Many-body Phase Research Articles

Topology and Broken Symmetry in Floquet Systems

Floquet systems are governed by periodic, time-dependent Hamiltonians. Prima facie they should absorb energy from the external drives involved in modulating their couplings and heat up to infinite temperature. However, this unhappy state of affairs can be avoided in many ways. Instead, as has become clear from much recent work, Floquet systems can exhibit a variety of nontrivial behavior—some of which is impossible in undriven systems. In this review, we describe the main ideas and themes of this work: novel Floquet drives that exhibit nontrivial topology in single-particle systems, the existence and classification of exotic Floquet drives in interacting systems, and the attendant notion of many-body Floquet phases and arguments for their stability to heating.

Discrete Time Crystals

Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those that do not thermalize under their own isolated quantum dynamics. In this review, we highlight the possibility for such systems to exhibit new nonequilibrium phases of matter. In particular, we focus on discrete time crystals, which are many-body phases of matter characterized by a spontaneously broken discrete time-translation symmetry. We give a definition of discrete time crystals from several points of view, emphasizing that they are a nonequilibrium phenomenon that is stabilized by many-body interactions, with no analog in noninteracting systems. We explain the theory behind several proposed models of discrete time crystals, and compare several recent realizations, in different experimental contexts.

Continuous feedback on a quantum gas coupled to an optical cavity

We present an active feedback scheme acting continuously on the state of a quantum gas dispersively coupled to a high-finesse optical cavity. The quantum gas is subject to a transverse pump laser field inducing a self-organization phase transition, where the gas acquires a density modulation and photons are scattered into the resonator. Photons leaking from the cavity allow for a real-time and non-destructive readout of the system. We stabilize the mean intra-cavity photon number through a micro-processor controlled feedback architecture acting on the intensity of the transverse pump field. The feedback scheme can keep the mean intra-cavity photon number nph constant, in a range between nph = 0.17(4) and nph = 27.6(5), and for up to 4 s. Thus we can engage the stabilization in a regime where the system is very close to criticality as well as deep in the self-organized phase. The presented scheme allows us to approach the self-organization phase transition in a highly controlled manner and is a first step on the path towards the realization of many-body phases driven by tailored feedback mechanisms.

Parametric Instabilities of Interacting Bosons in Periodically Driven 1D Optical Lattices

Periodically-driven quantum systems are currently explored in view of realizing novel many-body phases of matter. This approach is particularly promising in gases of ultracold atoms, where sophisticated shaking protocols can be realized and inter-particle interactions are well controlled. The combination of interactions and time-periodic driving, however, often leads to uncontrollable heating and instabilities, potentially preventing practical applications of Floquet-engineering in large many-body quantum systems. In this work, we experimentally identify the existence of parametric instabilities in weakly-interacting Bose-Einstein condensates in strongly-driven optical lattices through momentum-resolved measurements. Parametric instabilities can trigger the destruction of weakly-interacting Bose-Einstein condensates through the rapid growth of collective excitations, in particular in systems with weak harmonic confinement transverse to the lattice axis.

Effective Hamiltonian with tunable mixed pairing in driven optical lattices

Mixed pairing in ultracold Fermi gases can give rise to interesting many-body phases, such as topological nontrivial superfluids that support Majorana zero modes (MZMs) with various spatial configurations. Unfortunately, in ordinary lattice systems, the topological phase and the associated MZMs are suppressed by the dominant $s$-wave pairing. Here we present a proposal for engineering effective Hamiltonians with tunable mixed on- and off-site pairing based on driven optical lattices. The on- and off-site pairing can be changed independently by means of a periodical driving field rather than magnetic Feshbach resonances. It paves the way for suppressing the dominant on-site interaction that frustrates the emergence of topological superfluids and for synthesizing MZMs localized in edges or corners.

