Coherence measurements of polaritons in thermal equilibrium reveal a power law for two-dimensional condensates.

We have created a spatially homogeneous polariton condensate in thermal equilibrium, up to very high condensate fraction. Under these conditions, we have measured the coherence as a function of momentum and determined the total coherent fraction of this boson system from very low density up to density well above the condensation transition. These measurements reveal a consistent power law for the coherent fraction as a function of the total density over nearly three orders of its magnitude. The same power law is seen in numerical simulations solving the two-dimensional Gross-Pitaevskii equation for the equilibrium coherence.

Evidence for chiral graviton modes in fractional quantum Hall liquids.

Exotic physics could emerge from interplay between geometry and correlation. In fractional quantum Hall (FQH) states1, novel collective excitations called chiral graviton modes (CGMs) are proposed as quanta of fluctuations of an internal quantum metric under a quantum geometry description2-5. Such modes are condensed-matter analogues of gravitons that are hypothetical spin-2 bosons. They are characterized by polarized states with chirality6-8 of +2 or -2, and energy gaps coinciding with the fundamental neutral collective excitations (namely, magnetorotons9,10) in the long-wavelength limit. However, CGMs remain experimentally inaccessible. Here we observe chiral spin-2 long-wavelength magnetorotons using inelastic scattering of circularly polarized lights, providing strong evidence for CGMs in FQH liquids. At filling factor v = 1/3, a gapped mode identified as the long-wavelength magnetoroton emerges under a specific polarization scheme corresponding to angular momentum S = -2, which persists at extremely long wavelength. Remarkably, the mode chirality remains -2 at v = 2/5 but becomes the opposite at v = 2/3 and 3/5. The modes have characteristic energies and sharp peaks with marked temperature and filling-factor dependence, corroborating the assignment of long-wavelength magnetorotons. The observations capture the essentials of CGMs and support the FQH geometrical description, paving the way to unveil rich physics of quantum metric effects in topological correlated systems.

Critical fluctuations in a confined driven-dissipative quantum condensate.

Phase fluctuations determine the low-energy properties of quantum condensates. However, at the condensation threshold, both density and phase fluctuations are relevant. While strong emphasis has been given to the investigation of phase fluctuations, which dominate the physics of the quantum system away from the critical point, number fluctuations have been much less explored even in thermal equilibrium. In this work, we report experimental observation and theoretical description of fluctuations in a circularly confined nonequilibrium Bose-Einstein condensate of polaritons near the condensation threshold. We observe critical fluctuations, which combine the number fluctuations of a single-mode condensate state and competition between different states. The latter is analogous to mode hopping in photon lasers. Our theoretical analysis indicates that this phenomenon is of a quantum character, while classical noise of the pump is not sufficient to explain the experiments. The manifestation of a critical quantum state competition unlocks possibilities for the study of condensate formation while linking to practical realizations in photonic lasers.

Next-generation even-denominator fractional quantum Hall states of interacting composite fermions.

The discovery of the fractional quantum Hall state (FQHS) in 1982 ushered a new era of research in many-body condensed matter physics. Among the numerous FQHSs, those observed at even-denominator Landau level filling factors are of particular interest as they may host quasiparticles obeying non-Abelian statistics and be of potential use in topological quantum computing. The even-denominator FQHSs, however, are scarce and have been observed predominantly in low-disorder two-dimensional (2D) systems when an excited electron Landau level is half filled. An example is the well-studied FQHS at filling factor [Formula: see text] 5/2 which is believed to be a Bardeen-Cooper-Schrieffer-type, paired state of flux-particle composite fermions (CFs). Here, we report the observation of even-denominator FQHSs at [Formula: see text] 3/10, 3/8, and 3/4 in the lowest Landau level of an ultrahigh-quality GaAs 2D hole system, evinced by deep minima in longitudinal resistance and developing quantized Hall plateaus. Quite remarkably, these states can be interpreted as even-denominator FQHSs of CFs, emerging from pairing of higher-order CFs when a CF Landau level, rather than an electron or a hole Landau level, is half-filled. Our results affirm enhanced interaction between CFs in a hole system with significant Landau level mixing and, more generally, the pairing of CFs as a valid mechanism for even-denominator FQHSs, and suggest the realization of FQHSs with non-Abelian anyons.

