Nonequilibrium quantum condensation in an incoherently pumped dissipative system

Lasing in Non-Hermitian Flat Bands: Quantum Geometry, Coherence, and the Fate of Kardar-Parisi-Zhang Physics

We show that lasing in flat-band lattices can be stabilized by means of the geometrical properties of the Bloch states, in settings where the single-particle dispersion is flat in both its real and imaginary parts. We illustrate a general projection method and compute the collective excitations, which display a diffusive behavior ruled by quantum geometry through a peculiar coefficient involving gain, losses and interactions, and entailing resilience against modulational instabilities. Then, we derive an equation of motion for the phase dynamics and identify a Kardar-Parisi-Zhang term of geometric origin. This term is shown to exactly cancel whenever the real and imaginary parts of the laser nonlinearity are proportional to each other, or when the uniform-pairing condition is satisfied. We confirm our results through numerical studies of the π-flux diamond chain. This Letter highlights the key role of Bloch geometric effects in nonlinear dissipative systems and KPZ physics, with direct implications for the design of laser arrays with enhanced coherence.

Interaction between an Impurity and Nonlinear Excitations in a Polariton Condensate

Exploring the dynamics of a mobile impurity immersed in field excitations is challenging, as it requires to account for the entanglement between the impurity and the surrounding excitations. To this end, the impurity's effective mass has to be considered as finite, rather than infinite. Here, we theoretically investigate the interaction between a finite-mass impurity and a dissipative soliton representing nonlinear excitations in the polariton Bose-Einstein condensate (BEC). Using the Lagrange variational method and the open-dissipative Gross-Pitaevskii equation, we analytically derive the interaction phase diagram between the impurity and a dissipative bright soliton in the polariton BEC. Depending on the impurity mass, we find the dissipative soliton colliding with the impurity can transmit through, get trapped, or be reflected. This work opens a new perspective in understanding the impurity dynamics when immersed in field excitations, as well as potential applications in information processing with polariton solitons.

Rainbow Nambu-Goldstone Modes under a Shear Flow

We study an O(N) scalar model under shear flow and its Nambu-Goldstone modes associated with spontaneous symmetry breaking O(N)→O(N-1). We find that the Nambu-Goldstone mode splits into an infinite number of gapless modes, which we call the rainbow Nambu-Goldstone modes. They have different group velocities and the fractional dispersion relation ω∼k_{1}^{2/3}, where k_{1} is the wave number along the flow. Such behaviors do not have counterparts in an equilibrium state.

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.

Pattern Formation and Exotic Order in Driven-Dissipative Bose-Hubbard Systems

Modern experimental platforms such as superconducting circuit arrays call for the exploration of bosonic tight-binding models in unconventional situations with no counterpart in real materials. Here we investigate one such situation in which excitations are driven and damped by pairs, leading to pattern formation and exotic bosonic states emerging from a nonequilibrium quantum many-body system. Focusing on a two-dimensional driven-dissipative Bose-Hubbard model, we find that its steady states are characterized by the condensation of bosons around momenta lying on a "Bose surface," a bosonic analog of the Fermi surface in solid-state systems. The interplay between instabilities generated by the driving, the nonlinear dissipative mode coupling, and the underlying lattice effect allows the system to equilibrate into an exotic superfluid state of bosons condensed on a closed ring in momentum space instead of discrete points. Such an unconventional state with a spatially uniform density distribution goes beyond the traditional scope of pattern formation and thus has no counterpart in the classical literature. In addition, it is a state connected to several open problems in modern condensed-matter physics. Here we provide the means to stabilize it, opening the way to its experimental study. Moreover, we also provide a concrete experimental implementation of our model in currently available superconducting circuit arrays. We also investigate the relaxation spectrum around the condensate, which shows a characteristic purely diffusive behavior.

