Probing a Dissipative Phase Transition via Dynamical Optical Hysteresis

Arcsine Laws of Light

We demonstrate that the time-integrated light intensity transmitted by a coherently driven resonator obeys Lévy's arcsine laws-a cornerstone of extreme value statistics. We show that convergence to the arcsine distribution is algebraic, universal, and independent of nonequilibrium behavior due to nonconservative forces or nonadiabatic driving. We furthermore verify, numerically, that the arcsine laws hold in the presence of frequency noise and in Kerr-nonlinear resonators supporting non-Gaussian states. The arcsine laws imply a weak ergodicity breaking which can be leveraged to enhance the precision of resonant optical sensors with zero energy cost, as shown in our companion manuscript [V. G. Ramesh et al., companion paper, Phys. Rev. Res. (2024).PPRHAI2643-1564]. Finally, we discuss perspectives for probing the possible breakdown of the arcsine laws in systems with memory.

Dynamic hysteresis at a noisy saddle node shows power-law scaling but nonuniversal exponent

Dynamic hysteresis, viz., delay in switching of a bistable system on account of the finite sweep rate of the drive, has been extensively studied in dynamical and thermodynamic systems. Dynamic hysteresis results from slowing of the response around a saddle-node bifurcation. As a consequence, the hysteresis area increases with the sweep rate. Mean-field theory, relevant for noise-free situations, predicts power-law scaling with the area scaling exponent of 2/3. We have experimentally investigated the dynamic hysteresis for a thermally driven metal-insulator transition in a high-quality NdNiO_{3} thin film and found the scaling exponent to be about 1/3, far less than the mean-field value. To understand this, we have numerically studied Langevin dynamics of the order parameter and found that noise, which can be thought to parallel finite temperature effects, influences the character of dynamic hysteresis by systematically lowering the dynamical exponent to as small as 0.2. The power-law scaling character, on the other hand, is unaffected in the range of chosen parameters. This work rationalizes the ubiquitous power-law scaling of the dynamic hysteresis as well as the wide variation in the scaling exponent between 0.66 and 0.2 observed in different systems over the last 30 years.

Phonon Laser in the Quantum Regime

We demonstrate a trapped-ion system with two competing dissipation channels, implemented independently on two ion species cotrapped in a Paul trap. By controlling coherent spin-oscillator couplings and optical pumping rates we explore the phase diagram of this system, which exhibits a regime analogous to that of a (phonon) laser but operates close to the quantum ground state with an average phonon number of n[over ¯]<10. We demonstrate phase locking of the oscillator to an additional resonant drive, and also observe the phase diffusion of the resulting state under dissipation by reconstructing the quantum state from a measurement of the characteristic function.

Parametrically driving a quantum oscillator into exceptionality

The mathematical objects employed in physical theories do not always behave well. Einstein's theory of space and time allows for spacetime singularities and Van Hove singularities arise in condensed matter physics, while intensity, phase and polarization singularities pervade wave physics. Within dissipative systems governed by matrices, singularities occur at the exceptional points in parameter space whereby some eigenvalues and eigenvectors coalesce simultaneously. However, the nature of exceptional points arising in quantum systems described within an open quantum systems approach has been much less studied. Here we consider a quantum oscillator driven parametrically and subject to loss. This squeezed system exhibits an exceptional point in the dynamical equations describing its first and second moments, which acts as a borderland between two phases with distinctive physical consequences. In particular, we discuss how the populations, correlations, squeezed quadratures and optical spectra crucially depend on being above or below the exceptional point. We also remark upon the presence of a dissipative phase transition at a critical point, which is associated with the closing of the Liouvillian gap. Our results invite the experimental probing of quantum resonators under two-photon driving, and perhaps a reappraisal of exceptional and critical points within dissipative quantum systems more generally.

