Ultracold atoms in a disordered crystal of light: towards a bose glass

Mott Transition for a Lieb-Liniger Gas in a Shallow Quasiperiodic Potential: Delocalization Induced by Disorder

Disorder or quasidisorder is known to favor localization in many-body Bose systems. Here, in contrast, we demonstrate an anomalous delocalization effect induced by incommensurability in quasiperiodic lattices. Loading ultracold atoms in two shallow periodic lattices with equal amplitude and either equal or incommensurate spatial periods, we show the onset of a Mott transition not only in the periodic case but also in the quasiperiodic case. Switching from periodic to quasiperiodic potential with the same amplitude, we find that the Mott insulator turns into a delocalized superfluid. Our experimental results agree with quantum Monte Carlo calculations, showing this anomalous delocalization induced by the interplay between the disorder and interaction.

Observing the two-dimensional Bose glass in an optical quasicrystal

The presence of disorder substantially influences the behaviour of physical systems. It can give rise to slow or glassy dynamics, or to a complete suppression of transport as in Anderson insulators1, where normally extended wavefunctions such as light fields or electronic Bloch waves become exponentially localized. The combined effect of disorder and interactions is central to the richness of condensed-matter physics2. In bosonic systems, it can also lead to additional quantum states such as the Bose glass3,4-an insulating but compressible state without long-range phase coherence that emerges in disordered bosonic systems and is distinct from the well-known superfluid and Mott insulating ground states of interacting bosons. Here we report the experimental realization of the two-dimensional Bose glass using ultracold atoms in an eight-fold symmetric quasicrystalline optical lattice5. By probing the coherence properties of the system, we observe a Bose-glass-to-superfluid transition and map out the phase diagram in the weakly interacting regime. We furthermore demonstrate that it is not possible to adiabatically traverse the Bose glass on typical experimental timescales by examining the capability to restore coherence and discuss the connection to the expected non-ergodicity of the Bose glass. Our observations are in good agreement with recent quantum Monte Carlo predictions6 and pave the way for experimentally testing the connection between the Bose glass, many-body localization and glassy dynamics more generally7,8.

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.

Commensurate and incommensurate 1D interacting quantum systems

Single-atom imaging resolution of many-body quantum systems in optical lattices is routinely achieved with quantum-gas microscopes. Key to their great versatility as quantum simulators is the ability to use engineered light potentials at the microscopic level. Here, we employ dynamically varying microscopic light potentials in a quantum-gas microscope to study commensurate and incommensurate 1D systems of interacting bosonic Rb atoms. Such incommensurate systems are analogous to doped insulating states that exhibit atom transport and compressibility. Initially, a commensurate system with unit filling and fixed atom number is prepared between two potential barriers. We deterministically create an incommensurate system by dynamically changing the position of the barriers such that the number of available lattice sites is reduced while retaining the atom number. Our systems are characterised by measuring the distribution of particles and holes as a function of the lattice filling, and interaction strength, and we probe the particle mobility by applying a bias potential. Our work provides the foundation for preparation of low-entropy states with controlled filling in optical-lattice experiments.

Quasicrystalline Bose Glass in the Absence of Disorder and Quasidisorder

We study the low-temperature phases of interacting bosons on a two-dimensional quasicrystalline lattice. By means of numerically exact path integral Monte Carlo simulations, we show that for sufficiently weak interactions the system is a homogeneous Bose-Einstein condensate that develops density modulations for increasing filling factor. The simultaneous occurrence of sizeable condensate fraction and density modulation can be interpreted as the analogous, in a quasicrystalline lattice, of supersolid phases occurring in conventional periodic lattices. For sufficiently large interaction strength and particle density, global condensation is lost and quantum exchanges are restricted to specific spatial regions. The emerging quantum phase is therefore a Bose glass, which here is stabilized in the absence of any source of disorder or quasidisorder, purely as a result of the interplay between quantum effects, particle interactions and quasicrystalline substrate. This finding clearly indicates that (quasi)disorder is not essential to observe Bose glass physics. Our results are of interest for ongoing experiments on (quasi)disorder-free quasicrystalline lattices.

Exact New Mobility Edges between Critical and Localized States

The disorder systems host three types of fundamental quantum states, known as the extended, localized, and critical states, of which the critical states remain being much less explored. Here we propose a class of exactly solvable models which host a novel type of exact mobility edges (MEs) separating localized states from robust critical states, and propose experimental realization. Here the robustness refers to the stability against both single-particle perturbation and interactions in the few-body regime. The exactly solvable one-dimensional models are featured by a quasiperiodic mosaic type of both hopping terms and on-site potentials. The analytic results enable us to unambiguously obtain the critical states which otherwise require arduous numerical verification including the careful finite size scalings. The critical states and new MEs are shown to be robust, illustrating a generic mechanism unveiled here that the critical states are protected by zeros of quasiperiodic hopping terms in the thermodynamic limit. Further, we propose a novel experimental scheme to realize the exactly solvable model and the new MEs in an incommensurate Rydberg Raman superarray. This Letter may pave a way to precisely explore the critical states and new ME physics with experimental feasibility.