Flat-band many-body localization and ergodicity breaking in the Creutz ladder

We study disorder-free many-body localization in the flat-band Creutz ladder, which was recently realized in cold-atoms in an optical lattice. In a non-interacting case, the flat-band structure of the system leads to a Wannier wavefunction localized on four adjacent lattice sites. In the flat-band regime both with and without interactions, the level spacing analysis exhibits Poisson-like distribution indicating the existence of disorder-free localization. Calculations of the inverse participation ratio support this observation. Interestingly, this type of localization is robust to weak disorders, whereas for strong disorders, the system exhibits a crossover into the conventional disorder-induced many-body localizated phase. Physical picture of this crossover is investigated in detail. We also observe non-ergodic dynamics in the flat-band regime without disorder. The memory of an initial density wave pattern is preserved for long times.

Thermal and Quantum Fluctuation Effects in Quasiperiodic Systems in External Potentials

We analyze the many-body phases of an ensemble of particles interacting via a Lifshitz–Petrich–Gaussian pair potential in a harmonic confinement. We focus on specific parameter regimes where we expect decagonal quasiperiodic cluster arrangements. Performing classical Monte Carlo as well as path integral quantum Monte Carlo methods, we numerically simulate systems of a few thousand particles including thermal and quantum fluctuations. Our findings indicate that the competition between the intrinsic length scale of the harmonic oscillator and the wavelengths associated to the minima of the pair potential generically lead to a destruction of the quasicrystalline pattern. Extensions of this work are also discussed.

Resymmetrizing Broken Symmetry with Hydraulic Pressure.

Recent progress in condensed matter physics, such as for graphene, topological insulators, and Weyl semimetals, often originate from the specific topological symmetries of their lattice structures. Quantum states with different degrees of freedom, e.g., spin, valley, layer, etc., arise from these symmetries, and the coherent superposition of these states form multiple energy subbands. The pseudospin, a concept analogous to the Dirac spinor matrices, is a successful description of such multisubband systems. When the electron-electron interaction dominates, many-body quantum phases arise. They usually have discrete pseudospin polarizations and exhibit sharp phase transitions at certain universal critical pseudospin energy splittings. In this Letter, we present our discovery of hydrostatic-pressure-induced degeneracy between the two lowest Landau levels. This degeneracy is evidenced by the pseudospin polarization transitions of the fragile correlated quantum liquid phases near the Landau level filling factor ν=3/2. Benefitting from the constant hole concentration and the sensitive nature of these transitions, we study the fine-tuning effect of the hydrostatic pressure at the order of 10 μeV, well beyond the meV-level state-of-the-art resolution of other techniques.

Dynamical creation and detection of entangled many-body states in a chiral atom chain

Open quantum systems with chiral interactions can be realized by coupling atoms to guided radiation modes in photonic waveguides or optical fibers. In their steady state these systems can feature intricate many-body phases such as entangled dark states, but their detection and characterization remains a challenge. Here we show how such collective phenomena can be uncovered through monitoring the record of photons emitted into the guided modes. This permits the identification of dark entangled states but furthermore offers novel capabilities for probing complex dynamical behavior, such as the coexistence of a dark entangled and a mixed phase. Our results are of direct relevance for current optical experiments, as they provide a framework for probing, characterizing and classifying classical and quantum dynamical features of chiral light–matter systems.

Reversible Quantum Information Spreading in Many-Body Systems near Criticality.

Quantum chaotic interacting N-particle systems are assumed to show fast and irreversible spreading of quantum information on short (Ehrenfest) time scales ∼logN. Here, we show that, near criticality, certain many-body systems exhibit fast initial scrambling, followed subsequently by oscillatory behavior between reentrant localization and delocalization of information in Hilbert space. We consider both integrable and nonintegrable quantum critical bosonic systems with attractive contact interaction that exhibit locally unstable dynamics in the corresponding many-body phase space of the large-N limit. Semiclassical quantization of the latter accounts for many-body correlations in excellent agreement with simulations. Most notably, it predicts an asymptotically constant local level spacing ℏ/τ, again given by τ∼logN. This unique timescale governs the long-time behavior of out-of-time-order correlators that feature quasiperiodic recurrences indicating reversibility.

