Purification and many-body localization in cold atomic gases

Exploring Integrability-Chaos Transition with a Sequence of Independent Perturbations

A gas of interacting particles is a paradigmatic example of chaotic systems. It is shown here that, even if all but one particle are fixed in generic positions, the excited states of the moving particle are chaotic. They are characterized by the number of principal components (NPC)-the number of integrable system eigenstates involved into the nonintegrable one, which increases linearly with the number of strong scatterers. This rule is a particular case of the general effect of an additional perturbation on the system chaotic properties. The perturbation independence criteria supposing the system chaoticity increase are derived here as well. The effect can be observed in experiments with photons or cold atoms as the decay of observable fluctuation variance, which is inversely proportional to NPC and, therefore, to the number of scatterers. This decay indicates that the eigenstate thermalization is approached. The results are confirmed by numerical calculations for a harmonic waveguide with zero-range scatterers along its axis.

Evidence for Unbounded Growth of the Number Entropy in Many-Body Localized Phases

We investigate the number entropy S_{N}-which characterizes particle-number fluctuations between subsystems-following a quench in one-dimensional interacting many-body systems with potential disorder. We find evidence that in the regime which is expected to show many-body localization and where the entanglement entropy grows as S∼lnt as function of time t, the number entropy grows as S_{N}∼lnlnt, indicating continuing subdiffusive particle transport at a very slow rate. We demonstrate that this growth is consistent with a relation between entanglement and number entropy recently established for noninteracting systems.

Einstein Relation for a Driven Disordered Quantum Chain in the Subdiffusive Regime

A quantum particle propagates subdiffusively on a strongly disordered chain when it is coupled to itinerant hard-core bosons. We establish a generalized Einstein relation (GER) that relates such subdiffusive spread to an unusual time-dependent drift velocity, which appears as a consequence of a constant electric field. We show that GER remains valid much beyond the regime of the linear response. Qualitatively, it holds true up to strongest drivings when the nonlinear field effects lead to the Stark-like localization. Numerical calculations based on full quantum evolution are substantiated by much simpler rate equations for the boson-assisted transitions between localized Anderson states.

Quantum Slow Relaxation and Metastability due to Dynamical Constraints

One of the general mechanisms that give rise to the slow cooperative relaxation characteristic of classical glasses is the presence of kinetic constraints in the dynamics. Here we show that dynamical constraints can similarly lead to slow thermalization and metastability in translationally invariant quantum many-body systems. We illustrate this general idea by considering two simple models: (i) a one-dimensional quantum analogue to classical constrained lattice gases where excitation hopping is constrained by the state of neighboring sites, mimicking excluded-volume interactions of dense fluids; and (ii) fully packed quantum dimers on the square lattice. Both models have a Rokhsar-Kivelson (RK) point at which kinetic and potential energy constants are equal. To one side of the RK point, where kinetic energy dominates, thermalization is fast. To the other, where potential energy dominates, thermalization is slow, memory of initial conditions persists for long times, and separation of timescales leads to pronounced metastability before eventual thermalization. Furthermore, in analogy with what occurs in the relaxation of classical glasses, the slow-thermalization regime displays dynamical heterogeneity as manifested by spatially segregated growth of entanglement.

Metastability and avalanche dynamics in strongly correlated gases with long-range interactions

We experimentally study the stability of a bosonic Mott insulator against the formation of a density wave induced by long-range interactions and characterize the intrinsic dynamics between these two states. The Mott insulator is created in a quantum degenerate gas of 87-Rubidium atoms, trapped in a 3D optical lattice. The gas is located inside and globally coupled to an optical cavity. This causes interactions of global range, mediated by photons dispersively scattered between a transverse lattice and the cavity. The scattering comes with an atomic density modulation, which is measured by the photon flux leaking from the cavity. We initialize the system in a Mott-insulating state and then rapidly increase the global coupling strength. We observe that the system falls into either of two distinct final states. One is characterized by a low photon flux, signaling a Mott insulator, and the other is characterized by a high photon flux, which we associate with a density wave. Ramping the global coupling slowly, we observe a hysteresis loop between the two states-a further signature of metastability. A comparison with a theoretical model confirms that the metastability originates in the competition between short- and global-range interactions. From the increasing photon flux monitored during the switching process, we find that several thousand atoms tunnel to a neighboring site on the timescale of the single-particle dynamics. We argue that a density modulation, initially forming in the compressible surface of the trapped gas, triggers an avalanche tunneling process in the Mott-insulating region.

Complete Many-Body Localization in the t-J Model Caused by a Random Magnetic Field

The many body localization (MBL) of spin-1/2 fermions poses a challenging problem. It is known that the disorder in the charge sector may be insufficient to cause full MBL. Here, we study dynamics of a single hole in one dimensional t-J model subject to a random magnetic field. We show that strong disorder that couples only to the spin sector localizes both spin and charge degrees of freedom. Charge localization is confirmed also for a finite concentration of holes. While we cannot precisely pinpoint the threshold disorder, we conjecture that there are two distinct transitions. Weaker disorder first causes localization in the spin sector. Carriers become localized for somewhat stronger disorder, when the spin localization length is of the order of a single lattice spacing.