Thermodynamic Phase Diagram of Two-Dimensional Bosons in a Quasicrystal Potential

Quantum simulation of quasicrystals in synthetic bosonic matter now paves the way for the exploration of these intriguing systems in wide parameter ranges. Yet thermal fluctuations in such systems compete with quantum coherence and significantly affect the zero-temperature quantum phases. Here we determine the thermodynamic phase diagram of interacting bosons in a two-dimensional, homogeneous quasicrystal potential. We find our results using quantum Monte Carlo simulations. Finite-size effects are carefully taken into account and the quantum phases are systematically distinguished from thermal phases. In particular, we demonstrate stabilization of a genuine Bose glass phase against the normal fluid in sizable parameter ranges. We interpret our results for strong interactions using a fermionization picture and discuss experimental relevance.

Dynamical conductivity of disordered quantum chains

ABSTRACT

We study the transport properties of a one-dimensional quantum system with disorder. We numerically compute the frequency dependence of the conductivity of a fermionic chain with nearest-neighbor interaction and a random chemical potential by using the Chebyshev matrix product state (CheMPS) method. As a benchmark, we investigate the noninteracting case first. Comparison with exact diagonalization and analytical solutions demonstrates that the results of CheMPS are reliable over a wide range of frequencies. We then calculate the dynamical conductivity spectra of the interacting system for various values of the interaction and disorder strengths. In the high-frequency regime, the conductivity decays as a power law, with an interaction-dependent exponent. This behavior is qualitatively consistent with the bosonized field theory predictions, although the numerical evaluation of the exponent shows deviations from the analytically expected values. We also compute the characteristic pinning frequency at which a peak in the conductivity appears. We confirm that it is directly related to the inverse of the localization length, even in the interacting case. We demonstrate that the localization length follows a power law of the disorder strength with an exponent dependent on the interaction, and find good quantitative agreement with the field theory predictions. In the low-frequency regime, we find a behavior consistent with the one of the noninteracting system ω 2 ( ln ω ) 2 independently of the interaction. We discuss the consequences of our finding for experiments in cold atomic gases.

One-Dimensional Disordered Bosonic Systems

Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system. Despite the growing interest in this topic, a complete understanding of the issue is still missing. An open question, for example, is the description of the interplay of disorder and interactions, which has been predicted to give rise to exotic states of matter such as quantum glasses or many-body localization. In this review, we will present an overview of experimental observations with disordered quantum gases, focused on one-dimensional bosons, and we will connect them with theoretical predictions.

Observing two-particle Anderson localization in linear disordered photonic lattices

We theoretically and systematically investigate Anderson localization of two bosons with nearest-neighbor interaction in one dimension under short- and long-time scales, two types of disorders, and three types of initial states, which can be directly observed in linear disordered photonic lattices via two experimentally measurable physical quantities, participation ratio and spatial correlation. We find that the behavior of localization characterized by the participation ratio depends on the strength of interaction and the type of disorder and initial condition. Two-boson spatial correlation reveals more novel and unique features. In the ordered case, two types of two-boson bindings and bosonic "fermionization" are shown, which are intimately attributed to the band structure of the system. In the disordered case, the impact of interaction on the two-boson Anderson localization is reexamined and the joint effect of disorder and interaction is addressed. We further demonstrate that the independence of the participation ratio or spatial correlation on the sign of interaction can be eliminated by employing an initial state that breaks one of two specific symmetries. Finally, we elucidate the relevant details of the experimental implementation in a two-dimensional linear photonic lattice.

Localization transitions and mobility edges in quasiperiodic ladder

We investigate localization properties of two-coupled uniform chains (ladder) with quasiperiodic modulation on interchain coupling strength. We demonstrate that this ladder is equivalent to two Aubry-André chains when two legs are symmetric. Analytical and numerical results indicate the appearance of mobility edges in asymmetric ladder systems. We propose an easy-to-engineer quasiperiodic Moiré superlattice ladder system comprising two-coupled uniform chains. An irrational lattice constant difference results in a quasiperiodic structure. Numerical simulations indicate that such a system supports the existence of mobility edges. Furthermore, we demonstrate that the mobility edges can be detected through a dynamical method, that is based on the measurement of survival probability in the presence of a single imaginary negative potential. The results provide insights into localization transitions and mobility edges in experiments.

