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Thermalization in Periodically-Driven Interacting Quantum Systems

Citation

Seetharam, Karthik Iyengar (2018) Thermalization in Periodically-Driven Interacting Quantum Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3G0V-TW52. http://resolver.caltech.edu/CaltechTHESIS:06062018-171256773

Abstract

Periodically-driven (Floquet) quantum systems are ubiquitous in science and technology. For example, when a laser illuminates a material or an AC voltage is applied to a device, the system is well-described by a time-periodic Hamiltonian. In recent years, periodic driving has been proposed, not just as a tool to excite and probe devices, but actually as a mechanism of engineering new phases of matter, some of which have no equilibrium analog. However, with this promise comes a serious problem. Intuitively, if energy is injected into and distributed throughout a system, it is no surprise that it tends to heat up indefinitely to infinite temperature.

In this thesis, we study the mechanisms of heating, i.e. the process of thermalization, in Floquet systems and propose methods to control them. Specifically, for non-interacting Floquet systems that are coupled to external bosonic and fermionic baths (e.g. laser-driven electrons in a semiconductor that interact with phonons and an external lead), we classify the relevant scattering processes that contribute to cooling/heating in the Floquet bands and suggest methods to suppress heating via bandwidth-restrictions on the baths. We find that is possible, with appropriate dissipative engineering, to stabilize a controlled incompressible nonequilibrium steady-state resembling a ground state - a state we term the "Floquet insulator." We extend this analysis to include short-range interactions that contribute additional heating processes and show, under the same framework, that heating can be controlled with dissipation. In the process, we develop a simple effective model for the Floquet band densities that captures the essence of all the Floquet scattering processes and that is useful for ballparking experimentally-relevant estimates of heating. Next, we turn our attention to strongly-interacting closed Floquet systems and study how heating emerges through a proliferation of resonances. We find a novel integrable point governing the strong-interaction limit of the Floquet system and examine the breakdown of integrability via the proliferation of resonances. We observe two distinct scaling regimes, attributed to non-thermal and thermal behavior, and discover a power-law scaling of the crossover between them as a function of system size. The lingering ergodicity-breaking effects of the conserved quantities in the vicinity (in parameter space) of the integrable point at finite size is a phenomena we term "near-integrability." These results suggest that small quantum systems, which are accessible currently in many platforms (e.g. trapped ions, cold atoms, superconducting devices), intrinsically host non-thermal states that one may be able to utilize to avoid heating. Furthermore, our results suggest a "dual" interpretation, in the thermodynamic limit, that a periodically-driven system exhibits prethermalization as a power-law in interaction strength.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Condensed Matter Physics, Nonequilibrium physics, Floquet systems, Periodically-Driven systems
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Refael, Gil
Group:IQIM, Institute for Quantum Information and Matter
Thesis Committee:
  • Refael, Gil (chair)
  • Motrunich, Olexei I.
  • Alicea, Jason F.
  • Hsieh, David
Defense Date:14 May 2018
Non-Caltech Author Email:kseethar (AT) gmail.com
Funders:
Funding AgencyGrant Number
NSF Graduate Research FellowshipUNSPECIFIED
Record Number:CaltechTHESIS:06062018-171256773
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:06062018-171256773
DOI:10.7907/3G0V-TW52
Related URLs:
URLURL TypeDescription
https://link.aps.org/doi/10.1103/PhysRevX.5.041050UNSPECIFIEDArticle adapted for Ch. 2.
https://link.aps.org/doi/10.1103/PhysRevB.97.014311UNSPECIFIEDArticle adapted for Ch. 4.
ORCID:
AuthorORCID
Seetharam, Karthik Iyengar0000-0003-1928-8019
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11032
Collection:CaltechTHESIS
Deposited By: Karthik Seetharam
Deposited On:08 Jun 2018 23:48
Last Modified:13 Jul 2018 22:19

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