Stark Localization as a Resource for Weak-Field Sensing with Super-Heisenberg Precision

Gradient fields can effectively suppress particle tunneling in a lattice and localize the wave function at all energy scales, a phenomenon known as Stark localization. Here, we show that Stark systems can be used as a probe for the precise measurement of gradient fields, particularly in the weak-field regime where most sensors do not operate optimally. In the extended phase, Stark probes achieve super-Heisenberg precision, which is well beyond most of the known quantum sensing schemes. In the localized phase, the precision drops in a universal way showing fast convergence to the thermodynamic limit. For single-particle probes, we show that quantum-enhanced sensitivity, with super-Heisenberg precision, can be achieved through a simple position measurement for all the eigenstates across the entire spectrum. For such probes, we have identified several critical exponents of the Stark localization transition and established their relationship. Thermal fluctuations, whose universal behavior is identified, reduce the precision from super-Heisenberg to Heisenberg, still outperforming classical sensors. Multiparticle interacting probes also achieve super-Heisenberg scaling in their extended phase, which shows even further enhancement near the transition point. Quantum-enhanced sensitivity is still achievable even when state preparation time is included in resource analysis.

Quantum behavior of the Duffing oscillator at the dissipative phase transition

The non-deterministic behavior of the Duffing oscillator is classically attributed to the coexistence of two steady states in a double-well potential. However, this interpretation fails in the quantum-mechanical perspective which predicts a single unique steady state. Here, we measure the non-equilibrium dynamics of a superconducting Duffing oscillator and experimentally reconcile the classical and quantum descriptions as indicated by the Liouvillian spectral theory. We demonstrate that the two classically regarded steady states are in fact quantum metastable states. They have a remarkably long lifetime but must eventually relax into the single unique steady state allowed by quantum mechanics. By engineering their lifetime, we observe a first-order dissipative phase transition and reveal the two distinct phases by quantum state tomography. Our results reveal a smooth quantum state evolution behind a sudden dissipative phase transition and form an essential step towards understanding the intriguing phenomena in driven-dissipative systems.

Universal Subdiffusive Behavior at Band Edges from Transfer Matrix Exceptional Points

We discover a deep connection between parity-time symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with periodic on-site potential can be obtained by casting the problem in terms of 2×2 transfer matrices. We find that these non-Hermitian matrices have a symmetry exactly analogous to the parity-time symmetry of balanced-gain-loss optical systems, and hence show analogous transitions across exceptional points. We show that the exceptional points of the transfer matrix of a unit cell correspond to the band edges of the spectrum. When connected to two zero temperature baths at two ends, this consequently leads to subdiffusive scaling of conductance with system size, with an exponent 2, if the chemical potential of the baths are equal to the band edges. We further demonstrate the existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge. Remarkably, this feature is analogous to transition across a mobility edge in quasiperiodic systems. This behavior is universal, irrespective of the details of the periodic potential and the number of bands of the underlying lattice. It, however, has no analog in absence of the baths.

Ballistic transport of interacting Bose particles in a tight-binding chain

It is known that the quantum transport of noninteracting Bose particles across a tight-binding chain is ballistic in the sense that the current does not depend on the chain length. We address the question whether the transport of strongly interacting bosons can be ballistic as well. We find such a regime and show that, classically, it corresponds to the synchronized motion of local nonlinear oscillators. It is also argued that, unlike the case of noninteracting bosons, the transporting state responsible for the ballistic transport of interacting bosons is metastable, i.e., the current decays in the course of time. An estimate for the decay time is obtained.

Floquet Control of Optomechanical Bistability in Multimode Systems

Cavity optomechanical systems make possible the fine manipulation of mechanical degrees of freedom with light, adding functionality and having broad appeal in photonic technologies. We show that distinct mechanical modes can be exploited with a temporally modulated Floquet drive to steer between distinct steady states induced by changes of cavity radiation pressure. We investigate the additional influence of the thermo-optic nonlinearity on these dynamics and find that it can suppress or amplify the control mechanism in contrast to its often performance-limiting character. Our results provide new techniques for the characterization of thermal properties of optomechanical systems and their control, sensing and computational applications.

Enhanced Cavity Optomechanics with Quantum-Well Exciton Polaritons

Semiconductor microresonators embedding quantum wells can host tightly confined and mutually interacting excitonic, optical, and mechanical modes at once. We theoretically investigate the case where the system operates in the strong exciton-photon coupling regime, while the optical and excitonic resonances are parametrically modulated by the interaction with a mechanical mode. Owing to the large exciton-phonon coupling at play in semiconductors, we predict an enhancement of polariton-phonon interactions by 2 orders of magnitude with respect to mere optomechanical coupling: a near-unity single-polariton quantum cooperativity is within reach for current semiconductor resonator platforms. We further analyze how polariton nonlinearities affect dynamical backaction, modifying the capability to cool or amplify the mechanical motion.