Kibble-Zurek Mechanism in Driven Dissipative Systems Crossing a Nonequilibrium Phase Transition

The Kibble-Zurek mechanism constitutes one of the most fascinating and universal phenomena in the physics of critical systems. It describes the formation of domains and the spontaneous nucleation of topological defects when a system is driven across a phase transition exhibiting spontaneous symmetry breaking. While a characteristic dependence of the defect density on the speed at which the transition is crossed was observed in a vast range of equilibrium condensed matter systems, its extension to intrinsically driven dissipative systems is a matter of ongoing research. In this Letter, we numerically confirm the Kibble-Zurek mechanism in a paradigmatic family of driven dissipative quantum systems, namely exciton-polaritons in microcavities. Our findings show how the concepts of universality and critical dynamics extend to driven dissipative systems that do not conserve energy or particle number nor satisfy a detailed balance condition.

Directional Goldstone waves in polariton condensates close to equilibrium

Quantum fluids of light are realized in semiconductor microcavities using exciton-polaritons, solid-state quasi-particles with a light mass and sizeable interactions. Here, we use the microscopic analogue of oceanographic techniques to measure the excitation spectrum of a thermalised polariton condensate. Increasing the fluid density, we demonstrate the transition from a free-particle parabolic dispersion to a linear, sound-like Goldstone mode characteristic of superfluids at equilibrium. Notably, we reveal the effect of an asymmetric pumping by showing that collective excitations are created with a definite direction with respect to the condensate. Furthermore, we measure the critical sound speed for polariton superfluids close to equilibrium.

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.

Non-Hermitian Phase Transition from a Polariton Bose-Einstein Condensate to a Photon Laser

We propose a novel mechanism for a nonequilibrium phase transition in a U(1)-broken phase of an electron-hole-photon system, from a Bose-Einstein condensate of polaritons to a photon laser, induced by the non-Hermitian nature of the condensate. We show that a (uniform) steady state of the condensate can always be classified into two types, namely, arising either from lower or upper-branch polaritons. We prove (for a general model) and demonstrate (for a particular model of polaritons) that an exceptional point where the two types coalesce marks the end point of a first-order-like phase boundary between the two types, similar to a critical point in a liquid-gas phase transition. Since the phase transition found in this paper is not in general triggered by population inversion, our result implies that the second threshold observed in experiments is not necessarily a strong-to-weak-coupling transition, contrary to the widely believed understanding. Although our calculation mainly aims to clarify polariton physics, our discussion is applicable to general driven-dissipative condensates composed of two complex fields.

Manipulation of a stable dark soliton train in polariton condensate

With a potential trap to mimic the finite-size effect, we predict the generation of dark soliton train in a nonresonant polariton condensate excited with the spatially homogeneous continuous wave (cw) field by exploiting the quantum interference in spatial domain. The number of solitons in the train is demonstrated to be controllable on demand in the domain of material parameters. We show that, similar to dark solitons in conservative systems, these nonlinear excitations have infinite lifetime and remain spatially localized even for the periodically oscillating and colliding state of dark soliton train, which do not depend on the parameters of the condensate. Especially, a final state of anti-dark soliton is observed for all kinds of dark soliton trains with the increase of pump power.

Superradiant Quantum Materials

There is currently great interest in the strong coupling between the quantized photon field of a cavity and electronic or other degrees of freedom in materials. A major goal is the creation of novel collective states entangling photons with those degrees of freedom. Here we show that the cooperative effect between strong electron correlations in quantum materials and the long-range interactions induced by the photon field leads to the stabilization of coherent phases of light and matter. By studying a two-band model of interacting electrons coupled to a cavity field, we show that a phase characterized by the simultaneous condensation of excitons and photon superradiance can be realized, hence stabilizing and intertwining two collective phenomena which are rather elusive in the absence of this cooperative effect.

Coherently driven microcavity-polaritons and the question of superfluidity

Due to their driven-dissipative nature, photonic quantum fluids present new challenges in understanding superfluidity. Some associated effects have been observed, and notably the report of nearly dissipationless flow for coherently driven microcavity-polaritons was taken as a smoking gun for superflow. Here, we show that the superfluid response—the difference between responses to longitudinal and transverse forces—is zero for coherently driven polaritons. This is a consequence of the gapped excitation spectrum caused by external phase locking. Furthermore, while a normal component exists at finite pump momentum, the remainder forms a rigid state that is unresponsive to either longitudinal or transverse perturbations. Interestingly, the total response almost vanishes when the real part of the excitation spectrum has a linear dispersion, which was the regime investigated experimentally. This suggests that the observed suppression of scattering should be interpreted as a sign of this new rigid state and not a superfluid.

