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arXiv:2312.00976 · Physical Review Letters

Reversible Phasonic Control of a Quantum Phase Transition in a Quasicrystal

Toshihiko Shimasaki, Yifei Bai, H. Esat Kondakci, Peter Dotti, Jared E. Pagett, Anna R. Dardia, Max Prichard, André Eckardt, David Weld

Published Aug 22, 2024• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.133.083405

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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.
Light-induced quantum phases offer the potential for simple and powerful tuning of material properties. For example, simply illuminating 2D materials in the integer quantum Hall regime with polarized light is predicted to drive quantum phase transitions. Such phenomena are largely beyond the current frontier of solid state experiments due to technical limitations on laser intensity and material purity. However, the Harper-Hofstadter mapping which relates a two-dimensional integer quantum Hall system to a 1D quasicrystal enables the same polarization-dependent light-induced phase transitions to be observed using a quantum gas in a driven quasiperiodic optical lattice. We report results of such an experiment. We observe an interlaced phase diagram of localization-delocalization phase transitions as a function of drive polarization and amplitude. Elliptically polarized driving can stabilize an extended critical phase featuring multifractal wave functions; we observe signatures of this phenomenon in anomalous polarization-dependent subdiffusive transport. In this regime, increasing the strength of the quasiperiodic potential can enhance rather than suppress transport. These experiments demonstrate a simple method for synthesizing exotic multifractal states and exploring light-induced quantum phases across different dimensionalities.
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.
Phasonic degrees of freedom are unique to quasiperiodic structures and play a central role in poorly understood properties of quasicrystals from excitation spectra to wave function statistics to electronic transport. However, phasons are challenging to access dynamically in the solid state due to their complex long-range character and the effects of disorder and strain. We report phasonic spectroscopy of a quantum gas in a one-dimensional quasicrystalline optical lattice. We observe that strong phasonic driving produces a nonperturbative high-harmonic plateau strikingly different from the effects of standard dipolar driving. Tuning the potential from crystalline to quasicrystalline, we identify spectroscopic signatures of quasiperiodicity and interactions and map the emergence of a multifractal energy spectrum, opening a path to direct imaging of the Hofstadter butterfly.
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.
The tunneling properties of a quantum system of matter waves inside a periodic potential can be dramatically changed if the potential is driven back and forth. Similarly to an atom in a strong radiation field, the matter waves inside the strongly driven potential are "dressed" and acquire new properties. In this paper, the authors have demonstrated that such dressed matter waves can be coherently and adiabatically loaded and controlled in one, two and three dimensional strongly driven optical lattices. In the driven lattices the tunneling probability and the tunneling phase between adjacent lattice sites become a function of the driving parameters. The regimes in which the driving parameters can be changed without exciting the system have been identified, thus allowing coherent and adiabatic following. This coherent control is then used in order to reversibly induce the superfluid-Mott insulator phase transition by changing the the driving strength.
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.