Topological polarons, quasiparticle invariants, and their detection in one-dimensional symmetry-protected phases

In the presence of symmetries, one-dimensional quantum systems can exhibit topological order, which in many cases can be characterized by a quantized value of the many-body geometric Zak or Berry phase. We establish that this topological Zak phase is directly related to the Zak phase of an elementary quasiparticle excitation in the system. By considering various systems, we establish this connection for a number of different interacting phases including: the Su-Schrieffer-Heeger model, p-wave topological superconductors, and the Haldane chain. Crucially, in contrast to the bulk many-body Zak phase associated with the ground state of such systems, the topological invariant associated with quasiparticle excitations (above this ground-state) exhibit a more natural route for direct experimental detection. To this end, we build upon recent work [Nature Communications 7, 11994 (2016)] and demonstrate that mobile quantum impurities can be used, in combination with Ramsey interferometry and Bloch oscillations, to directly measure these quasiparticle topological invariants. Finally, a concrete experimental realization of our protocol for dimerized Mott insulators in ultracold atomic systems is discussed and analyzed.

On the time evolution of fermionic occupation numbers.

We derive an approximate equation for the time evolution of the natural occupation numbers for fermionic systems. The evolution of such numbers is connected with the symmetry-adapted generalized Pauli exclusion principle, as well as with the evolution of the natural orbitals and a set of many-body relative phases. We then relate the evolution of these phases to a geometrical and a dynamical term attached to some of the Slater determinants appearing in the configuration-interaction expansion of the wave function. Our approach becomes exact for highly symmetric systems whenever the wave function possesses as many Slater determinants as independent occupation numbers.

Operating behavior of micro-LEDs on a GaN substrate at ultrahigh injection current densities.

Near-ultraviolet micro-LEDs with different diameters were fabricated on GaN substrates. The electroluminescence and the light output power-current density and current density-voltage relationships were measured. A saturated current density of 358 kA/cm2 was achieved with a 20 µm LED. The ideality factor curves showed steps and peaks when the injection current density was increased from 20 to 150 kA/cm2 and an abnormal efficiency increase. The transport and recombination processes of micro-LEDs at high injection current densities were simulated, and the many-body effect and phase space filling in the integrated quantum drift-diffusion model were considered. Serious current crowding was observed above 100 kA/cm2, even for the 20 µm LED.

Unconventional quantum optics in topological waveguide QED.

The discovery of topological materials has motivated recent developments to export topological concepts into photonics to make light behave in exotic ways. Here, we predict several unconventional quantum optical phenomena that occur when quantum emitters interact with a topological waveguide quantum electrodynamics bath, namely, the photonic analog of the Su-Schrieffer-Heeger model. When the emitters' frequency lies within the topological bandgap, a chiral bound state emerges, which is located on just one side (right or left) of the emitter. In the presence of several emitters, this bound state mediates topological, tunable interactions between them, which can give rise to exotic many-body phases such as double Néel ordered states. Furthermore, when the emitters' optical transition is resonant with the bands, we find unconventional scattering properties and different super/subradiant states depending on the band topology. Last, we propose several implementations where these phenomena can be observed with state-of-the-art technology.

Finite temperature phase transition in a cross-dimensional triangular lattice

Atomic many-body phase transitions and quantum criticality have recently attracted much attention in non-standard optical lattices. Here we perform an experimental study of finite temperature superfluid transition of bosonic atoms confined in a three dimensional triangular lattice, whose structure can be continuously deformed to dimensional crossover regions including quasi-one and two dimensions. This non-standard lattice system provides a versatile platform to investigate many-body correlated phases. For the three dimensional case, we find that the finite temperature superfluid transition agrees quantitatively with the Gutzwiller mean field theory prediction, whereas tuning towards reduced dimensional cases, both quantum and thermal fluctuation effects are more dramatic, and the experimental measurement for the critical point becomes strongly deviated from the mean field theory. We characterize the fluctuation effects in the whole dimension crossover process. Our experimental results imply strong many-body correlations in the system beyond mean field description, paving a way to study quantum criticality near Mott-superfluid transition in finite temperature dimension-crossover lattices.