Driven-dissipative microcavity polariton experiments find superfluid-like behaviour but the intuition developed from equilibrium systems cannot be straightforwardly applied. Juggins et al. show coherently-driven polaritons are not superfluid and earlier observations instead arise from a distinct rigid state.

On the number of Bose-selected modes in driven-dissipative ideal Bose gases

In an ideal Bose gas that is driven into a steady state far from thermal equilibrium, a generalized form of Bose condensation can occur. Namely, the single-particle states unambiguously separate into two groups: the group of Bose-selected states, whose occupations increase linearly with the total particle number, and the group of all other states whose occupations saturate [Phys. Rev. Lett. 111, 240405 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.240405]. However, so far very little is known about how the number of Bose-selected states depends on the properties of the system and its coupling to the environment. The answer to this question is crucial since systems hosting a single, a few, or an extensive number of Bose-selected states will show rather different behavior. While in the former two scenarios each selected mode acquires a macroscopic occupation, corresponding to (fragmented) Bose condensation, the latter case rather bears resemblance to a high-temperature state of matter. In this paper, we systematically investigate the number of Bose-selected states, considering different classes of the rate matrices that characterize the driven-dissipative ideal Bose gases in the limit of weak system-bath coupling. These include rate matrices with continuum limit, rate matrices of chaotic driven systems, random rate matrices, and rate matrices resulting from thermal baths that couple to a few observables only.

Topological order and thermal equilibrium in polariton condensates

The Berezinskii-Kosterlitz-Thouless phase transition from a disordered to a quasi-ordered state, mediated by the proliferation of topological defects in two dimensions, governs seemingly remote physical systems ranging from liquid helium, ultracold atoms and superconducting thin films to ensembles of spins. Here we observe such a transition in a short-lived gas of exciton-polaritons, bosonic light-matter particles in semiconductor microcavities. The observed quasi-ordered phase, characteristic for an equilibrium two-dimensional bosonic gas, with a decay of coherence in both spatial and temporal domains with the same algebraic exponent, is reproduced with numerical solutions of stochastic dynamics, proving that the mechanism of pairing of the topological defects (vortices) is responsible for the transition to the algebraic order. This is made possible thanks to long polariton lifetimes in high-quality samples and in a reservoir-free region. Our results show that the joint measurement of coherence both in space and time is required to characterize driven-dissipative phase transitions and enable the investigation of topological ordering in open systems.

Solvable Family of Driven-Dissipative Many-Body Systems

Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.

High-Temperature Nonequilibrium Bose Condensation Induced by a Hot Needle

We investigate theoretically a one-dimensional ideal Bose gas that is driven into a steady state far from equilibrium via the coupling to two heat baths: a global bath of temperature T and a "hot needle," a bath of temperature T_{h}≫T with localized coupling to the system. Remarkably, this system features a crossover to finite-size Bose condensation at temperatures T that are orders of magnitude larger than the equilibrium condensation temperature. This counterintuitive effect is explained by a suppression of long-wavelength excitations resulting from the competition between both baths. Moreover, for sufficiently large needle temperatures ground-state condensation is superseded by condensation into an excited state, which is favored by its weaker coupling to the hot needle. Our results suggest a general strategy for the preparation of quantum degenerate nonequilibrium steady states with unconventional properties and at large temperatures.

Quantum fluctuations and stability of vortex lattices in a nonresonantly pumped exciton-polariton condensate

The dynamics of an exciton-polariton condensate (EPC) subject to harmonic confinement can cause spontaneously formed vortices to arrange into a triangular vortex lattice. The stability of such a spontaneously formed vortex lattice is still unknown. We investigate the quantum fluctuations of vortex lattices in a rapidly rotating EPC with a rotation frequency close to the harmonic trap. In such a large condensate, we find that a vortex lattice with a triangular structure is stable, whereas one with a square structure becomes unstable. This result indicates that a driven-dissipative vortex array with strong quantum fluctuations can occur in an EPC.

