The interplay of various localizing mechanisms is a central topic of modern condensed matter physics. In this work we experimentally explore the interplay between quasiperiodic disorder and periodic driving, each of which in isolation is capable of driving a metal-insulator phase transition. Using a 1D quasiperiodic cold-atom chain we measure transport across the full phase diagram varying both drive strength and quasidisorder strength. We observe lobes of metallic phases bounded by quantum phase transitions which depend on both drive and disorder. While these observations are broadly consistent with expectations from a high-drive-frequency theoretical model, we also observe clear departures from the predictions of this model, including anomalous changes in localization behavior at lower drive frequency. We demonstrate experimentally and theoretically that understanding the full measured phase diagram requires an extension to commonly used approximate theories of Floquet matter.
The interplay of various localizing mechanisms is a central topic of modern condensed matter physics. In this work we experimentally explore the interplay between quasiperiodic disorder and periodic driving, each of which in isolation is capable of driving a metal-insulator phase transition. Using a 1D quasiperiodic cold-atom chain we measure transport across the full phase diagram varying both drive strength and quasidisorder strength. We observe lobes of metallic phases bounded by quantum phase transitions which depend on both drive and disorder. While these observations are broadly consistent with expectations from a high-drive-frequency theoretical model, we also observe clear departures from the predictions of this model, including anomalous changes in localization behavior at lower drive frequency. We demonstrate experimentally and theoretically that understanding the full measured phase diagram requires an extension to commonly used approximate theories of Floquet matter.
Abstract Quantum transport can distinguish between dynamical phases of matter. For instance, ballistic propagation characterizes the absence of disorder, whereas in many-body localized phases, particles do not propagate for exponentially long times. Additional possibilities include states of matter exhibiting anomalous transport in which particles propagate with a non-trivial exponent. Here we report the experimental observation of anomalous transport across a broad range of the phase diagram of a kicked quasicrystal. The Hamiltonian of our system has been predicted to exhibit a rich phase diagram, including not only fully localized and fully delocalized phases but also an extended region comprising a nested pattern of localized, delocalized and multifractal states, which gives rise to anomalous transport. Our cold-atom realization is enabled by new Floquet engineering techniques, which expand the accessible phase diagram by five orders of magnitude. Mapping transport properties throughout the phase diagram, we observe disorder-driven re-entrant delocalization and sub-ballistic transport, and we present a theoretical explanation of these phenomena based on eigenstate multifractality.
Periodic driving can tune the quasistatic properties of quantum matter. A well-known example is the dynamical modification of tunneling by an oscillating electric field. Here we show experimentally that driving the phasonic degree of freedom of a cold-atom quasicrystal can continuously tune the effective quasidisorder strength, reversibly toggling a localization-delocalization quantum phase transition. Measurements agree with fit-parameter-free theoretical predictions, and illuminate a fundamental connection between Aubry-André localization in one dimension and dynamic localization in the associated two-dimensional Harper-Hofstadter model. These results open up new experimental possibilities for dynamical coherent control of quantum phase transitions.
Particle transport and energy flow are central to a wide range of phenomena in the natural sciences. While interactions generically promote ergodicity and diffusion, quantum interference can arrest transport, defying classical expectations. Here, we experimentally investigate their interplay in a periodically driven 3D quantum gas with tunable interactions. Strikingly, we find a sharp dynamical boundary separating localization from diffusive energy absorption. By tuning the driving amplitude and interaction strength, we map the localization-delocalization phase diagram and characterize this boundary via finite-time scaling. On the insulating side, we observe many-body dynamical localization (MBDL) featuring arrested momentum-space transport. Transport becomes subdiffusive near the boundary and diffusive in the delocalized regime, yielding a metal-insulator transition that we interpret as localization in many-body Hilbert space. Our results exemplify an interaction-enabled dynamical phase transition in a closed Floquet many-body system, and clarify how coherence and interactions jointly govern the quantum-to-classical transition.
Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g. disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important. The first is the so-called “dirty” or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder. The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting (“ergodic”) phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.
Abstract The intricate relationship between topology and disorder in non-equilibrium quantum systems presents a captivating avenue for exploring localization phenomenon. Here, we look for a suitable platform that enables an in-depth investigation of the topic. To this end, we delve into the nuanced analysis of the topological and localization characteristics exhibited by a one-dimensional dimerized Kitaev chain under periodic driving and perform detailed analyses of the Floquet Majorana modes. Such a non-equilibrium scenario is made further interesting by including a spatially varying quasiperiodic potential with a temporally modulated amplitude. Apriori, the motivation is to explore an interplay between dimerization and a quasiperiodic disorder in a topological setting which is also known to demonstrate unique (re-entrant) localization properties. While the topological properties of the driven system confirm the presence of zero and π π Majorana modes, the phase diagram obtained by constructing a pair of topological invariants ( Z×Z Z × Z ), also referred to as the real space winding numbers, at different driving frequencies reveal intriguing features that are distinct from the static scenario. In particular, at either low or intermediate frequency regimes, the phase diagram concerning the zero mode involves two distinct phase transitions, one from a topologically trivial to a non-trivial phase, and another from a topological phase to an Anderson localized phase. On the other hand, the study of the Majorana π π mode unveils the emergence of a unique topological phase, characterized by complete localization of both the bulk and the edge modes, which may be called as the Floquet topological Anderson phase. Moreover, different frequency regimes showcase distinct localization features which can be examined via the localization toolbox, namely, the inverse and the normalized participation ratios. Specifically, the low and high-frequency regimes demonstrate the existence of completely extended and localized phases, respectively. While at intermediate frequencies, we observe the critical (multifractal) phase of the model which is further investigated via a finite-size scaling analysis of the fractal dimension. Finally, to add depth into our study, we have performed a mean level spacing analyses and computed the Hausdorff dimension which yields specific characteristics inherent to the critical phase, offering profound insights into its underlying properties.
Periodic driving provides a powerful route for controlling localization and engineering effective Hamiltonians in quantum systems. A localized one-dimensional Aubry-André chain can be driven into a fully delocalized phase when the entire system is driven below a critical frequency. Here, we ask whether such delocalization can be achieved by driving only a part of the system. We address this question using a two-leg ladder comprising an Aubry-André chain coupled to a periodically driven clean tight-binding chain. Exact numerical calculations show that, starting from a localized static ladder, subsystem driving below a critical frequency cannot achieve complete delocalization. Instead, a mixed phase emerges, with localized and delocalized states coexisting and the fraction of delocalized states varying nonmonotonically with the driving frequency. This behavior can be understood using local effective Hamiltonians. Although these effective Hamiltonians are derived analytically in the high-frequency regime, they can nevertheless predict the localization transition occurring in the moderate-frequency regime. In fact, by quantifying the emergent nonlocality of the Floquet Hamiltonian, we show that these effective Hamiltonians provide a valid description up to a crossover frequency that is lower than the critical frequency associated with the localization transition. Our results demonstrate an alternative route to Floquet engineering, in which the transport properties of a quantum lattice system can be modified by driving only a subsystem.