Anomalous High-Temperature Magnetoresistance in a Dilute 2D Hole System.

We report an unusual magnetoresistance that strengthens with the temperature in a dilute two-dimensional (2D) hole system in GaAs/AlGaAs quantum wells with densities p=1.98-0.99×10^{10}/cm^{2} where r_{s}, the ratio between Coulomb energy and Fermi energy, is as large as 20-30. We show that, while the system exhibits a negative parabolic magnetoresistance at low temperatures (≲0.4 K) characteristic of an interacting Fermi liquid, a positive magnetoresistance emerges unexpectedly at higher temperatures, and grows with increasing temperature even in the regime T∼E_{F}, close to the Fermi energy. This unusual positive magnetoresistance at high temperatures can be attributed to the viscous transport of 2D hole fluid in the hydrodynamic regime where holes scatter frequently with each other. These findings give insight into the collective transport of strongly interacting carriers in the r_{s}≫1 regime and new routes toward magnetoresistance at high temperatures.

Dynamic Response of Wigner Crystals.

The Wigner crystal, an ordered array of electrons, is one of the very first proposed many-body phases stabilized by the electron-electron interaction. We examine this quantum phase with simultaneous capacitance and conductance measurements, and observe a large capacitive response while the conductance vanishes. We study one sample with four devices whose length scale is comparable with the crystal's correlation length, and deduce the crystal's elastic modulus, permittivity, pinning strength, etc. Such a systematic quantitative investigation of all properties on a single sample has a great promise to advance the study of Wigner crystals.

Domain Textures in the Fractional Quantum Hall Effect.

Impacts of domain textures on low-lying neutral excitations in the bulk of fractional quantum Hall effect (FQHE) systems are probed by resonant inelastic light scattering. We demonstrate that large domains of quantum fluids support long-wavelength neutral collective excitations with well-defined wave vector (momentum) dispersion that could be interpreted by theories for uniform phases. Access to dispersive low-lying neutral collective modes in large domains of FQHE fluids such as long wavelength magnetorotons at filling factor v=1/3 offer significant experimental access to strong electron correlation physics in the FQHE.

Transport in helical Luttinger liquids in the fractional quantum Hall regime.

Domain walls in fractional quantum Hall ferromagnets are gapless helical one-dimensional channels formed at the boundaries of topologically distinct quantum Hall (QH) liquids. Naïvely, these helical domain walls (hDWs) constitute two counter-propagating chiral states with opposite spins. Coupled to an s-wave superconductor, helical channels are expected to lead to topological superconductivity with high order non-Abelian excitations1-3. Here we investigate transport properties of hDWs in the ν = 2/3 fractional QH regime. Experimentally we found that current carried by hDWs is substantially smaller than the prediction of the naïve model. Luttinger liquid theory of the system reveals redistribution of currents between quasiparticle charge, spin and neutral modes, and predicts the reduction of the hDW current. Inclusion of spin-non-conserving tunneling processes reconciles theory with experiment. The theory confirms emergence of spin modes required for the formation of fractional topological superconductivity.

Observation of Flat Bands in Gated Semiconductor Artificial Graphene.

Flat bands near M points in the Brillouin zone are key features of honeycomb symmetry in artificial graphene (AG) where electrons may condense into novel correlated phases. Here we report the observation of van Hove singularity doublet of AG in GaAs quantum well transistors, which presents the evidence of flat bands in semiconductor AG. Two emerging peaks in photoluminescence spectra tuned by backgate voltages probe the singularity doublet of AG flat bands and demonstrate their accessibility to the Fermi level. As the Fermi level crosses the doublet, the spectra display dramatic stability against electron density, indicating interplays between electron-electron interactions and honeycomb symmetry. Our results provide a new flexible platform to explore intriguing flat band physics.

Quantum hydrodynamics of a single particle.