Dissipative Phase Transition in Systems with Two-Photon Drive and Nonlinear Dissipation near the Critical Point

In this paper, we examine dissipative phase transition (DPT) near the critical point for a system with two-photon driving and nonlinear dissipations. The proposed mean-field theory, which explicitly takes into account quantum fluctuations, allowed us to describe properly the evolutionary dynamics of the system and to demonstrate new effects in its steady-state. We show that the presence of quantum fluctuations leads to a power-law dependence of the anomalous average at the phase transition point, with which the critical exponent is associated. Also, we investigate the effect of the quantum fluctuations on the critical point renormalization and demonstrate the existence of a two-photon pump “threshold”. It is noteworthy that the obtained results are in a good agreement with the numerical simulations.

Exceptional Precision of a Nonlinear Optical Sensor at a Square-Root Singularity

Exceptional points (EPs)-spectral singularities of non-Hermitian linear systems-have recently attracted interest for sensing. While initial proposals and experiments focused on enhanced sensitivities neglecting noise, subsequent studies revealed issues with EP sensors in noisy environments. Here we propose a single-mode Kerr-nonlinear resonator for exceptional sensing in noisy environments. Based on the resonator's dynamic hysteresis, we define a signal that displays a square-root singularity reminiscent of an EP. However, our sensor has crucial fundamental and practical advantages over EP sensors: the signal-to-noise ratio increases with the measurement speed, the square-root singularity is easily detected through intensity measurements, and both sensing precision and information content of the signal are enhanced around the singularity. Our sensor also overcomes the fundamental trade-off between precision and averaging time characterizing all linear sensors. All these unconventional features open up new opportunities for fast and precise sensing using hysteretic resonators.

Hierarchical classical metastability in an open quantum East model

We study in detail an open quantum generalization of a classical kinetically constrained model-the East model-known to exhibit slow glassy dynamics stemming from a complex hierarchy of metastable states with distinct lifetimes. Using the recently introduced theory of classical metastability for open quantum systems, we show that the driven open quantum East model features a hierarchy of classical metastabilities at low temperature and weak driving field. We find that the effective long-time description of its dynamics not only is classical, but shares many properties with the classical East model, such as obeying an effective detailed balance condition and lacking static interactions between excitations, but with this occurring within a modified set of metastable phases which are coherent, and with an effective temperature that is dependent on the coherent drive.

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.

Subdiffusive Phases in Open Clean Long-Range Systems

We show that a one-dimensional ordered fermionic lattice system with power-law-decaying hopping, when connected to two baths at its two ends with different chemical potentials at zero temperature, features two phases showing subdiffusive scaling of conductance with system size. These phases have no analogues in the isolated system (i.e., in absence of the baths) where the transport is perfectly ballistic. In the open system scenario, interestingly, there occurs two chemical-potential-driven subdiffusive to ballistic phase transitions at zero temperature. We discuss how these phase transitions, to our knowledge, are different from all the known nonequilibrium quantum phase transitions. We provide a clear understanding of the microscopic origin of these phases and argue that the subdiffusive phases are robust against the presence of arbitrary number-conserving many-body interactions in the system. These phases showing subdiffusive scaling of conductance with system size in a two-terminal setup are therefore universal properties of all ordered one-dimensional number-conserving fermionic systems with power-law-decaying hopping at zero temperature.

Fano Lineshapes and Rabi Splittings: Can They Be Artificially Generated or Obscured by the Numerical Aperture?