Anderson localization induced by interaction in linearly coupled binary Bose-Einstein condensates

In this paper we investigate the existence of Anderson localization induced by one specific component of a binary Bose-Einstein condensate (BEC). We use a mean-field approach, in which each type of particle of the BEC is considered as a specific field, and we consider that only one kind of particle is subject to a quasiperiodic potential, which induces a localization in the partner field. We assume the system is under a Rabi coupling, i.e., a linear coupling mixing the two-field component, and we investigate the conditions associated with the parameter values of the system for observing the localization. Numerical simulations are performed, confirming the existence of Anderson localization in the partner field.

Localization on a Synthetic Hall Cylinder

By engineering laser-atom interactions, both Hall ribbons and Hall cylinders as fundamental theoretical tools in condensed matter physics have recently been synthesized in laboratories. Here, we show that turning a synthetic Hall ribbon into a synthetic Hall cylinder could naturally lead to localization. Unlike a Hall ribbon, a Hall cylinder hosts an intrinsic lattice, which arises due to the periodic boundary condition in the azimuthal direction, in addition to the external periodic potential imposed by extra lasers. When these two lattices are incommensurate, localization may occur on a synthetic Hall cylinder. Near the localization-delocalization transitions, physical observables strongly depend on the axial magnetic flux, providing us a sensitive means to probe either the transition or the axial flux using one another. In the irrational limit, physical observables are no longer affected by the axial flux, signifying a scheme to suppress decoherence induced by fluctuations of the axial flux.

Interactions and Mobility Edges: Observing the Generalized Aubry-André Model

Using synthetic lattices of laser-coupled atomic momentum modes, we experimentally realize a recently proposed family of nearest-neighbor tight-binding models having quasiperiodic site energy modulation that host an exact mobility edge protected by a duality symmetry. These one-dimensional tight-binding models can be viewed as a generalization of the well-known Aubry-André model, with an energy-dependent self-duality condition that constitutes an analytical mobility edge relation. By adiabatically preparing low and high energy eigenstates of this model system and performing microscopic measurements of their participation ratio, we track the evolution of the mobility edge as the energy-dependent density of states is modified by the model's tuning parameter. Our results show strong deviations from single-particle predictions, consistent with attractive interactions causing both enhanced localization of the lowest energy state due to self-trapping and inhibited localization of high energy states due to screening. This study paves the way for quantitative studies of interaction effects on self-duality induced mobility edges.

One-Dimensional Quasiperiodic Mosaic Lattice with Exact Mobility Edges

The mobility edges (MEs) in energy that separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain cases, the analytic results that allow for an exact understanding are rare. Here we uncover a class of exactly solvable 1D models with MEs in the spectra, where quasiperiodic on-site potentials are inlaid in the lattice with equally spaced sites. The analytical solutions provide the exact results not only for the MEs, but also for the localization and extended features of all states in the spectra, as derived through computing the Lyapunov exponents from Avila's global theory and also numerically verified by calculating the fractal dimension. We further propose a novel scheme with experimental feasibility to realize our model based on an optical Raman lattice, which paves the way for experimental exploration of the predicted exact ME physics.

Lieb-Liniger Bosons in a Shallow Quasiperiodic Potential: Bose Glass Phase and Fractal Mott Lobes

The emergence of a compressible insulator phase, known as the Bose glass, is characteristic of the interplay of interactions and disorder in correlated Bose fluids. While widely studied in tight-binding models, its observation remains elusive owing to stringent temperature effects. Here we show that this issue may be overcome by using Lieb-Liniger bosons in shallow quasiperiodic potentials. A Bose glass, surrounded by superfluid and Mott phases, is found above a critical potential and for finite interactions. At finite temperature, we show that the melting of the Mott lobes is characteristic of a fractal structure and find that the Bose glass is robust against thermal fluctuations up to temperatures accessible in quantum gases. Our results raise questions about the universality of the Bose glass transition in such shallow quasiperiodic potentials.

Localization Driven Superradiant Instability

The prominent Dicke superradiant phase arises from coupling an ensemble of atoms to a cavity optical field when an external optical pumping exceeds a threshold strength. Here we report a prediction of the superradiant instability driven by Anderson localization, realized with a hybrid system of the Dicke and Aubry-André (DAA) model for bosons trapped in a one-dimensional (1D) quasiperiodic optical lattice and coupled to a cavity. Our central finding is that for bosons condensed in a localized phase given by the DAA model, the resonant superradiant scattering is induced, for which the critical optical pumping of the superradiant phase transition approaches zero, giving an instability driven by the Anderson localization. The superradiant phase for the DAA model with or without a mobility edge is investigated, showing that the localization driven superradiant instability is in sharp contrast to the superradiance as widely observed for a Bose-Einstein condensate in extended states, and should be insensitive to the temperature of the system. This study unveils a novel effect of localization on the Dicke superradiance, and is well accessible based on the current experiments.