Semiconductor devices are strong competitors in the race for the development of quantum computational systems. In this work, we interface two semiconductor building blocks of different dimensionalities with complementary properties: (1) a quantum dot hosting a single exciton and acting as a nearly ideal single-photon emitter and (2) a quantum well in a 2D microcavity sustaining polaritons, which are known for their strong interactions and unique hydrodynamic properties, including ultrafast real-time monitoring of their propagation and phase mapping. In the present experiment, we can thus observe how the injected single particles propagate and evolve inside the microcavity, giving rise to hydrodynamic features typical of macroscopic systems despite their genuine intrinsic quantum nature. In the presence of a structural defect, we observe the celebrated quantum interference of a single particle that produces fringes reminiscent of wave propagation. While this behavior could be theoretically expected, our imaging of such an interference pattern, together with a measurement of antibunching, constitutes the first demonstration of spatial mapping of the self-interference of a single quantum particle impinging on an obstacle.

Observation of quantum depletion in a non-equilibrium exciton-polariton condensate.

Superfluidity, first discovered in liquid 4He, is closely related to Bose-Einstein condensation (BEC) phenomenon. However, even at zero temperature, a fraction of the quantum liquid is excited out of the condensate into higher momentum states via interaction-induced fluctuations-the phenomenon of quantum depletion. Quantum depletion of atomic BECs in thermal equilibrium is well understood theoretically but is difficult to measure. This measurement is even more challenging in driven-dissipative exciton-polariton condensates, since their non-equilibrium nature is predicted to suppress quantum depletion. Here, we observe quantum depletion of a high-density exciton-polariton condensate by detecting the spectral branch of elementary excitations populated by this process. Analysis of this excitation branch shows that quantum depletion of exciton-polariton condensates can closely follow or strongly deviate from the equilibrium Bogoliubov theory, depending on the exciton fraction in an exciton polariton. Our results reveal beyond mean-field effects of exciton-polariton interactions and call for a deeper understanding of the relationship between equilibrium and non-equilibrium BECs.

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.

Light-Driven Electron-Hole Bardeen-Cooper-Schrieffer-Like State in Bulk GaAs.

We investigate the photon-dressed state of excitons in bulk GaAs by optical pump-probe spectroscopy. We reveal that the high-energy branch of the dressed states continuously evolves into a singular enhancement at the absorption edge in the high-density region where the exciton picture is no longer valid. Comparing the experimental result with a simulation based on semiconductor Bloch equations, we show that the dressed state in such a high-density region is better viewed as a Bardeen-Cooper-Schrieffer-like state, which has been theoretically anticipated to exist over decades. Having seen that the dressed state can be regarded as a macroscopic coherent state driven by an external light field, we also discuss the decoherence from the dressed state to an incoherent state after the photoexcitation in view of the Coulomb enhancement in the transient absorption.

Self-Trapping of Exciton-Polariton Condensates in GaAs Microcavities.

The self-trapping of exciton-polariton condensates is demonstrated and explained by the formation of a new polaronlike state. Above the polariton lasing threshold, local variation of the lattice temperature provides the mechanism for an attractive interaction between polaritons. Because of this attraction, the condensate collapses into a small bright spot. Its position and momentum variances approach the Heisenberg quantum limit. The self-trapping does not require either a resonant driving force or a presence of defects. The trapped state is stabilized by the phonon-assisted stimulated scattering of excitons into the polariton condensate. While the formation mechanism of the observed self-trapped state is similar to the Landau-Pekar polaron model, this state is populated by several thousands of quasiparticles, in a striking contrast to the conventional single-particle polaron state.

Observation of new plasmons in the fractional quantum Hall effect: Interplay of topological and nematic orders.

Collective modes of exotic quantum fluids reveal underlying physical mechanisms responsible for emergent quantum states. We observe unexpected new collective modes in the fractional quantum Hall (FQH) regime: intra-Landau-level plasmons measured by resonant inelastic light scattering. The plasmons herald rotational-symmetry-breaking (nematic) phases in the second Landau level and uncover the nature of long-range translational invariance in these phases. The intricate dependence of plasmon features on filling factor provides insights on interplays between topological quantum Hall order and nematic electronic liquid crystal phases. A marked intensity minimum in the plasmon spectrum at Landau level filling factor v = 5/2 strongly suggests that this paired state, which may support non-Abelian excitations, overwhelms competing nematic phases, unveiling the robustness of the 5/2 superfluid state for small tilt angles. At v = 7/3, a sharp and strong plasmon peak that links to emerging macroscopic coherence supports the proposed model of a FQH nematic state.