Scanning Tunneling Microscopy Observation of Phonon Condensate

Using quantum tunneling of electrons into vibrating surface atoms, phonon oscillations can be observed on the atomic scale. Phonon interference patterns with unusually large signal amplitudes have been revealed by scanning tunneling microscopy in intercalated van der Waals heterostructures. Our results show that the effective radius of these phonon quasi-bound states, the real-space distribution of phonon standing wave amplitudes, the scattering phase shifts, and the nonlinear intermode coupling strongly depend on the presence of defect-induced scattering resonance. The observed coherence of these quasi-bound states most likely arises from phase- and frequency-synchronized dynamics of all phonon modes, and indicates the formation of many-body condensate of optical phonons around resonant defects. We found that increasing the strength of the scattering resonance causes the increase of the condensate droplet radius without affecting the condensate fraction inside it. The condensate can be observed at room temperature.

Bose-Einstein Condensation of Long-Lifetime Polaritons in Thermal Equilibrium

The experimental realization of Bose-Einstein condensation (BEC) with atoms and quasiparticles has triggered wide exploration of macroscopic quantum effects. Microcavity polaritons are of particular interest because quantum phenomena such as BEC and superfluidity can be observed at elevated temperatures. However, polariton lifetimes are typically too short to permit thermal equilibration. This has led to debate about whether polariton condensation is intrinsically a nonequilibrium effect. Here we report the first unambiguous observation of BEC of optically trapped polaritons in thermal equilibrium in a high-Q microcavity, evidenced by equilibrium Bose-Einstein distributions over broad ranges of polariton densities and bath temperatures. With thermal equilibrium established, we verify that polariton condensation is a phase transition with a well-defined density-temperature phase diagram. The measured phase boundary agrees well with the predictions of basic quantum gas theory.

Emergent equilibrium in many-body optical bistability

Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold Rydberg gases, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, nonequilibrium setting of cavity QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability, a foundational and patently nonequilibrium model of cavity QED, the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by making new connections between traditional techniques from many-body physics (functional integrals) and quantum optics (the system-size expansion). To lowest order in a controlled expansion-organized around the experimentally relevant limit of weak interactions-the full quantum dynamics reduces to nonequilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, revealing that canonical behavior associated with the Ising model manifests readily in simple experimental observables.

Keldysh field theory for driven open quantum systems

Recent experimental developments in diverse areas-ranging from cold atomic gases to light-driven semiconductors to microcavity arrays-move systems into the focus which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in equilibrium condensed matter physics. This concerns both their non-thermal stationary states and their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.

An exciton-polariton laser based on biologically produced fluorescent protein

Under adequate conditions, cavity polaritons form a macroscopic coherent quantum state, known as polariton condensate. Compared to Wannier-Mott excitons in inorganic semiconductors, the localized Frenkel excitons in organic emitter materials show weaker interaction with each other but stronger coupling to light, which recently enabled the first realization of a polariton condensate at room temperature. However, this required ultrafast optical pumping, which limits the applications of organic polariton condensates. We demonstrate room temperature polariton condensates of cavity polaritons in simple laminated microcavities filled with biologically produced enhanced green fluorescent protein (eGFP). The unique molecular structure of eGFP prevents exciton annihilation even at high excitation densities, thus facilitating polariton condensation under conventional nanosecond pumping. Condensation is clearly evidenced by a distinct threshold, an interaction-induced blueshift of the condensate, long-range coherence, and the presence of a second threshold at higher excitation density that is associated with the onset of photon lasing.