Superfluid-Insulator Transition unambiguously detected by entanglement in one-dimensional disordered superfluids

We use entanglement to track the superfluid-insulator transition (SIT) in disordered fermionic superfluids described by the one-dimensional Hubbard model. Entanglement is found to have remarkable signatures of the SIT driven by i) the disorder strength V, ii) the concentration of impurities C and iii) the particle density n. Our results reveal the absence of a critical potential intensity on the SIT driven by V, i.e. any small V suffices to decrease considerably the degree of entanglement: it drops ∼50% for V = -0.25t. We also find that entanglement is non-monotonic with the concentration C, approaching to zero for a certain critical value CC. This critical concentration is found to be related to a special type of localization, here named as fully-localized state, which can be also reached for a particular density nC. Our results show that the SIT driven by n or C has distinct nature whether it leads to the full localization or to the ordinary one: it is a first-order quantum phase transition only when leading to full localization. In contrast, the SIT driven by V is never a first-order quantum phase transition independently on the type of localization reached.

Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials

Quasiperiodic systems offer an appealing intermediate between long-range ordered and genuine disordered systems, with unusual critical properties. One-dimensional models that break the so-called self-dual symmetry usually display a mobility edge, similarly as truly disordered systems in a dimension strictly higher than two. Here, we determine the critical localization properties of single particles in shallow, one-dimensional, quasiperiodic models and relate them to the fractal character of the energy spectrum. On the one hand, we determine the mobility edge and show that it separates the localized and extended phases, with no intermediate phase. On the other hand, we determine the critical potential amplitude and find the universal critical exponent ν≃1/3. We also study the spectral Hausdorff dimension and show that it is nonuniversal but always smaller than unity, hence showing that the spectrum is nowhere dense. Finally, applications to ongoing studies of Anderson localization, Bose-glass physics, and many-body localization in ultracold atoms are discussed.

Observation of a Dynamical Sliding Phase Superfluid with P-Band Bosons

Sliding phases have been long sought after in the context of coupled XY models, as they are of relevance to various many-body systems such as layered superconductors, freestanding liquid-crystal films, and cationic lipid-DNA complexes. Here we report an observation of a dynamical sliding phase superfluid that emerges in a nonequilibrium setting from the quantum dynamics of a three-dimensional ultracold atomic gas loaded into the P band of a one-dimensional optical lattice. A shortcut loading method is used to transfer atoms into the P band at zero quasimomentum within a very short time duration. The system can be viewed as a series of "pancake"-shaped atomic samples. For this far-out-of-equilibrium system, we find an intermediate time window with a lifetime around tens of milliseconds, where the atomic ensemble exhibits robust superfluid phase coherence in the pancake directions, but no coherence in the lattice direction, which implies a dynamical sliding phase superfluid. The emergence of the sliding phase is attributed to a mechanism of cross-dimensional energy transfer in our proposed phenomenological theory, which is consistent with experimental measurements. This experiment potentially opens up a novel venue to search for exotic dynamical phases by creating high-band excitations in optical lattices.

Quantum Relaxation and Metastability of Lattice Bosons with Cavity-Induced Long-Range Interactions

The coupling of cold atoms to the radiation field within a high-finesse optical resonator, an optical cavity, induces long-range interactions which can compete with an underlying optical lattice. The interplay between short- and long-range interactions gives rise to new phases of matter including supersolidity (SS) and density waves (DW), and interesting quantum dynamics. Here it is shown that for hard-core bosons in one dimension the ground state phase diagram and the quantum relaxation after sudden quenches can be calculated exactly in the thermodynamic limit. Remanent DW order is observed for quenches from a DW ground state into the superfluid (SF) phase below a dynamical transition line. After sufficiently strong SF to DW quenches beyond a static metastability line DW order emerges on top of remanent SF order, giving rise to a dynamically generated SS state. Our method to handle infinite- and short-range interactions in the infinite system size limit opens a way to solve exactly other Hamiltonians with infinite- and short-range interactions as well.

Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice

A single-particle mobility edge (SPME) marks a critical energy separating extended from localized states in a quantum system. In one-dimensional systems with uncorrelated disorder, a SPME cannot exist, since all single-particle states localize for arbitrarily weak disorder strengths. However, in a quasiperiodic system, the localization transition can occur at a finite detuning strength and SPMEs become possible. In this Letter, we find experimental evidence for the existence of such a SPME in a one-dimensional quasiperiodic optical lattice. Specifically, we find a regime where extended and localized single-particle states coexist, in good agreement with theoretical simulations, which predict a SPME in this regime.

Quantum Glass of Interacting Bosons with Off-Diagonal Disorder

We study disordered interacting bosons described by the Bose-Hubbard model with Gaussian-distributed random tunneling amplitudes. It is shown that the off-diagonal disorder induces a spin-glass-like ground state, characterized by randomly frozen quantum-mechanical U(1) phases of bosons. To access criticality, we employ the "n-replica trick," as in the spin-glass theory, and the Trotter-Suzuki method for decomposition of the statistical density operator, along with numerical calculations. The interplay between disorder, quantum, and thermal fluctuations leads to phase diagrams exhibiting a glassy state of bosons, which are studied as a function of model parameters. The considered system may be relevant for quantum simulators of optical-lattice bosons, where the randomness can be introduced in a controlled way. The latter is supported by a proposition of experimental realization of the system in question.