Spatial Mapping of Local Density Variations in Two-dimensional Electron Systems Using Scanning Photoluminescence.

We have developed a scanning photoluminescence technique that can directly map out the local two-dimensional electron density with a relative accuracy of ∼2.2 × 108 cm-2. The validity of this approach is confirmed by the observation of the expected density gradient in a high-quality GaAs quantum well sample that was not rotated during the molecular beam epitaxy of its spacer layer. In addition to this global variation in electron density, we observe local density fluctuations across the sample. These random density fluctuations are also seen in samples that were continuously rotated during growth, and we attribute them to residual space charges at the substrate-epitaxy interface. This is corroborated by the fact that the average magnitude of density fluctuations is increased to ∼9 × 109 cm-2 from ∼1.2 × 109 cm-2 when the buffer layer between the substrate and the quantum well is decreased by a factor of 7. Our data provide direct evidence for local density inhomogeneities even in very high-quality two-dimensional carrier systems.

Negative longitudinal magnetoresistance in gallium arsenide quantum wells.

Negative longitudinal magnetoresistances (NLMRs) have been recently observed in a variety of topological materials and often considered to be associated with Weyl fermions that have a defined chirality. Here we report NLMRs in non-Weyl GaAs quantum wells. In the absence of a magnetic field the quantum wells show a transition from semiconducting-like to metallic behaviour with decreasing temperature. We observe pronounced NLMRs up to 9 Tesla at temperatures above the transition and weak NLMRs in low magnetic fields at temperatures close to the transition and below 5 K. The observed NLMRs show various types of magnetic field behaviour resembling those reported in topological materials. We attribute them to microscopic disorder and use a phenomenological three-resistor model to account for their various features. Our results showcase a contribution of microscopic disorder in the occurrence of unusual phenomena. They may stimulate further work on tuning electronic properties via disorder/defect nano-engineering.

Emerging many-body effects in semiconductor artificial graphene with low disorder.

The interplay between electron-electron interactions and the honeycomb topology is expected to produce exotic quantum phenomena and find applications in advanced devices. Semiconductor-based artificial graphene (AG) is an ideal system for these studies that combines high-mobility electron gases with AG topology. However, to date, low-disorder conditions that reveal the interplay of electron-electron interaction with AG symmetry have not been achieved. Here, we report the creation of low-disorder AG that preserves the near-perfection of the pristine electron layer by fabricating small period triangular antidot lattices on high-quality quantum wells. Resonant inelastic light scattering spectra show collective spin-exciton modes at the M-point's nearly flatband saddle-point singularity in the density of states. The observed Coulomb exchange interaction energies are comparable to the gap of Dirac bands at the M-point, demonstrating interplay between quasiparticle interactions and the AG potential. The saddle-point exciton energies are in the terahertz range, making low-disorder AG suitable for contemporary optoelectronic applications.

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.

Observation of Dirac bands in artificial graphene in small-period nanopatterned GaAs quantum wells.

Charge carriers in graphene behave like massless Dirac fermions (MDFs) with linear energy-momentum dispersion 1, 2 , providing a condensed-matter platform for studying quasiparticles with relativistic-like features. Artificial graphene (AG)-a structure with an artificial honeycomb lattice-exhibits novel phenomena due to the tunable interplay between topology and quasiparticle interactions 3-6 . So far, the emergence of a Dirac band structure supporting MDFs has been observed in AG using molecular 5 , atomic 6, 7 and photonic systems 8-10 , including those with semiconductor microcavities 11 . Here, we report the realization of an AG that has a band structure with vanishing density of states consistent with the presence of MDFs. This observation is enabled by a very small lattice constant (a = 50 nm) of the nanofabricated AG patterns superimposed on a two-dimensional electron gas hosted by a high-quality GaAs quantum well. Resonant inelastic light-scattering spectra reveal low-lying transitions that are not present in the unpatterned GaAs quantum well. These excitations reveal the energy dependence of the joint density of states for AG band transitions. Fermi level tuning through the Dirac point results in a collapse of the density of states at low transition energy, suggesting the emergence of the MDF linear dispersion in the AG.