High-energy side-peak emission of exciton-polariton condensates in high density regime

In a standard semiconductor laser, electrons and holes recombine via stimulated emission to emit coherent light, in a process that is far from thermal equilibrium. Exciton-polariton condensates–sharing the same basic device structure as a semiconductor laser, consisting of quantum wells coupled to a microcavity–have been investigated primarily at densities far below the Mott density for signatures of Bose-Einstein condensation. At high densities approaching the Mott density, exciton-polariton condensates are generally thought to revert to a standard semiconductor laser, with the loss of strong coupling. Here, we report the observation of a photoluminescence sideband at high densities that cannot be accounted for by conventional semiconductor lasing. This also differs from an upper-polariton peak by the observation of the excitation power dependence in the peak-energy separation. Our interpretation as a persistent coherent electron-hole-photon coupling captures several features of this sideband, although a complete understanding of the experimental data is lacking. A full understanding of the observations should lead to a development in non-equilibrium many-body physics.

Driven Markovian Quantum Criticality

We identify a new universality class in one-dimensional driven open quantum systems with a dark state. Salient features are the persistence of both the microscopic nonequilibrium conditions as well as the quantum coherence of dynamics close to criticality. This provides a nonequilibrium analogue of quantum criticality, and is sharply distinct from more generic driven systems, where both effective thermalization as well as asymptotic decoherence ensue, paralleling classical dynamical criticality. We quantify universality by computing the full set of independent critical exponents within a functional renormalization group approach.

Detuning-Controlled Internal Oscillations in an Exciton-Polariton Condensate

We theoretically analyze exciton-photon oscillatory dynamics within a homogenous polariton gas in the presence of energy detuning between the cavity and quantum well modes. Whereas pure Rabi oscillations consist of the particle exchange between the photon and exciton states in the polariton system without any oscillations of the phases of the two subcondensates, we demonstrate that any nonzero detuning results in oscillations of the relative phase of the photon and exciton macroscopic wave functions. Different initial conditions reveal a variety of behaviors of the relative phase between the two condensates, and a crossover from Rabi-like to Josephson-like oscillations is predicted.

Nonequilibrium Quantum Criticality and Non-Markovian Environment: Critical Exponent of a Quantum Phase Transition

We show that the critical exponent of a quantum phase transition in a damped-driven open system is determined by the spectral density function of the reservoir. We consider the open-system variant of the Dicke model, where the driven boson mode and also the large N spin couple to independent reservoirs at zero temperature. The critical exponent, which is 1 if there is no spin-bath coupling, decreases below 1 when the spin couples to a sub-Ohmic reservoir.

Spatial Coherence and Stability in a Disordered Organic Polariton Condensate

Although only a handful of organic materials have shown polariton condensation, their study is rapidly becoming more accessible. The spontaneous appearance of long-range spatial coherence is often recognized as a defining feature of such condensates. In this Letter, we study the emergence of spatial coherence in an organic microcavity and demonstrate a number of unique features stemming from the peculiarities of this material set. Despite its disordered nature, we find that correlations extend over the entire spot size, and we measure g(1)(r,r') values of nearly unity at short distances and of 50% for points separated by nearly 10  μm . We show that for large spots, strong shot-to-shot fluctuations emerge as varying phase gradients and defects, including the spontaneous formation of vortices. These are consistent with the presence of modulation instabilities. Furthermore, we find that measurements with flat-top spots are significantly influenced by disorder and can, in some cases, lead to the formation of mutually incoherent localized condensates.

Manipulation of a two-photon pump in superconductor-semiconductor heterostructures

We investigate the photon statistics, entanglement, and squeezing of a p-n junction sandwiched between two superconducting leads and show that such an electrically driven photon pump generates correlated and entangled pairs of photons. In particular, we demonstrate that the squeezing of the fluctuations in the quadrature amplitudes of the emitted light can be manipulated by changing the relative phase of the order parameters of the superconductors. This reveals how macroscopic coherence of the superconducting state can be used to tailor the properties of a two-photon state.

Superfluid stiffness of a driven dissipative condensate with disorder

Observations of macroscopic quantum coherence in driven systems, e.g. polariton condensates, have strongly stimulated experimental as well as theoretical efforts during the last decade. We address the question of whether a driven quantum condensate is a superfluid, allowing for the effects of disorder and its nonequilibrium nature. We predict that for spatial dimensions d<4 the superfluid stiffness vanishes once the condensate exceeds a critical size, and treat in detail the case d=2. Thus a nonequilibrium condensate is not a superfluid in the thermodynamic limit, even for weak disorder, although superfluid behavior would persist in small systems.