Fano resonances and Rabi splittings are routinely reported in the scientific literature. Asymmetric resonance lineshapes are usually associated with Fano resonances, and two split peaks in the spectrum are often attributed to a Rabi splitting. True Fano resonances and Rabi splittings are unequivocal signatures of coherent coupling between subsystems. However, can the same spectral lineshapes characterizing Fano resonances and Rabi splittings arise from a purely incoherent sum of intensities? Here we answer this question through experiments with a tunable Fabry-Pérot cavity containing a CsPbBr₃ perovskite crystal. By measuring the transmission and photoluminescence of this system using microscope objectives with different numerical aperture (NA), we find that even a modest NA = 0.4 can artificially generate Fano resonances and Rabi splittings. We furthermore show that this modest NA can obscure the anticrossing of a bona fide strongly coupled light-matter system. Through transfer matrix calculations we confirm that these spectral artifacts are due to the incoherent sum of transmitted intensities at different angles captured by the NA. Our results are relevant to the wide nanophotonics community, characterizing dispersive optical systems with high numerical aperture microscope objectives. We conclude with general guidelines to avoid pitfalls in the characterization of such optical systems.

Symmetry Breaking and Error Correction in Open Quantum Systems

Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system-a Lindbladian-a unitary symmetry can be imposed in a "weak" or a "strong" way. We characterize the possible Z_{n} symmetry-breaking transitions for both cases. In the case of Z_{2}, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correction.

Cooperative Breakdown of the Oscillator Blockade in the Dicke Model

The Dicke model, which describes the coupling of an ensemble of spins to a harmonic oscillator, is known for its superradiant phase transition, which can both be observed in the ground state in a purely Hamiltonian setting, as well as in the steady state of an open-system Dicke model with dissipation. We demonstrate that, in addition, the dissipative Dicke model can undergo a second phase transition to a nonstationary phase, characterized by unlimited heating of the harmonic oscillator. Identifying the mechanism of the phase transition and deriving the scaling of the critical coupling with the system size we conclude that the novel phase transition can be understood as a cooperative breakdown of the oscillator blockade which otherwise prevents higher excitation of the system. We discuss an implementation with trapped ions and investigate the role of cooling, by which the breakdown can be suppressed.

Multi-orbital tight binding model for cavity-polariton lattices

In this work we present a tight-binding model that allows to describe with a minimal amount of parameters the band structure of exciton-polariton lattices. This model based on s and p non-orthogonal photonic orbitals faithfully reproduces experimental results reported for polariton graphene ribbons. We analyze in particular the influence of the non-orthogonality, the inter-orbitals interaction and the photonic spin-orbit coupling on the polarization and dispersion of bulk bands and edge states.

Universal Scaling in the Dynamic Hysteresis, and Non-Markovian Dynamics, of a Tunable Optical Cavity

We investigate, experimentally and theoretically, the dynamics of a laser-driven cavity with noninstantaneous effective photon-photon interactions. Scanning the laser-cavity frequency detuning at different speeds across an optical bistability, we find a hysteresis area that is a nonmonotonic function of the speed. In the limit of fast scans comparable to the memory time of the interactions, we demonstrate that the hysteresis area decays following a universal power law with scaling exponent -1. We further demonstrate a regime of non-Markovian dynamics emerging from white noise. This regime is evidenced by peaked distributions of residence times in the metastable states of our system. Our results offer new perspectives for exploring the physics of scaling, universality, and metastability, in non-Markovian regimes using arrays of bistable optical cavities with low quality factors, driven by low laser powers, and at room temperature.

Nonequilibrium Fixed Points of Coupled Ising Models

Driven-dissipative systems are expected to give rise to nonequilibrium phenomena that are absent in their equilibrium counterparts. However, phase transitions in these systems generically exhibit an effectively classical equilibrium behavior in spite of their nonequilibrium origin. In this paper, we show that multicritical points in such systems lead to a rich and genuinely nonequilibrium behavior. Specifically, we investigate a driven-dissipative model of interacting bosons that possesses two distinct phase transitions: one from a high- to a low-density phase-reminiscent of a liquid-gas transition-and another to an antiferromagnetic phase. Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) ℤ 2 symmetry. However, they coalesce at a multicritical point, giving rise to a nonequilibrium model of coupled Ising-like order parameters described by a ℤ 2 × ℤ 2 symmetry. Using a dynamical renormalization-group approach, we show that a pair of nonequilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system. We elucidate various exotic features of these NEFPs. In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance. This further results in complex-valued critical exponents and spiraling phase boundaries, and it is also accompanied by a complex Liouvillian gap even close to the phase transition. As direct evidence of the nonequilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes "hotter" and "hotter" at longer and longer wavelengths. Finally, we argue that this nonequilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.