Absence of Ergodicity without Quenched Disorder: From Quantum Disentangled Liquids to Many-Body Localization

We study the time evolution after a quantum quench in a family of models whose degrees of freedom are fermions coupled to spins, where quenched disorder appears neither in the Hamiltonian parameters nor in the initial state. Focusing on the behavior of entanglement, both spatial and between subsystems, we show that the model supports a state exhibiting combined area and volume-law entanglement, being characteristic of the quantum disentangled liquid. This behavior appears for one set of variables, which is related via a duality mapping to another set, where this structure is absent. Upon adding density interactions between the fermions, we identify an exact mapping to an XXZ spin chain in a random binary magnetic field, thereby establishing the existence of many-body localization with its logarithmic entanglement growth in a fully disorder-free system.

Quantum Mutual Information as a Probe for Many-Body Localization

We demonstrate that the quantum mutual information (QMI) is a useful probe to study many-body localization (MBL). First, we focus on the detection of a metal-insulator transition for two different models, the noninteracting Aubry-André-Harper model and the spinless fermionic disordered Hubbard chain. We find that the QMI in the localized phase decays exponentially with the distance between the regions traced out, allowing us to define a correlation length, which converges to the localization length in the case of one particle. Second, we show how the QMI can be used as a dynamical indicator to distinguish an Anderson insulator phase from a MBL phase. By studying the spread of the QMI after a global quench from a random product state, we show that the QMI does not spread in the Anderson insulator phase but grows logarithmically in time in the MBL phase.

Robustness of Many-Body Localization in the Presence of Dissipation

Many-body localization (MBL) has emerged as a novel paradigm for robust ergodicity breaking in closed quantum many-body systems. However, it is not yet clear to which extent MBL survives in the presence of dissipative processes induced by the coupling to an environment. Here we study heating and ergodicity for a paradigmatic MBL system-an interacting fermionic chain subject to quenched disorder-in the presence of dephasing. We find that, even though the system is eventually driven into an infinite-temperature state, heating as monitored by the von Neumann entropy can progress logarithmically slowly, implying exponentially large time scales for relaxation. This slow loss of memory of initial conditions makes signatures of nonergodicity visible over a long, but transient, time regime. We point out a potential controlled realization of the considered setup with cold atomic gases held in optical lattices.

Nonequilibrium localization and the interplay between disorder and interactions

We study the nonequilibrium interplay between disorder and interactions in a closed quantum system. We base our analysis on the notion of dynamical state-space localization, calculated via the Loschmidt echo. Although real-space and state-space localization are independent concepts in general, we show that both perspectives may be directly connected through a specific choice of initial states, namely, maximally localized states (ML-states). We show numerically that in the noninteracting case the average echo is found to be monotonically increasing with increasing disorder; these results are in agreement with an analytical evaluation in the single particle case in which the echo is found to be inversely proportional to the localization length. We also show that for interacting systems, the length scale under which equilibration may occur is upper bounded and such bound is smaller the greater the average echo of ML-states. When disorder and interactions, both being localization mechanisms, are simultaneously at play the echo features a non-monotonic behaviour indicating a non-trivial interplay of the two processes. This interplay induces delocalization of the dynamics which is accompanied by delocalization in real-space. This non-monotonic behaviour is also present in the effective integrability which we show by evaluating the gap statistics.

QUANTUM GASES. Observation of many-body localization of interacting fermions in a quasirandom optical lattice

Many-body localization (MBL), the disorder-induced localization of interacting particles, signals a breakdown of conventional thermodynamics because MBL systems do not thermalize and show nonergodic time evolution. We experimentally observed this nonergodic evolution for interacting fermions in a one-dimensional quasirandom optical lattice and identified the MBL transition through the relaxation dynamics of an initially prepared charge density wave. For sufficiently weak disorder, the time evolution appears ergodic and thermalizing, erasing all initial ordering, whereas above a critical disorder strength, a substantial portion of the initial ordering persists. The critical disorder value shows a distinctive dependence on the interaction strength, which is in agreement with numerical simulations. Our experiment paves the way to further detailed studies of MBL, such as in noncorrelated disorder or higher dimensions.

Many-Body Localization Characterized from a One-Particle Perspective

We show that the one-particle density matrix ρ can be used to characterize the interaction-driven many-body localization transition in closed fermionic systems. The natural orbitals (the eigenstates of ρ) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues of ρ) reveals the distinctive Fock-space structure of the many-body eigenstates, exhibiting a steplike discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition. We analyze the inverse participation ratio of the natural orbitals and find that it is independent of system size in the localized phase.

Anomalous diffusion and griffiths effects near the many-body localization transition

We explore the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase. In the vicinity of the transition, we find that this phase has the following properties: (i) local magnetization fluctuations relax subdiffusively; (ii) the ac conductivity vanishes near zero frequency as a power law; and (iii) the distribution of resistivities becomes increasingly broad at low frequencies, approaching a power law in the zero-frequency limit. We argue that these effects can be understood in a unified way if the metallic phase near the MBL transition is a quantum Griffiths phase. We establish scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. A phenomenological classical resistor-capacitor model captures all the essential features.