Nonequilibrium model of photon condensation

We develop a nonequilibrium model of condensation and lasing of photons in a dye filled microcavity. We examine in detail the nature of the thermalization process induced by absorption and emission of photons by the dye molecules, and investigate when the photons are able to reach a thermal equilibrium Bose-Einstein distribution. At low temperatures, or large cavity losses, the absorption and emission rates are too small to allow the photons to reach thermal equilibrium and the behavior becomes more like that of a conventional laser.

Second thresholds in BEC-BCS-laser crossover of exciton-polariton systems

The mechanism of second thresholds observed in several experiments is theoretically revealed by studying the BEC-BCS-laser crossover in exciton-polariton systems. We find that there are two different types of second thresholds: one is a crossover within quasiequilibrium phases and the other is into nonequilibrium (lasing). In both cases, the light-induced band renormalization causes gaps in the conduction and valence bands, which indicates the existence of bound electron-hole pairs in contrast to earlier expectations. We also show that these two types can be distinguished by the gain spectra.

Dynamical critical phenomena in driven-dissipative systems

We explore the nature of the Bose condensation transition in driven open quantum systems, such as exciton-polariton condensates. Using a functional renormalization group approach formulated in the Keldysh framework, we characterize the dynamical critical behavior that governs decoherence and an effective thermalization of the low frequency dynamics. We identify a critical exponent special to the driven system, showing that it defines a new dynamical universality class. Hence critical points in driven systems lie beyond the standard classification of equilibrium dynamical phase transitions. We show how the new critical exponent can be probed in experiments with driven cold atomic systems and exciton-polariton condensates.

Polariton Bose-Einstein condensate at room temperature in an Al(Ga)N nanowire-dielectric microcavity with a spatial potential trap

A spatial potential trap is formed in a 6.0-μm Al(Ga)N nanowire by varying the Al composition along its length during epitaxial growth. The polariton emission characteristics of a dielectric microcavity with the single nanowire embedded in-plane have been studied at room temperature. Excitation is provided at the Al(Ga)N end of the nanowire, and polariton emission is observed from the lowest bandgap GaN region within the potential trap. Comparison of the results with those measured in an identical microcavity with a uniform GaN nanowire and having an identical exciton-photon detuning suggests evaporative cooling of the polaritons as they are transported into the trap in the Al(Ga)N nanowire. Measurement of the spectral characteristics of the polariton emission, their momentum distribution, first-order spatial coherence, and time-resolved measurements of polariton cooling provides strong evidence of the formation of a near-equilibrium Bose-Einstein condensate in the GaN region of the nanowire at room temperature. In contrast, the condensate formed in the uniform GaN nanowire-dielectric microcavity without the spatial potential trap is only in self-equilibrium.

Interplay between periodicity and nonlinearity of indirect excitons in coupled quantum wells

Inspired by a recent experiment of localization-delocalization transition (LDT) of indirect excitons in lateral electrostatic lattices (Remeika et al 2009 Phys. Rev. Lett. 102 186803), we theoretically investigate the interplay between periodic potential and nonlinear interactions of indirect excitons in coupled quantum wells. It is shown that the model involving both attractive two-body and repulsive three-body interactions can lead to a natural account for the LDT of excitons across the lattice when reducing lattice amplitude or increasing particle density. In addition, the observations that the smooth component of the photoluminescent energy increases with increasing exciton density and that the exciton interaction energy is close to the lattice amplitude at the transition are also qualitatively explained. Our model provides an alternative way of understanding the underlying physics of the exciton dynamics in lattice potential wells.

