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.
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.
“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.
We study the combined effect of quasiperiodic disorder, driven, and interaction in the periodically kicked Aubry-Andr\'e model. In the noninteracting limit, by analyzing the quasienergy spectrum statistics, we verify the existence of a dynamical localization transition in the high-frequency region, whereas the spectrum statistics becomes intricate in the low-frequency region due to the emergence of the extended/localized-to-multifractal edges in the quasienergy spectrum, which separate the multifractal states from the extended (localized) states. When the interaction is introduced, we find the periodically kicked incommensurate potential can lead to a transition from the ergodic to many-body-localization phase in the high-frequency region. However, the many-body localization phase vanishes in the low-frequency region even for the strong quasiperiodic disorder. Our studies demonstrate that the periodically kicked Aubry-Andr\'e model displays rich dynamical phenomena and the driving frequency plays an important role in the formation of many-body localization in addition to the disorder strength.
Anderson localization and the mobility edge (ME) have been extensively studied in isolated aperiodic systems. Conventional theory suggests that dephasing and decoherence should disrupt localization and facilitate transport. In this work, we investigate localization behaviors in a dimerized off-diagonal Aubry-Andre-Harper (AAH) quasicrystal subject to on-site pure dephasing. In the strong-dephasing limit, we apply adiabatic elimination within the Lindblad master equation framework to derive an effective classical Markov transition matrix that governs the dissipative relaxation dynamics. Counterintuitively, we demonstrate that pure dephasing can induce distinct MEs, including both conventional MEs separating extended and localized states and anomalous MEs separating multifractal critical states from localized states, even when all eigenstates of the original closed coherent system are delocalized or multifractal. Using fractal dimension finite-size scaling, wave-packet spreading dynamics, and energy spectrum statistics, we numerically verify the coexistence of fully extended, multifractal critical, and localized regions within the relaxation spectrum of the dissipative system, and construct the global dissipative phase diagram. These findings reveal that dephasing can see as a powerful mechanism for controlling localization transitions, thus enhancing our understanding of dissipative quasicrystal systems.
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.
Localization in non-Hermitian quasicrystals can differ fundamentally from its Hermitian counterpart when non-reciprocity is spatially disordered. Here we study a one-dimensional non-Hermitian Aubry-André-Harper chain with a Bernoulli imaginary gauge field and quasiperiodic onsite modulation. In the nearest-neighbor limit, we identify an anomalous transition from a fully erratic non-Hermitian skin effect (ENHSE) phase to a fully localized phase. Although the fractal dimension vanishes in both regimes, the Lyapunov exponent and the fluctuation of the eigenstate center of mass sharply distinguish them. For generic finite-size realizations, this transition is further accompanied by a complex-to-real spectral change under periodic boundary conditions and a change of spectral winding from nontrivial to trivial. With weak next-nearest-neighbor hopping, we uncover an anomalous mobility edge at the same location as in the Hermitian generalized Aubry-André-Harper model, but separating Anderson-localized states from ENHSE-type macroscopic-accumulation states rather than extended states. We further show that this anomalous localization structure is reflected in spectral winding and wave-packet dynamics: single realizations exhibit winding-dependent drift, winding-resolved averaging preserves opposite directional responses, and full disorder averaging largely restores Hermitian-like transport. Our results establish practical diagnostics of anomalous localization and mobility edges in non-Hermitian quasicrystals.