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arXiv:1901.08385 · SciPost Physics

Exponentially long lifetime of universal quasi-steady states in topological Floquet pumps

Tobias Gulden, Erez Berg, Mark Spencer Rudner, Netanel Lindner

Published Jul 29, 2020• 15 citations
arXivHTMLPDF

Abstract

We investigate a mechanism to transiently stabilize topological phenomena in long-lived quasi-steady states of isolated quantum many-body systems driven at low frequencies. We obtain an analytical bound for the lifetime of the quasi-steady states which is exponentially large in the inverse driving frequency. Within this lifetime, the quasi-steady state is characterized by maximum entropy subject to the constraint of fixed number of particles in the system's Floquet-Bloch bands. In such a state, all the non-universal properties of these bands are washed out, hence only the topological properties persist.

DOI
10.21468/scipostphys.9.1.015

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We investigate a mechanism to transiently stabilize topological phenomena in long-lived quasi-steady states of isolated quantum many-body systems driven at low frequencies. We obtain an analytical bound for the lifetime of the quasi-steady states which is exponentially large in the inverse driving frequency. Within this lifetime, the quasi-steady state is characterized by maximum entropy subject to the constraint of fixed number of particles in the system's Floquet-Bloch bands. In such a state, all the non-universal properties of these bands are washed out, hence only the topological properties persist.
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We investigate the formation of quasisteady states in one-dimensional pumps of interacting fermions at noninteger filling fraction, in the regime where the driving frequency and the interaction strength are small compared to the instantaneous single-particle band gap throughout the driving cycle. The system rapidly absorbs energy from the driving field and approaches a quasisteady state that locally resembles a maximal entropy state subject to the constraint of a fixed particle number in each of the system's single-particle Floquet bands. We explore the nature of this quasisteady state through one-body observables including the pumped current and natural orbital occupations, as well as the (many-body) entanglement spectrum and entropy. Potential disorder significantly reduces the amplitude of fluctuations of the quasisteady-state current around its universal value, while the lifetime of the quasisteady state remains nearly unaffected for disorder strengths up to the scale of the single-particle band gap. Interestingly, the natural orbital occupations and the entanglement entropy display patterns signifying the periodic entangling and disentangling of the system's degrees of freedom over each driving cycle. Moreover, prominent features in the system's time-dependent entanglement spectrum reveal the emergence of long timescales associated with the equilibration of many-particle correlations.
We investigate a class of periodically driven many-body systems that allows us to extend the phenomenon of prethermalization to the vicinity of isolated intermediate-to-low drive frequencies away from the high-frequency limit. We provide numerical evidence for the formation of a parametrically long-lived prethermal plateau, captured by an effective Floquet Hamiltonian computed using the replica inverse-frequency expansion, and demonstrate its stability w.r.t.~random perturbations in the drive period. Considering exclusively nonintegrable Floquet Hamiltonians, we find that heating rates are non-universal: we observe Fermi's Golden Rule scaling, power-law scaling inconsistent with the Golden Rule, and non-power law scaling, depending on the drive. Despite the asymptotic character of the inverse-frequency expansion, we show that it describes the thermostatic properties of the state all along the evolution up to infinite temperature, with higher-order terms improving the accuracy. Our results suggest a dynamical mechanism to gradually increase temperature in isolated quantum simulators, such as ultracold atoms, and open up an alternative possibility to investigate thermal phase transitions and the interplay between thermal and quantum criticality using Floquet drives.
We review methods for using time-periodic fields (e.g., laser or microwave fields) to induce non-equilibrium topological phenomena in quantum many-body systems. We discuss how such fields can be used to change the topological properties of the single particle spectrum, and key experimental demonstrations in solid state, cold atomic, and photonic systems. The single particle Floquet band structure provides a stage on which the system's dynamics play out; the crucial question is then how to obtain robust topological behaviour in the many-particle setting. In the regime of mesoscopic transport, we discuss manifestations of topological edge states induced in the Floquet spectrum. Outside the context of mesoscopic transport, the main challenge of inducing stable topological phases in many-body Floquet systems is their tendency to absorb energy from the drive and thereby to heat up. We discuss three routes to overcoming this challenge: long-lived transient dynamics and prethermalization, disorder-induced many-body localization, and engineered couplings to external baths. We discuss the types of phenomena that can be explored in each of these regimes, and their experimental realizations.
We discuss the universal nature of relaxation in isolated many-body quantum systems subjected to global and strong periodic driving. Our rigorous Floquet analysis shows that the energy of the system remains almost constant up to an exponentially long time in frequency for arbitrary initial states and that an effective Hamiltonian obtained by a truncation of the Floquet-Magnus expansion is a quasiconserved quantity in a long time scale. These two general properties lead to an intriguing classification on the initial stage of relaxation, one of which is similar to the prethermalization phenomenon in nearly integrable systems.
Floquet topological insulators are noninteracting quantum systems that, when driven by a time-periodic field, are described by effective Hamiltonians whose bands carry nontrivial topological invariants. A longstanding question concerns the possibility of selectively populating one of these effective bands, thereby maximizing the system's resemblance to a static topological insulator. We study such Floquet systems coupled to a zero-temperature thermal reservoir that provides dissipation. We find that the resulting electronic steady states are generically characterized by a finite density of excitations above the effective ground state, even when the driving has a small amplitude and/or large frequency. We discuss the role of reservoir engineering in mitigating this problem.