Drag in a resonantly driven polariton fluid

We study the linear response of a coherently driven polariton fluid in the pump-only configuration scattering against a point-like defect and evaluate analytically the drag force exerted by the fluid on the defect. When the system is excited near the bottom of the lower polariton dispersion, the sign of the interaction-renormalised pump detuning classifies the collective excitation spectra into three different categories (Ciuti and Carusotto 2005 Phys. Status Solidi b 242 2224): linear for zero, diffusive-like for positive and gapped for negative detuning. We show that both cases of zero and positive detuning share a qualitatively similar crossover of the drag force from the subsonic to the supersonic regime as a function of the fluid velocity, with a critical velocity given by the speed of sound found for the linear regime. In contrast, for gapped spectra, we find that the critical velocity exceeds the speed of sound. In all cases, the residual drag force in the subcritical regime depends on the polariton lifetime only. Also, well below the critical velocity, the drag force varies linearly with the polariton lifetime, in agreement with previous work (Cancellieri et al 2010 Phys. Rev. B 82 224512), where the drag was determined numerically for a finite-size defect.

Thermodynamics of exciton/polaritons in one and two dimensional organic single-crystal microcavities

We consider here the thermodynamics and phase-diagram of exciton/polaritons formed in low-dimensional organic single-crystal microcavities. Using the Dicke model for a lattice of Frenkel excitons coupled to a common cavity mode, we explore the transition between normal and condensate regimes as depending upon the exciton band-width and temperature of the polariton gas. We show that for one-dimensional conjugated polymers, the coexistence curve at low temperatures shifts towards lower critical coupling strengths as the exciton band-width is increased. We also consider the effect of orientational disorder in a two-dimensional polyacene slab on the formation of the polariton BEC. Our results indicate that while a small degree of orientational disorder will not have a profound effect on the critical exciton/photon coupling strength needed to produce the transition from normal to BEC regimes, BEC will likely be suppressed in glassy or strongly disordered molecular films.

Power-law decay of the spatial correlation function in exciton-polariton condensates

We create a large exciton-polariton condensate and employ a Michelson interferometer setup to characterize the short- and long-distance behavior of the first order spatial correlation function. Our experimental results show distinct features of both the two-dimensional and nonequilibrium characters of the condensate. We find that the gaussian short-distance decay is followed by a power-law decay at longer distances, as expected for a two-dimensional condensate. The exponent of the power law is measured in the range 0.9-1.2, larger than is possible in equilibrium. We compare the experimental results to a theoretical model to understand the features required to observe a power law and to clarify the influence of external noise on spatial coherence in nonequilibrium phase transitions. Our results indicate that Berezinskii-Kosterlitz-Thouless-like phase order survives in open-dissipative systems.

General coupled-nonlinear-oscillator model for event-related (de)synchronization

Changes in the level of synchronization and desynchronization in coupled oscillator systems due to an external stimulus are called event-related synchronization or desynchronization (ERS or ERD). Such changes occur in real-life systems where the collective activity of the entities of a coupled system is affected by some external influence. In order to understand the role played by the external influence in the occurrence of ERD and ERS, we study a system of coupled nonlinear oscillators in the presence of an external stimulus signal. We find that the phenomena of ERS and ERD are generic and occur in all types of coupled oscillator systems. We also find that the same external stimulus signal can cause ERS and ERD depending upon the strength of the signal. We identify the stability of the ERS and ERD states and also find analytical and numerical boundaries between the different synchronization regimes involved in the occurrence of ERD and ERS.

Superfluid density of an open dissipative condensate

I calculate the superfluid density of a nonequilibrium steady state condensate of particles with finite lifetime. Despite the absence of a simple Landau critical velocity, a superfluid response survives, but dissipation reduces the superfluid fraction. I also suggest an idea for how the superfluid density of an example of such a system, i.e., microcavity polaritons, might be measured.

From polariton condensates to highly photonic quantum degenerate states of bosonic matter

Bose-Einstein condensation (BEC) is a thermodynamic phase transition of an interacting Bose gas. Its key signatures are remarkable quantum effects like superfluidity and a phonon-like Bogoliubov excitation spectrum, which have been verified for atomic BECs. In the solid state, BEC of exciton-polaritons has been reported. Polaritons are strongly coupled light-matter quasiparticles in semiconductor microcavities and composite bosons. However, they are subject to dephasing and decay and need external pumping to reach a steady state. Accordingly the polariton BEC is a nonequilibrium process of a degenerate polariton gas in self-equilibrium, but out of equilibrium with the baths it is coupled to and therefore deviates from the thermodynamic phase transition seen in atomic BECs. Here we show that key signatures of BEC can even be observed without fulfilling the self-equilibrium condition in a highly photonic quantum degenerate nonequilibrium system.

