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.
Multifractal states offer a "third way" for quantum matter, neither fully localized nor ergodic, exhibiting singular continuous spectra, self-similar wavefunctions, and transport and entanglement scaling exponents intermediate between extended and localized states. While multifractality in equilibrium systems generally requires fine-tuning to a critical point, externally driven quantum matter can exhibit multifractal states with no equilibrium counterpart. We report the experimental observation of multifractal matter and anomalous localization in a kicked Aubry-André-Harper quasicrystal. Our cold-atom realization of this previously-unexplored model is enabled by apodized Floquet engineering techniques which expand the accessible phase diagram by five orders of magnitude. This kicked quantum quasicrystal exhibits a rich phase diagram including not only fully localized and fully delocalized phases but also an extended region comprising an intricate nested pattern of localized, delocalized, and multifractal states. Mapping transport properties throughout the phase diagram, we observe disorder-driven re-entrant delocalization and sub-ballistic transport, and present a theoretical explanation of these phenomena based on eigenstate multifractality. These results open up the exploration of new states of matter characterized by an intricate interplay of fractal structure and quantum dynamics.
“Kicking” a quantum system by subjecting it to a pulsed time-dependent Hamiltonian can give rise to a rich array of behaviors, from localization to multifractality. In this talk we will describe two recent experiments on kicked quantum matter using ultracold neutral atoms. In the first experiment, we measured the “quantum boomerang effect,” a fundamental dynamical feature of Anderson-localized matter which was only recently theoretically predicted and has not to our knowledge been observed before. The second experiment explores an extended multifractal phase in a kicked quasicrystal, using a technique of “apodized” Floquet engineering. The results illuminate a variety of phenomena ranging from the interplay of ergodicity and localization to new techniques of quantum control.
The critical phase of a non-Hermitian quasicrystal can support stronger transport than its surrounding delocalized phase. We demonstrate this anomalous behavior in the one-dimensional nonreciprocal Aubry-André-Harper model through a combined study of dynamical quantum phase transitions (DQPTs) and wavepacket diffusion. Using a parity-sorted energy-spectrum classification that directly encodes the generalized
PT symmetry, we find that DQPTs in this system are energy-resolved, in contrast to the energy-independent DQPTs of Hermitian quasicrystals. The energy-resolved features are most pronounced when the initial and final Hamiltonians belong to different phases (localized or extended), and they are tied to the even-odd index structure of the spectrum, which we exploit to organize the quench-dynamical landscape. For wavepacket dynamics after a single-site quench, the diffusion exponent
β, extracted from the long-time power-law scaling of the root-mean-square displacement
σ(τ), partitions the phase diagram into four distinct regimes. In the Hermitian limit the extended phase is ballistic (
β=1), the critical phase is normally diffusive (
β=0.5), and the localized phase yields
β→0. Nonreciprocity reverses this hierarchy: the extended phase becomes normally diffusive, while the critical phase turns ballistic. We trace the anomalous
β=1 at criticality to the self-similar multifractal structure of the critical eigenstates, whose nodal positions are organized by the golden ratio. A finite-size scaling ansatz built on the wave-front propagation yields
σ(τ)∝τ. The parity-resolved DQPTs and the
β-phase diagram establish two complementary dynamical diagnostics of nonreciprocal quasicrystals, in which nonreciprocity promotes transport at the critical point and suppresses it in the delocalized phase.
The disordered XXZ model is a prototype model of the many-body localization transition (MBL). Despite numerous studies of this model, the available numerical evidence of multifractality of its eigenstates is not very conclusive due severe finite size effects. Moreover it is not clear if similarly to the case of single-particle physics, multifractal properties of the many-body eigenstates are related to anomalous transport, which is observed in this model. In this work, using a state-of-the-art, massively parallel, numerically exact method, we study systems of up to 24 spins and show that a large fraction of the delocalized phase flows towards ergodicity in the thermodynamic limit, while a region immediately preceding the MBL transition appears to be multifractal in this limit. We discuss the implication of our finding on the mechanism of subdiffusive transport.
The disordered XXZ model is a prototype model of the many-body localization (MBL) transition. Despite numerous studies of this model, the available numerical evidence of multifractality of its eigenstates is not very conclusive due to severe finite size effects. Moreover it is not clear if similarly to the case of single-particle physics, multifractal properties of the many-body eigenstates are related to anomalous transport, which is observed in this model. In this work, using a state-of-the-art, massively parallel, numerically exact method, we study systems of up to 24 spins and show that a large fraction of the delocalized phase flows towards ergodicity in the thermodynamic limit, while a region immediately preceding the MBL transition appears to be multifractal in this limit. We discuss the implication of our finding on the mechanism of subdiffusive transport.
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.