Few-Mode Geometric Description of a Driven-Dissipative Phase Transition in an Open Quantum System

By example of the nonlinear Kerr mode driven by a laser, we show that hysteresis phenomena in systems featuring a driven-dissipative phase transition can be accurately described in terms of just two collective, dissipative Liouvillian eigenmodes. The key quantities are just two components of a non-Abelian geometric connection, even though a single parameter is driven. This powerful geometric approach considerably simplifies the description of driven-dissipative phase transitions, extending the range of computationally accessible parameter regimes, and providing a new starting point for both experimental studies and analytical insights.

Towards polariton blockade of confined exciton-polaritons

Cavity-polaritons in semiconductor microstructures have emerged as a promising system for exploring non-equilibrium dynamics of many-body systems¹. Key advances in this field, including the observation of polariton condensation², superfluidity³, realization of topological photonic bands⁴, and dissipative phase transitions^5-7, generically allow for a description based on a mean-field Gross-Pitaevskii formalism. Observation of polariton intensity squeezing^8,9 and decoherence of a polarization entangled photon pair by a polariton condensate¹⁰, on the other hand, demonstrate quantum effects that show up at high polariton occupancy. Going beyond and into the regime of strongly correlated polaritons requires the observation of a photon blockade effect^11,12 where interactions are strong enough to suppress double occupancy of a photonic lattice site. Here, we report evidence of quantum correlations between polaritons spatially confined in a fibre cavity. Photon correlation measurements show that careful tuning of the coupled system can lead to a modest reduction of simultaneous two-polariton generation probability by 5%. Concurrently, our experiments allow us to measure the polariton interaction strength, thereby resolving the controversy stemming from recent experimental reports¹³. Our findings constitute an essential step towards the realization of strongly interacting photonic systems.

Fluorescence Spectrum and Thermalization in a Driven Coupled Cavity Array

We calculate the fluorescence spectra of a driven lattice of coupled cavities. To do this, we extend methods of evaluating two-time correlations in infinite lattices to open quantum systems; this allows access to momentum-resolved fluorescence spectrum. We illustrate this for a driven-dissipative transverse-field anisotropic XY model. By studying the fluctuation-dissipation theorem, we find the emergence of a quasithermalized steady state with a temperature dependent on system parameters; for blue-detuned driving, we show this effective temperature is negative. In the low excitation density limit, we compare these numerical results to analytical spin-wave theory, providing an understanding of the form of the distribution function and the origin of quasithermalization.

Integrable Quantum Dynamics of Open Collective Spin Models

We consider a collective quantum spin s in contact with Markovian spin-polarized baths. Using a conserved superoperator charge, a differential representation of the Liouvillian is constructed to find its exact spectrum and eigenmodes. We study the spectral properties of the model in the large-s limit using a semiclassical quantization condition and show that the spectral density may diverge along certain curves in the complex plane. We exploit our exact solution to characterize steady-state properties, in particular at the discontinuous phase transition that arises for unpolarized environments, and to determine the decay rates of coherences and populations. Our approach provides a systematic way of finding integrable Liouvillian operators with nontrivial steady states as well as a way to study their spectral properties and eigenmodes.

Dissipative phase transitions in systems with nonreciprocal effective interactions

The reciprocity of effective interparticle forces can be violated in various open and nonequilibrium systems, in particular, in colloidal suspensions and complex (dusty) plasmas. Here, we obtain a criterion under which a nonreciprocal system can be strictly reduced to a pseudo-Hamiltonian system with a detailed dynamic equilibrium. In particular, the criterion is satisfied for catalytically active colloids interacting via nonreciprocal diffusiophoretic forces. However, in the general case, when this criterion is not satisfied, the steady state is determined by the interplay between dissipation and the energy source due to the nonreciprocity of interactions. The results indicate the realization of bistability and dissipative spinodal decomposition in a broad class of systems with nonreciprocal effective interactions.

