Down-conversion of a single photon as a probe of many-body localization.

Decay of a particle into more particles is a ubiquitous phenomenon to interacting quantum systems, taking place in colliders, nuclear reactors or solids. In a nonlinear medium, even a single photon would decay by down-converting (splitting) into lower-frequency photons with the same total energy1, at a rate given by Fermi's golden rule. However, the energy-conservation condition cannot be matched precisely if the medium is finite and only supports quantized modes. In this case, the fate of the photon becomes the long-standing question of many-body localization, originally formulated as a gedanken experiment for the lifetime of a single Fermi-liquid quasiparticle confined to a quantum dot2. Here we implement such an experiment using a superconducting multimode cavity, the nonlinearity of which was tailored to strongly violate the photon-number conservation. The resulting interaction attempts to convert a single photon excitation into a shower of low-energy photons but fails owing to the many-body localization mechanism, which manifests as a striking spectral fine structure of multiparticle resonances at the standing-wave-mode frequencies of the cavity. Each resonance was identified as a many-body state of radiation composed of photons from a broad frequency range and not obeying Fermi's golden rule theory. Our result introduces a new platform to explore the fundamentals of many-body localization without having to control many atoms or qubits3-9.

Remote gate control of topological transitions in moiré superlattices via cavity vacuum fields.

Placed in cavity resonators with three-dimensionally confined electromagnetic wave, the interaction between quasiparticles in solids can be induced by exchanging virtual cavity photons, which can have a nonlocal characteristic. Here, we investigate the possibility of utilizing this nonlocality to realize the remote control of the topological transition in mesoscopic moiré superlattices at full filling (one electron/hole per supercell) embedded in a split-ring terahertz electromagnetic resonator. We show that gate tuning one moiré superlattice can remotely drive a topological band inversion in another moiré superlattice not in contact but embedded in the same cavity. Our study of remote on/off switching of a topological transition provides a paradigm for the control of material properties via cavity vacuum fields.

Electron-Photon Chern Number in Cavity-Embedded 2D Moiré Materials.

We explore theoretically how the topological properties of 2D materials can be manipulated by cavity quantum electromagnetic fields for both resonant and off-resonant electron-photon coupling, with a focus on van der Waals moiré superlattices. We investigate an electron-photon topological Chern number for the cavity-dressed energy minibands that is well defined for any degree of hybridization and entanglement of the electron and photon states. While an off-resonant cavity mode can renormalize electronic topological phases that exist without cavity coupling, we show that when the cavity mode is resonant to electronic miniband transitions, new and higher electron-photon Chern numbers can emerge.

Dissipative Phase Transition with Driving-Controlled Spatial Dimension and Diffusive Boundary Conditions.

We investigate theoretically and experimentally a first-order dissipative phase transition, with diffusive boundary conditions and the ability to tune the spatial dimension of the system. The considered physical system is a planar semiconductor microcavity in the strong light-matter coupling regime, where polariton excitations are injected by a quasiresonant optical driving field. The spatial dimension of the system from 1D to 2D is tuned by designing the intensity profile of the driving field. We investigate the emergence of criticality by increasing the spatial size of the driven region. The system is nonlinear due to polariton-polariton interactions and the boundary conditions are diffusive because the polaritons can freely diffuse out of the driven region. We show that no phase transition occurs using a 1D driving geometry, while for a 2D geometry we do observe both in theory and experiments the emergence of a first-order phase transition. The demonstrated technique allows all-optical and in situ control of the system geometry, providing a versatile platform for exploring the many-body physics of photons.

Non-Hermitian bath model for arrays of coupled nanoresonators.

Nanophotonics systems have recently been studied under the perspective of non-Hermitian physics. Given their potential for wavefront control, nonlinear optics and quantum optics, it is crucial to develop predictive tools to assist their design. We present here a simple model relying on the coupling to an effective bath consisting of a continuum of modes to describe systems of coupled resonators, and test it on dielectric nanocylinder chains accessible to experiments. The effective coupling constants, which depend non-trivially on the distance between resonators, are extracted from numerical simulations in the case of just two coupled elements. The model predicts successfully the dispersive and reactive nature of modes for configurations with multiple resonators, as validated by numerical solutions. It can be applied to larger systems, which are hardly solvable with finite-element approaches.

Permanent Directional Heat Currents in Lattices of Optomechanical Resonators.

We study the phonon dynamics in lattices of optomechanical resonators where the mutually coupled photonic modes are coherently driven and the mechanical resonators are uncoupled and connected to independent thermal baths. We present a general procedure to obtain the effective Lindblad dynamics of the phononic modes for an arbitrary lattice geometry, where the light modes play the role of an effective reservoir that mediates the phonon nonequilibrium dynamics. We show how to stabilize stationary states exhibiting directional heat currents over arbitrary distance, despite the absence of thermal gradient and of direct coupling between the mechanical resonators.

Quantum Critical Regime in a Quadratically Driven Nonlinear Photonic Lattice.

We study an array of coupled optical cavities in the presence of two-photon driving and dissipation. The system displays a critical behavior similar to that of a quantum Ising model at finite temperature. Using the corner-space renormalization method, we compute the steady-state properties of finite lattices of varying size, both in one and two dimensions. From a finite-size scaling of the average of the photon number parity, we highlight the emergence of a critical point in regimes of small dissipations, belonging to the quantum Ising universality class. For increasing photon loss rates, a departure from this universal behavior signals the onset of a quantum critical regime, where classical fluctuations induced by losses compete with long-range quantum correlations.

Variational Neural-Network Ansatz for Steady States in Open Quantum Systems.

We present a general variational approach to determine the steady state of open quantum lattice systems via a neural-network approach. The steady-state density matrix of the lattice system is constructed via a purified neural-network Ansatz in an extended Hilbert space with ancillary degrees of freedom. The variational minimization of cost functions associated to the master equation can be performed using a Markov chain Monte Carlo sampling. As a first application and proof of principle, we apply the method to the dissipative quantum transverse Ising model.

Ancillary qubit spectroscopy of vacua in cavity and circuit quantum electrodynamics.

We investigate theoretically how the spectroscopy of an ancillary qubit can probe cavity (circuit) QED ground states containing photons. We consider three classes of systems (Dicke, Tavis-Cummings, and Hopfield-like models), where nontrivial vacua are the result of ultrastrong coupling between N two-level systems and a single-mode bosonic field. An ancillary qubit detuned with respect to the boson frequency is shown to reveal distinct spectral signatures depending on the type of vacua. In particular, the Lamb shift of the ancilla is sensitive to both ground state photon population and correlations. Backaction of the ancilla on the cavity ground state is investigated, taking into account the dissipation via a consistent master equation for the ultrastrong coupling regime. The conditions for high-fidelity measurements are determined.

Controlling discrete and continuous symmetries in "superradiant" phase transitions with circuit QED systems.

We explore theoretically the physics of a collection of two-level systems coupled to a single-mode bosonic field in the nonstandard configuration where each (artificial) atom is coupled to both field quadratures of the boson mode. We show that such an unusual coupling scheme can be implemented in circuit QED systems, where artificial Josephson atoms are coupled both capacitively and inductively to a superconducting resonator. We demonstrate that it is possible to pass from a discrete, paritylike Z(2) symmetry to a continuous U(1) with the appearance of photonic Goldstone and amplitude modes above a critical point even in the ultrastrong coupling regime (where the rotating wave approximation for the interaction between field and two-level systems is no longer applicable). We determine the rich phase diagram showing "superradiant" phases with different symmetries and phase boundaries of both first and second order.