context of semi-classical theories. We provide the description for conditioning the light field on different electronic processes, and their consequences for quantum state engineering of light. Finally, we discuss the extension of the approach to more complex materials, and the impact to quantum technologies for a new photonic platform composed by the symbiosis of attosecond physics and quantum information science.

An important challenge in non-Markovian open quantum systems is to understand what information we gain from continuous measurement of an output field. For example, atoms in multimode cavity QED systems provide an exciting platform to study many-body phenomena in regimes where the atoms are strongly coupled amongst themselves and with the cavity, but the strong coupling makes it complicated to infer the conditioned state of the atoms from the output light. In this work we address this problem, describing the reduced atomic state via a conditioned hierarchy of equations of motion, which provides an exact conditioned reduced description under monitoring (and continuous feedback). We utilize this formalism to study how different monitoring for modes of a multimode cavity affects our information gain for an atomic state, and to improve spin squeezing via measurement and feedback in a strong coupling regime. This work opens opportunities to understand continuous monitoring of non-Markovian open quantum systems, both on a practical and fundamental level.