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.

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.

Dual-density waves with neutral and charged dipolar excitons of GaAs bilayers.

Strongly correlated quantum particles in lattice potentials are the building blocks for a wide variety of quantum insulators-for instance, Mott phases and density waves breaking lattice symmetry1-3. Such collective states are accessible to bosonic and fermionic systems2,4-10,11,12. To expand further the spectrum of accessible quantum matter phases, mixing both species is theoretically appealing because density order then competes with phase separation13-16. Here we manipulate such a Bose-Fermi mixture by confining neutral (boson-like) and charged (fermion-like) dipolar excitons in an artificial square lattice of a GaAs bilayer. At unitary lattice filling, strong inter- and intraspecies interactions stabilize insulating phases when the fraction of charged excitons is around (1/3, 1/2, 2/3). We evidence that dual Bose-Fermi density waves are then realized, with species ordered in alternating stripes. Our observations highlight that dipolar excitons allow for controlled implementations of Bose-Fermi Hubbard models extended by off-site interactions.

Superlattice Quantum Solid of Dipolar Excitons.

We study dipolar excitons confined at 330 mK in a square electrostatic lattice of a GaAs double quantum well. In the dipolar occupation blockade regime, at 3/2 filling, we evidence that excitons form a face-centered superlattice quantum solid. This phase is realized with high purity across 36 lattice sites, in a regime where the mean interaction energy exceeds the depth of the electrostatic lattice confinement. The superlattice solid then closely relates to Wigner crystals.

Probing Quantum Phases in Ultra-High-Mobility Two-Dimensional Electron Systems Using Surface Acoustic Waves.

Transport measurement, which applies an electric field and studies the migration of charged particles, i.e., the current, is the most widely used technique in condensed matter studies. It is generally assumed that the quantum phase remains unchanged when it hosts a sufficiently small probing current, which is, surprisingly, rarely examined experimentally. In this Letter, we study the ultra-high-mobility two-dimensional electron system using a propagating surface acoustic wave, whose traveling speed is affected by the electrons' compressibility. The acoustic power used in our Letter is several orders of magnitude lower than previous reports, and its induced perturbation to the system is smaller than the transport current. Therefore we are able to observe the quantum phases become more incompressible when hosting a perturbative current.

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.

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.

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.

Dynamical formation of a strongly correlated dark condensate of dipolar excitons.

Strongly interacting bosons display a rich variety of quantum phases, the study of which has so far been focused in the dilute regime, at a fixed number of particles. Here we demonstrate the formation of a dense Bose-Einstein condensate in a long-lived dark spin state of 2D dipolar excitons. A dark condensate of weakly interacting excitons is very fragile, being unstable against a coherent coupling of dark and bright spin states. Remarkably, we find that strong dipole-dipole interactions stabilize the dark condensate. As a result, the dark phase persists up to densities high enough for a dark quantum liquid to form. The striking experimental observation of a step-like dependence of the exciton density on the pump power is reproduced quantitatively by a model describing the nonequilibrium dynamics of driven coupled dark and bright condensates. This unique behavior marks a dynamical condensation to dark states with lifetimes as long as a millisecond, followed by a brightening transition at high densities.

Correlated Double-Electron Additions at the Edge of a Two-Dimensional Electronic System.

We create laterally large and low-disorder GaAs quantum-well-based quantum dots that act as small two-dimensional electron systems. We monitor tunneling of single electrons to the dots by means of capacitance measurements and identify single-electron capacitance peaks in the addition spectrum from occupancies of one up to thousands of electrons. The data show two remarkable phenomena in the Landau level filling factor range ν=2 to ν=5 in selective probing of the edge states of the dot: (i) Coulomb blockade peaks arise from the entrance of two electrons rather than one; (ii) at and near ν=5/2 and at fixed gate voltage, these double-height peaks appear uniformly in a magnetic field with a flux periodicity of h/2e, but they group into pairs at other filling factors.

Quasicondensation of Bilayer Excitons in a Periodic Potential.

We study two-dimensional excitons confined in a lattice potential, for high fillings of the lattice sites. We show that a quasicondensate is possibly formed for small values of the lattice depth, but for larger ones the critical phase-space density for quasicondensation rapidly exceeds our experimental reach, due to an increase of the exciton effective mass. On the other hand, in the regime of a deep lattice potential where excitons are strongly localized at the lattice sites, we show that an array of phase-independent quasicondensates, different from a Mott insulator, is realized.

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.

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.

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.

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.

Competing ν = 5/2 fractional quantum Hall states in confined geometry.

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current-tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.

Optical frequency combs from high-order sideband generation.

We report on the generation of frequency combs from the recently-discovered phenomenon of high-order sideband generation (HSG). A near-band gap continuous-wave (cw) laser with frequency fNIR was transmitted through an epitaxial layer containing GaAs/AlGaAs quantum wells that were driven by quasi-cw in-plane electric fields FTHz between 4 and 50 kV/cm oscillating at frequencies fTHz between 240 and 640 GHz. Frequency combs with teeth at fsideband = fNIR + nfTHz (n even) were produced, with maximum reported n > 120, corresponding to a maximum comb span > 80 THz. Comb spectra with the identical product fTHz × FTHz were found to have similar spans and shapes in most cases, as expected from the picture of HSG as a scattering-limited electron-hole recollision phenomenon. The HSG combs were used to measure the frequency and linewidth of our THz source as a demonstration of potential applications.

A new type of half-quantum circulation in a macroscopic polariton spinor ring condensate.

We report the observation of coherent circulation in a macroscopic Bose-Einstein condensate of polaritons in a ring geometry. Because they are spinor condensates, half-quanta are allowed in where there is a phase rotation of π in connection with a polarization vector rotation of π around a closed path. This half-quantum behavior is clearly seen in the experimental observations of the polarization rotation around the ring. In our ring geometry, the half-quantum state that we see is one in which the handedness of the spin flips from one side of the ring to the other side in addition to the rotation of the linear polarization component; such a state is allowed in a ring geometry but will not occur in a simply connected geometry. This state is lower in energy than a half-quantum state with no change of the spin direction and corresponds to a superposition of two different elementary half-quantum states. The direction of circulation of the flow around the ring fluctuates randomly between clockwise and counterclockwise from one shot to the next; this fluctuation corresponds to spontaneous breaking of time-reversal symmetry in the system. This type of macroscopic polariton ring condensate allows for the possibility of direct control of the circulation to excite higher quantized states and the creation of Josephson junction tunneling barriers.

Ultra-low threshold polariton condensation.

We demonstrate the condensation of microcavity polaritons with a very sharp threshold occurring at a two orders of magnitude pump intensity lower than previous demonstrations of condensation. The long cavity lifetime and trapping and pumping geometries are crucial to the realization of this low threshold. Polariton condensation, or "polariton lasing" has long been proposed as a promising source of coherent light at a lower threshold than traditional lasing, and these results indicate some considerations for optimizing designs for lower thresholds.