Quantum anomalous Hall-quantum spin Hall effect in optical superlattices

We consider the topological characteristics of the spin-orbital coupling particles loaded in one-dimensional (1D) optical superlattices subject to the Zeeman field. The phase shift of the superlattice provides a virtual dimension which allows us to simulate two-dimensional topological phases with a physically 1D system. The system possesses a variety of quantum phase transitions over a large parametric space and two important topological phases, namely, quantum anomalous Hall (QAH) and quantum spin Hall (QSH) phases are found to coexist in the system, but they reside in different bandgaps. This new category of gap-dependent QAH--QSH insulator paves the way for the possible observation of the coexistence of QSH and QAH effects at one platform.

Two-terminal transport measurements with cold atoms

In recent years, the ability of cold atom experiments to explore condensed-matter-related questions has dramatically progressed. Transport experiments, in particular, have expanded to the point in which conductance and other transport coefficients can now be measured in a way that is directly analogous to solid-state physics, extending cold-atom-based quantum simulations into the domain of quantum electronic devices. In this topical review, we describe the transport experiments performed with cold gases in the two-terminal configuration, with an emphasis on the specific features of cold atomic gases compared to solid-state physics. We present the experimental techniques and the main experimental findings, focusing on-but not restricted to-the recent experiments performed by our group. We finally discuss the perspectives opened up by this approach, the main technical and conceptual challenges for future developments, and potential applications in quantum simulation for transport phenomena and mesoscopic physics problems.

Diffusive and arrested transport of atoms under tailored disorder

Ultracold atoms in optical lattices offer a unique platform for investigating disorder-driven phenomena. While static disordered site potentials have been explored in a number of experiments, a more general, dynamical control over site-energy and off-diagonal tunnelling disorder has been lacking. The use of atomic quantum states as synthetic dimensions has introduced the spectroscopic, site-resolved control necessary to engineer more tailored realisations of disorder. Here, we present explorations of dynamical and tunneling disorder in an atomic system by controlling laser-driven dynamics of atomic population in a momentum-space lattice. By applying static tunnelling phase disorder to a one-dimensional lattice, we observe ballistic quantum spreading. When the applied disorder fluctuates on time scales comparable to intersite tunnelling, we instead observe diffusive atomic transport, signalling a crossover from quantum to classical expansion dynamics. We compare these observations to the case of static site-energy disorder, where we directly observe quantum localisation.

Cold atom quantum simulation has had challenges in realising the tailored, dynamic types of disorder relevant to real materials. Here, the authors use synthetic momentum-space lattices to engineer spatially and dynamically controlled disorder to observe ballistic, diffusive, and arrested atomic transport.

Nuclear Magnetic Resonance Reveals Disordered Level-Crossing Physics in the Bose-Glass Regime of the Br-Doped Ni(Cl_{1-x}Br_{x})_{2}-4SC(NH_{2})_{2} Compound at a High Magnetic Field

By measuring the nuclear magnetic resonance (NMR) T_{1}^{-1} relaxation rate in the Br (bond) doped DTN compound, Ni(Cl_{1-x}Br_{x})_{2}-4SC(NH_{2})_{2}(DTNX), we show that the low-energy spin dynamics of its high magnetic field "Bose-glass" regime is dominated by a strong peak of spin fluctuations found at the nearly doping-independent position H^{*}≅13.6  T. From its temperature and field dependence, we conclude that this corresponds to a level crossing of the energy levels related to the doping-induced impurity states. Observation of the local NMR signal from the spin adjacent to the doped Br allowed us to fully characterize this impurity state. We have thus quantified a microscopic theoretical model that paves the way to better understanding of the Bose-glass physics in DTNX, as revealed in the related theoretical study [M. Dupont, S. Capponi, and N. Laflorencie, Phys. Rev. Lett. 118, 067204 (2017).PRLTAO0031-900710.1103/PhysRevLett.118.067204].

Unidirectional transport of wave packets through tilted discrete breathers in nonlinear lattices with asymmetric defects

We consider the transfer of lattice wave packets through a tilted discrete breather (TDB) in opposite directions in the discrete nonlinear Schrödinger model with asymmetric defects, which may be realized as a Bose-Einstein condensate trapped in a deep optical lattice, or as optical beams in a waveguide array. A unidirectional transport mode is found, in which the incident wave packets, whose energy belongs to a certain interval between full reflection and full passage regions, pass the TDB only in one direction, while in the absence of the TDB, the same lattice admits bidirectional propagation. The operation of this mode is accurately explained by an analytical consideration of the respective energy barriers. The results suggest that the TDB may emulate the unidirectional propagation of atomic and optical beams in various settings. In the case of the passage of the incident wave packet, the scattering TDB typically shifts by one lattice unit in the direction from which the wave packet arrives, which is an example of the tractor-beam effect, provided by the same system, in addition to the rectification of incident waves.