What determines the wave function of electron-hole pairs in polariton condensates?

The ground state of a microcavity polariton Bose-Einstein condensate is determined by considering experimentally tunable parameters such as excitation density and detuning. During a change in the ground state of Bose-Einstein condensate from excitonic to photonic, which occurs as the excitation density is increased, the origin of the binding force of electron-hole pairs changes from Coulomb to photon-mediated interactions. The change in the origin gives rise to the strongly bound pairs with a small radius, like Frenkel excitons, in the photonic regime. The phase diagram obtained provides valuable information that can be used to build theoretical models for each regime.

Superfluidity and critical velocities in nonequilibrium Bose-Einstein condensates

We theoretically study the superfluidity properties of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity under incoherent pumping. The dynamics of the condensate is described at mean-field level in terms of a generalized Gross-Pitaevskii equation. The drag force on a small moving object and the onset of fringes in the density profile are shown to have a sharp threshold as a function of the velocity; a generalized Landau criterion is developed to explain this behavior in terms of the dispersion of elementary excitations. Metastability of supercurrents in multiply-connected geometries is shown to persist up to higher flow speeds.

Event-related desynchronization in diffusively coupled oscillator models

We seek an explanation for the neurophysiological phenomenon of event-related desynchronization (ERD) by using models of diffusively coupled nonlinear oscillators. We demonstrate that when the strength of the event is sufficient, ERD is found to emerge and the accomplishment of a behavioral or functional task is determined by the nature of the desynchronized state. We illustrate the phenomenon for the case of limit cycle and chaotic systems. We numerically demonstrate the occurrence of ERD and provide an analytical explanation. We also discuss possible applications of the observed phenomenon in real physical systems other than the brain.

Spontaneous rotating vortex lattices in a pumped decaying condensate

Injection and decay of particles in an inhomogeneous quantum condensate can significantly change its behavior. We model trapped, pumped, decaying condensates by a complex Gross-Pitaevskii equation and analyze the density and currents in the steady state. With homogeneous pumping, rotationally symmetric solutions are unstable. Stability may be restored by a finite pumping spot. However if the pumping spot is larger than the Thomas-Fermi cloud radius, then rotationally symmetric solutions are replaced by solutions with spontaneous arrays of vortices. These vortex arrays arise without any rotation of the trap, spontaneously breaking rotational symmetry.

Synchronized and desynchronized phases of exciton-polariton condensates in the presence of disorder

Condensation of exciton polaritons in semiconductor microcavities takes place despite in-plane disorder. Below the critical density, the inhomogeneity of the disorder limits the spatial extension of the ground state. Above the critical density, in the presence of weak disorder, this limitation is spontaneously overcome by the nonlinear interaction, resulting in an extended synchronized phase. In the case of strong disorder, several non-phase-locked condensates can be evidenced. The transition from a synchronized phase to a desynchronized phase is addressed by sampling the cavity disorder.

Polariton laser using single micropillar GaAs-GaAlAs semiconductor cavities

Polariton lasing is demonstrated on the zero-dimensional states of single GaAs/GaAlAs micropillar cavities. Under nonresonant excitation, the measured polariton ground-state occupancy is found as large as 10(4). Changing the spatial excitation conditions, competition between several polariton lasing modes is observed, ruling out Bose-Einstein condensation. When the polariton state occupancy increases, the emission blueshift is the signature of self-interaction within the half-light half-matter polariton lasing mode.

Excitations in a nonequilibrium Bose-Einstein condensate of exciton polaritons

We develop a mean-field theory of the dynamics of a nonequilibrium Bose-Einstein condensate of exciton polaritons in a semiconductor microcavity. The spectrum of elementary excitations around the stationary state is analytically studied by means of a generalized Gross-Pitaevskii equation. A diffusive behavior of the Goldstone mode is found in the spatially homogeneous case and new features are predicted for the Josephson effect in a two-well geometry.