Enhanced Interactions between Dipolar Polaritons

Nonperturbative coupling between cavity photons and excitons leads to the formation of hybrid light-matter excitations, termed polaritons. In structures where photon absorption leads to the creation of excitons with aligned permanent dipoles, the elementary excitations, termed dipolar polaritons, are expected to exhibit enhanced interactions. Here, we report a substantial increase in interaction strength between dipolar polaritons as the size of the dipole is increased by tuning the applied gate voltage. To this end, we use coupled quantum well structures embedded inside a microcavity where coherent electron tunneling between the wells creates the excitonic dipole. Modifications of the interaction strength are characterized by measuring the changes in the reflected light intensity when polaritons are driven with a resonant laser. The factor of 6.5 increase in the interaction-strength-to-linewidth ratio that we obtain indicates that dipolar polaritons could constitute an important step towards a demonstration of the polariton blockade effect, and thereby to form the building blocks of many-body states of light.

Thermoacoustic Instability in Two-Dimensional Fluid Complex Plasmas

Thermoacoustic instability in a fluid monolayer complex plasma is studied for the first time. Experiments, theory, and simulations demonstrate that nonreciprocal effective interactions between particles (mediated by plasma flows) provide positive thermal feedback leading to acoustic sound amplification. The form of the generated sound spectra obtained both in experiments and simulations excellently agrees with theory, justifying thermoacoustic instability in the fluid complex plasma. The results indicate a physical analogy between collective fluctuation dynamics in reactive media and in systems with nonreciprocal effective interactions exposing an activation behavior.

Optical Bistability under Nonresonant Excitation in Spinor Polariton Condensates

We realize bistability in the spinor of polariton condensates under nonresonant optical excitation and in the absence of biasing external fields. Numerical modeling of the system using the Ginzburg-Landau equation with an internal Josephson coupling between the two spin components of the condensate qualitatively describes the experimental observations. We demonstrate that polariton spin bistability strongly depends on the condensate's overlap with the exciton reservoir by tuning the excitation geometry and sample temperature. We obtain noncollapsing bistability hysteresis loops for a record range of sweep times, [10  μs, 1 s], offering a promising route to spin switches and spin memory elements.

Exciton Polaritons in a Two-Dimensional Lieb Lattice with Spin-Orbit Coupling

We study exciton polaritons in a two-dimensional Lieb lattice of micropillars. The energy spectrum of the system features two flat bands formed from S and P_{x,y} photonic orbitals, into which we trigger bosonic condensation under high power excitation. The symmetry of the orbital wave functions combined with photonic spin-orbit coupling gives rise to emission patterns with pseudospin texture in the flat band condensates. Our Letter shows the potential of polariton lattices for emulating flat band Hamiltonians with spin-orbit coupling, orbital degrees of freedom, and interactions.

Bistability of Cavity Magnon Polaritons

We report the first observation of the magnon-polariton bistability in a cavity magnonics system consisting of cavity photons strongly interacting with the magnons in a small yttrium iron garnet (YIG) sphere. The bistable behaviors emerged as sharp frequency switchings of the cavity magnon polaritons (CMPs) and related to the transition between states with large and small numbers of polaritons. In our experiment, we align, respectively, the [100] and [110] crystallographic axes of the YIG sphere parallel to the static magnetic field and find very different bistable behaviors (e.g., clockwise and counter-clockwise hysteresis loops) in these two cases. The experimental results are well fitted and explained as being due to the Kerr nonlinearity with either a positive or negative coefficient. Moreover, when the magnetic field is tuned away from the anticrossing point of CMPs, we observe simultaneous bistability of both magnons and cavity photons by applying a drive field on the lower branch.

Ultralong relaxation times in bistable hybrid quantum systems

Nonlinear systems, whose outputs are not directly proportional to their inputs, are well known to exhibit many interesting and important phenomena that have profoundly changed our technological landscape over the last 50 years. Recently, the ability to engineer quantum metamaterials through hybridization has allowed us to explore these nonlinear effects in systems with no natural analog. We investigate amplitude bistability, which is one of the most fundamental nonlinear phenomena, in a hybrid system composed of a superconducting resonator inductively coupled to an ensemble of nitrogen-vacancy centers. One of the exciting properties of this spin system is its long spin lifetime, which is many orders of magnitude longer than other relevant time scales of the hybrid system. This allows us to dynamically explore this nonlinear regime of cavity quantum electrodynamics and demonstrate a critical slowing down of the cavity population on the order of several tens of thousands of seconds-a time scale much longer than observed so far for this effect. Our results provide a foundation for future quantum technologies based on nonlinear phenomena.