Quantum correlations in quenched disordered spin models: Enhanced order from disorder by thermal fluctuations

We investigate the behavior of quantum correlations of paradigmatic quenched disordered quantum spin models, viz., the XY spin glass and random-field XY models. We show that quenched averaged quantum correlations can exhibit the order-from-disorder phenomenon for finite-size systems as well as in the thermodynamic limit. Moreover, we find that the order-from-disorder can become more pronounced in the presence of temperature by suitable tuning of the system parameters. The effects are found for entanglement measures as well as for information-theoretic quantum correlation ones, although the former show them more prominently. We also observe that the equivalence between the quenched averages and their self-averaged cousins--for classical and quantum correlations--is related to the quantum critical point in the corresponding ordered system.

Quantum discord length is enhanced while entanglement length is not by introducing disorder in a spin chain

Classical correlation functions of ground states typically decay exponentially and polynomially, respectively, for gapped and gapless short-range quantum spin systems. In such systems, entanglement decays exponentially even at the quantum critical points. However, quantum discord, an information-theoretic quantum correlation measure, survives long lattice distances. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY and XYZ spin glass and random field chains. We find that there is virtually neither reduction nor enhancement in entanglement length while quantum discord length increases significantly with the introduction of the quenched disorder.

Cooling Atomic Gases With Disorder

Cold atomic gases have proven capable of emulating a number of fundamental condensed matter phenomena including Bose-Einstein condensation, the Mott transition, Fulde-Ferrell-Larkin-Ovchinnikov pairing, and the quantum Hall effect. Cooling to a low enough temperature to explore magnetism and exotic superconductivity in lattices of fermionic atoms remains a challenge. We propose a method to produce a low temperature gas by preparing it in a disordered potential and following a constant entropy trajectory to deliver the gas into a nondisordered state which exhibits these incompletely understood phases. We show, using quantum Monte Carlo simulations, that we can approach the Néel temperature of the three-dimensional Hubbard model for experimentally achievable parameters. Recent experimental estimates suggest the randomness required lies in a regime where atom transport and equilibration are still robust.

Many-Body Localization in the Presence of a Single-Particle Mobility Edge

In one dimension, noninteracting particles can undergo a localization-delocalization transition in a quasiperiodic potential. Recent studies have suggested that this transition transforms into a many-body localization (MBL) transition upon the introduction of interactions. It has also been shown that mobility edges can appear in the single particle spectrum for certain types of quasiperiodic potentials. Here, we investigate the effect of interactions in two models with such mobility edges. Employing the technique of exact diagonalization for finite-sized systems, we calculate the level spacing distribution, time evolution of entanglement entropy, optical conductivity, and return probability to detect MBL. We find that MBL does indeed occur in one of the two models we study, but the entanglement appears to grow faster than logarithmically with time unlike in other MBL systems.

Observation of a Fragmented, Strongly Interacting Fermi Gas

We study the emergence of a fragmented state in a strongly interacting Fermi gas subject to a tunable disorder. We investigate its properties using a combination of high-resolution in situ imaging and conductance measurements. The fragmented state exhibits saturated density modulations, a strongly reduced density percolation threshold, lower than the average density, and a resistance equal to that of a noninteracting Fermi gas in the same potential landscape. The transport measurements further indicate that this state is connected to the superfluid state as disorder is reduced. We propose that the fragmented state consists of unpercolated islands of bound pairs, whose binding energy is enhanced by the disorder.

Anomalous quantum glass of bosons in a random potential in two dimensions

We present a quantum Monte Carlo study of the "quantum glass" phase of the two-dimensional Bose-Hubbard model with random potentials at filling ρ=1. In the narrow region between the Mott and superfluid phases, the compressibility has the form κ∼exp(-b/T^{α})+c with α<1 and c vanishing or very small. Thus, at T=0 the system is either incompressible (a Mott glass) or nearly incompressible (a Mott-glass-like anomalous Bose glass). At stronger disorder, where a glass reappears from the superfluid, we find a conventional highly compressible Bose glass. On a path connecting these states, away from the superfluid at larger Hubbard repulsion, a change of the disorder strength by only 10% changes the low-temperature compressibility by more than 4 orders of magnitude, lending support to two types of glass states separated by a phase transition or a sharp crossover.