Coherence, entanglement, and quantumness in closed and open systems with conserved charge, with an application to many-body localization

While the scaling of entanglement in a quantum system can be used to distinguish many-body quantum phases, it is usually hard to quantify the amount of entanglement in mixed states of open quantum systems, while measuring entanglement experimentally, even for the closed systems, requires in general quantum state tomography. In this work we show how to remedy this situation in system with a fixed or conserved charge, e.g., density or magnetization, due to an emerging relation between quantum correlations and coherence. First, we show how, in these cases, the presence of multipartite entanglement or quantumness can be faithfully witnessed simply by detecting coherence in the quantum system, while bipartite entanglement or bipartite quantum discord are implied by asymmetry (block coherence) in the system. Second, we prove that the relation between quantum correlations and coherence is also quantitative. Namely, we establish upper and lower bounds on the amount of multipartite and bipartite entanglement in a many-body system with a fixed local charge, in terms of the amount of coherence and asymmetry present in the system. Importantly, both for pure and mixed quantum states, these bounds are expressed as closed formulas, and furthermore, for bipartite entanglement, are experimentally accessible by means of the multiple quantum coherence spectra. In particular, in one-dimensional systems, our bounds may detect breaking of the area law of entanglement entropy. We illustrate our results on the example of a many-body localized system, also in the presence of dephasing.

Observation of the Crossover from Photon Ordering to Delocalization in Tunably Coupled Resonators.

Networks of nonlinear resonators offer intriguing perspectives as quantum simulators for nonequilibrium many-body phases of driven-dissipative systems. Here, we employ photon correlation measurements to study the radiation fields emitted from a system of two superconducting resonators in a driven-dissipative regime, coupled nonlinearly by a superconducting quantum interference device, with cross-Kerr interactions dominating over on-site Kerr interactions. We apply a parametrically modulated magnetic flux to control the linear photon hopping rate between the two resonators and its ratio with the cross-Kerr rate. When increasing the hopping rate, we observe a crossover from an ordered to a delocalized state of photons. The presented coupling scheme is intrinsically robust to frequency disorder and may therefore prove useful for realizing larger-scale resonator arrays.

Observation of Many-Body Localization in a One-Dimensional System with a Single-Particle Mobility Edge.

We experimentally study many-body localization (MBL) with ultracold atoms in a weak one-dimensional quasiperiodic potential, which in the noninteracting limit exhibits an intermediate phase that is characterized by a mobility edge. We measure the time evolution of an initial charge density wave after a quench and analyze the corresponding relaxation exponents. We find clear signatures of MBL when the corresponding noninteracting model is deep in the localized phase. We also critically compare and contrast our results with those from a tight-binding Aubry-André model, which does not exhibit a single-particle intermediate phase, in order to identify signatures of a potential many-body intermediate phase.

Topological bands for ultracold atoms.

There have been significant recent advances in realizing band structures with geometrical and topological features in experiments on cold atomic gases. This review summarizes these developments, beginning with a summary of the key concepts of geometry and topology for Bloch bands. Descriptions are given of the different methods that have been used to generate these novel band structures for cold atoms and of the physical observables that have allowed their characterization. The focus is on the physical principles that underlie the different experimental approaches, providing a conceptual framework within which to view these developments. Also described is how specific experimental implementations can influence physical properties. Moving beyond single-particle effects, descriptions are given of the forms of interparticle interactions that emerge when atoms are subjected to these energy bands and of some of the many-body phases that may be sought in future experiments.

A dissipatively stabilized Mott insulator of photons.

Superconducting circuits are a competitive platform for quantum computation because they offer controllability, long coherence times and strong interactions-properties that are essential for the study of quantum materials comprising microwave photons. However, intrinsic photon losses in these circuits hinder the realization of quantum many-body phases. Here we use superconducting circuits to explore strongly correlated quantum matter by building a Bose-Hubbard lattice for photons in the strongly interacting regime. We develop a versatile method for dissipative preparation of incompressible many-body phases through reservoir engineering and apply it to our system to stabilize a Mott insulator of photons against losses. Site- and time-resolved readout of the lattice allows us to investigate the microscopic details of the thermalization process through the dynamics of defect propagation and removal in the Mott phase. Our experiments demonstrate the power of superconducting circuits for studying strongly correlated matter in both coherent and engineered dissipative settings. In conjunction with recently demonstrated superconducting microwave Chern insulators, we expect that our approach will enable the exploration of topologically ordered phases of matter.