Transparent lattices and their solitary waves

We provide a family of transparent tight-binding models with nontrivial potentials and site-dependent hopping parameters. Their feasibility is discussed in electromagnetic resonators, dielectric slabs, and quantum-mechanical traps. In the second part of the paper, the arrays are obtained through a generalization of supersymmetric quantum mechanics in discrete variables. The formalism includes a finite-difference Darboux transformation applied to the scattering matrix of a periodic array. A procedure for constructing a hierarchy of discrete Hamiltonians is indicated and a particular biparametric family is given. The corresponding potentials and hopping functions are identified as solitary waves, pointing to a discrete spinorial generalization of the Korteweg-deVries family.

Observation of a disordered bosonic insulator from weak to strong interactions

We employ ultracold atoms with controllable disorder and interaction to study the paradigmatic problem of disordered bosons in the full disorder-interaction plane. Combining measurements of coherence, transport and excitation spectra, we get evidence of an insulating regime extending from weak to strong interaction and surrounding a superfluidlike regime, in general agreement with the theory. For strong interaction, we reveal the presence of a strongly correlated Bose glass coexisting with a Mott insulator.

Quantum tricriticality at the superfluid-insulator transition of binary Bose mixtures

Quantum criticality near a tricritical point is studied in the two-component Bose-Hubbard model on square lattices. The existence of a quantum tricritical point on a boundary of a superfluid-insulator transition is confirmed by quantum Monte Carlo simulations. Moreover, we analytically derive the quantum tricritical behaviors on the basis of an effective field theory. We find two significant features of the quantum tricriticality that are its characteristic chemical potential dependence of the superfluid transition temperature and a strong density fluctuation. We suggest that these features are directly observable in existing experimental setups of Bose-Bose mixtures in optical lattices.

Transport of a Bose gas in 1D disordered lattices at the fluid-insulator transition

We investigate the momentum-dependent transport of 1D quasicondensates in quasiperiodic optical lattices. We observe a sharp crossover from a weakly dissipative regime to a strongly unstable one at a disorder-dependent critical momentum. In the limit of nondisordered lattices the observations suggest a contribution of quantum phase slips to the dissipation. We identify a set of critical disorder and interaction strengths for which such critical momentum vanishes, separating a fluid regime from an insulating one. We relate our observation to the predicted zero-temperature superfluid-Bose glass transition.

Fractional topological states of dipolar fermions in one-dimensional optical superlattices

We study the properties of dipolar fermions trapped in one-dimensional bichromatic optical lattices and show the existence of fractional topological states in the presence of strong dipole-dipole interactions. We find some interesting connections between fractional topological states in one-dimensional superlattices and the fractional quantum Hall states: (i) the one-dimensional fractional topological states for systems at filling factor ν=1/p have p-fold degeneracy, (ii) the quasihole excitations fulfill the same counting rule as that of fractional quantum Hall states, and (iii) the total Chern number of p-fold degenerate states is a nonzero integer. The existence of crystalline order in our system is also consistent with the thin-torus limit of the fractional quantum Hall state on a torus. The possible experimental realization in cold atomic systems offers a new platform for the study of fractional topological phases in one-dimensional superlattice systems.

Superfluidity with disorder in a thin film of quantum gas

We investigate the properties of a strongly interacting superfluid gas of (6)Li(2) Feshbach molecules forming a thin film confined in a quasi-two-dimensional channel with a tunable random potential, creating a microscopic disorder. We measure the atomic current, extract the resistance of the film in a two-terminal configuration, and identify a superfluid state at low disorder strength, which evolves into a normal poorly conducting state for strong disorder. The transition takes place when the chemical potential reaches the percolation threshold of the disorder. The evolution of the conduction properties contrasts with the smooth behavior of the density and compressibility across the transition, measured in situ at equilibrium. These features suggest the emergence of a glasslike phase at strong disorder.

Topological Bose-Mott insulators in a one-dimensional optical superlattice

We study topological properties of the Bose-Hubbard model with repulsive interactions in a one-dimensional optical superlattice. We find that the Mott insulator states of the single-component (two-component) Bose-Hubbard model under fractional fillings are topological insulators characterized by a nonzero charge (or spin) Chern number with nontrivial edge states. For ultracold atomic experiments, we show that the topological Chern number can be detected through measuring the density profiles of the bosonic atoms in a harmonic trap.

Fast dynamics for atoms in optical lattices

Cold atoms in optical lattices allow for accurate studies of many body dynamics. Rapid time-dependent modifications of optical lattice potentials may result in significant excitations in atomic systems. The dynamics in such a case is frequently quite incompletely described by standard applications of tight-binding models (such as, e.g., Bose-Hubbard model or its extensions) that typically neglect the effect of the dynamics on the transformation between the real space and the tight-binding basis. We illustrate the importance of a proper quantum mechanical description using a multiband extended Bose-Hubbard model with time-dependent Wannier functions. We apply it to situations directly related to experiments.

Phase transition of light on complex quantum networks

Recent advances in quantum optics and atomic physics allow for an unprecedented level of control over light-matter interactions, which can be exploited to investigate new physical phenomena. In this work we are interested in the role played by the topology of quantum networks describing coupled optical cavities and local atomic degrees of freedom. In particular, using a mean-field approximation, we study the phase diagram of the Jaynes-Cummings-Hubbard model on complex networks topologies, and we characterize the transition between a Mott-like phase of localized polaritons and a superfluid phase. We found that, for complex topologies, the phase diagram is nontrivial and well defined in the thermodynamic limit only if the hopping coefficient scales like the inverse of the maximal eigenvalue of the adjacency matrix of the network. Furthermore we provide numerical evidences that, for some complex network topologies, this scaling implies an asymptotically vanishing hopping coefficient in the limit of large network sizes. The latter result suggests the interesting possibility of observing quantum phase transitions of light on complex quantum networks even with very small couplings between the optical cavities.

Disordered bosons in one dimension: from weak- to strong-randomness criticality

We investigate the superfluid-insulator quantum phase transition of one-dimensional bosons with off-diagonal disorder by means of large-scale Monte Carlo simulations. For weak disorder, we find the transition to be in the same universality class as the superfluid-Mott insulator transition of the clean system. The nature of the transition changes for stronger disorder. Beyond a critical disorder strength, we find nonuniversal, disorder-dependent critical behavior. We compare our results to recent perturbative and strong-disorder renormalization group predictions. We also discuss experimental implications as well as extensions of our results to other systems.

Nanoplasmonic lattices for ultracold atoms

We propose to use subwavelength confinement of light associated with the near field of plasmonic systems to create nanoscale optical lattices for ultracold atoms. Our approach combines the unique coherence properties of isolated atoms with the subwavelength manipulation and strong light-matter interaction associated with nanoplasmonic systems. It allows one to considerably increase the energy scales in the realization of Hubbard models and to engineer effective long-range interactions in coherent and dissipative many-body dynamics. Realistic imperfections and potential applications are discussed.

Particle-wave duality in quantum tunneling of a bright soliton

One of the most fundamental difference between classical and quantum mechanics is observed in the particle tunneling through a localized potential: the former predicts a discontinuous transmission coefficient (T) as a function in incident velocity between one (complete penetration) and zero (complete reflection); while in the latter T always changes smoothly with a wave nature. Here we report a systematic study of the quantum tunneling property for a bright soliton, which behaves as a classical particle (wave) in the limit of small (large) incident velocity. In the intermediate regime, the classical and quantum properties are combined via a finite (but not full) discontinuity in the tunneling transmission coefficient. We demonstrate that the formation of a localized bound state is essential to describe such inelastic collisions, showing a nontrivial nonlinear effect on the quantum transportation of a bright soliton.

Edge states and topological phases in one-dimensional optical superlattices

We show that one-dimensional quasiperiodic optical lattice systems can exhibit edge states and topological phases which are generally believed to appear in two-dimensional systems. When the Fermi energy lies in gaps, the Fermi system on the optical superlattice is a topological insulator characterized by a nonzero topological invariant. The topological nature can be revealed by observing the density profile of a trapped fermion system, which displays plateaus with their positions uniquely determined by the ration of wavelengths of the bichromatic optical lattice. The butterflylike spectrum of the superlattice system can be also determined from the finite-temperature density profiles of the trapped fermion system. This finding opens an alternative avenue to study the topological phases and Hofstadter-like spectrum in one-dimensional optical lattices.

Phase diagram of the commensurate two-dimensional disordered Bose-Hubbard model

We establish the full ground state phase diagram of the disordered Bose-Hubbard model in two dimensions at a unity filling factor via quantum Monte Carlo simulations. Similarly to the three-dimensional case we observe extended superfluid regions persisting up to extremely large values of disorder and interaction strength which, however, have small superfluid fractions and thus low transition temperatures. In the vicinity of the superfluid-insulator transition of the pure system, we observe an unexpectedly weak--almost not resolvable--sensitivity of the critical interaction to the strength of (weak) disorder.

Glassy behavior in a binary atomic mixture

We experimentally study one-dimensional, lattice-modulated Bose gases in the presence of an uncorrelated disorder potential formed by localized impurity atoms, and compare to the case of correlated quasidisorder formed by an incommensurate lattice. While the effects of the two disorder realizations are comparable deeply in the strongly interacting regime, both showing signatures of Bose-glass formation, we find a dramatic difference near the superfluid-to-insulator transition. In this transition region, we observe that random, uncorrelated disorder leads to a shift of the critical lattice depth for the breakdown of transport as opposed to the case of correlated quasidisorder, where no such shift is seen. Our findings, which are consistent with recent predictions for interacting bosons in one dimension, illustrate the important role of correlations in disordered atomic systems.