skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Topological Frequency Conversion in Strongly Driven Quantum Systems

Abstract

When a physical system is subjected to a strong external multi-frequency drive, its dynamics can be conveniently represented in the multi-dimensional Floquet lattice. The number of the Floquet lattice dimensions equals the number of irrationally-related drive frequencies, and the evolution occurs in response to a built-in effective \electric" field, whose components are proportional to the corresponding drive frequencies. The mapping allows to engineer and study temporal analogs of many real-space phenomena. Here we focus on the specifc example of a two-level system under two-frequency drive that induces topologically nontrivial band structure in the 2D Floquet space. The observable consequence of such construction is quantized pumping of energy between the sources with frequencies w 1 and w 2. Finally, when the system is initialized into a Floquet band with the Chern number C, the pumping occurs at the rate P 12 = – P 21 = ( C/2π)hw 1w 2, an exact counterpart of the transverse current in a conventional topological insulator.

Authors:
; ;
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1399642
Alternate Identifier(s):
OSTI ID: 1400405
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Journal Article: Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Name: Physical Review. X Journal Volume: 7 Journal Issue: 4; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Martin, Ivar, Refael, Gil, and Halperin, Bertrand. Topological Frequency Conversion in Strongly Driven Quantum Systems. United States: N. p., 2017. Web. doi:10.1103/PhysRevX.7.041008.
Martin, Ivar, Refael, Gil, & Halperin, Bertrand. Topological Frequency Conversion in Strongly Driven Quantum Systems. United States. doi:10.1103/PhysRevX.7.041008.
Martin, Ivar, Refael, Gil, and Halperin, Bertrand. Mon . "Topological Frequency Conversion in Strongly Driven Quantum Systems". United States. doi:10.1103/PhysRevX.7.041008.
@article{osti_1399642,
title = {Topological Frequency Conversion in Strongly Driven Quantum Systems},
author = {Martin, Ivar and Refael, Gil and Halperin, Bertrand},
abstractNote = {When a physical system is subjected to a strong external multi-frequency drive, its dynamics can be conveniently represented in the multi-dimensional Floquet lattice. The number of the Floquet lattice dimensions equals the number of irrationally-related drive frequencies, and the evolution occurs in response to a built-in effective \electric" field, whose components are proportional to the corresponding drive frequencies. The mapping allows to engineer and study temporal analogs of many real-space phenomena. Here we focus on the specifc example of a two-level system under two-frequency drive that induces topologically nontrivial band structure in the 2D Floquet space. The observable consequence of such construction is quantized pumping of energy between the sources with frequencies w1 and w2. Finally, when the system is initialized into a Floquet band with the Chern number C, the pumping occurs at the rate P12 = –P21 = (C/2π)hw1w2, an exact counterpart of the transverse current in a conventional topological insulator.},
doi = {10.1103/PhysRevX.7.041008},
journal = {Physical Review. X},
issn = {2160-3308},
number = 4,
volume = 7,
place = {United States},
year = {2017},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevX.7.041008

Citation Metrics:
Cited by: 22 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Theory of many-body localization in periodically driven systems
journal, September 2016


Metallic Phase with Long-Range Orientational Order and No Translational Symmetry
journal, November 1984


Single fermion manipulation via superconducting phase differences in multiterminal Josephson junctions
journal, October 2014


Floquet topological insulator in semiconductor quantum wells
journal, March 2011

  • Lindner, Netanel H.; Refael, Gil; Galitski, Victor
  • Nature Physics, Vol. 7, Issue 6
  • DOI: 10.1038/nphys1926

Stark Ladders in a Two-Dimensional Tight-Binding Lattice
journal, August 1993

  • Nakanishi, Takeshi; Ohtsuki, Tomi; Saitoh, Motohiko
  • Journal of the Physical Society of Japan, Vol. 62, Issue 8
  • DOI: 10.1143/JPSJ.62.2773

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
journal, December 2006

  • Bernevig, B. A.; Hughes, T. L.; Zhang, S.-C.
  • Science, Vol. 314, Issue 5806, p. 1757-1761
  • DOI: 10.1126/science.1133734

Prethermal Phases of Matter Protected by Time-Translation Symmetry
journal, March 2017


Photoinduced Transition between Conventional and Topological Insulators in Two-Dimensional Electronic Systems
journal, June 2010


Quasicrystals: A New Class of Ordered Structures
journal, December 1984


Topological nodal semimetals
journal, December 2011


Floquet topological phases with symmetry in all dimensions
journal, May 2017


Anderson Transition in a One-Dimensional System with Three Incommensurate Frequencies
journal, January 1989


�ber die Quantenmechanik der Elektronen in Kristallgittern
journal, July 1929


Topological electronic structure and Weyl semimetal in the TlBiSe 2 class of semiconductors
journal, September 2012


Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
journal, June 1999


Quantization of particle transport
journal, May 1983


Theory of Zener tunneling and Wannier-Stark states in semiconductors
journal, September 1994


Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems
journal, July 2013


Observation of Floquet-Bloch States on the Surface of a Topological Insulator
journal, October 2013

  • Wang, Y. H.; Steinberg, H.; Jarillo-Herrero, P.
  • Science, Vol. 342, Issue 6157, p. 453-457
  • DOI: 10.1126/science.1239834

Low-Temperature Line-Width Maximum in Yttrium Iron Garnet
journal, July 1959


Multiple Nonlinear Optical Interactions with Arbitrary Wave Vector Differences
journal, December 2001


Photonic Floquet topological insulators
journal, April 2013

  • Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan
  • Nature, Vol. 496, Issue 7444
  • DOI: 10.1038/nature12066

Eight-Dimensional Quantum Hall Effect and “Octonions”
journal, December 2003


Photovoltaic Hall effect in graphene
journal, February 2009


Multi-terminal Josephson junctions as topological matter
journal, April 2016

  • Riwar, Roman-Pascal; Houzet, Manuel; Meyer, Julia S.
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms11167

Fluxonium: Single Cooper-Pair Circuit Free of Charge Offsets
journal, October 2009


Ueber die angen�herte Darstellung der Irrationalzahlen durch rationale Br�che
journal, June 1891


Weyl Semimetal in a Topological Insulator Multilayer
journal, September 2011


Topological Insulators with SU(2) Landau Levels
journal, October 2013


Topological Insulators in Three Dimensions
journal, March 2007


Absolute stability and spatiotemporal long-range order in Floquet systems
journal, August 2016


High-Dimensional Topological Insulators with Quaternionic Analytic Landau Levels
journal, May 2013


Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump
journal, May 2016


Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels
journal, December 2011


Photonic gauge potential in a system with a synthetic frequency dimension
journal, January 2016


Topological Floquet spectrum in three dimensions via a two-photon resonance
journal, June 2013


Classification of Interacting Topological Floquet Phases in One Dimension
journal, October 2016

  • Potter, Andrew C.; Morimoto, Takahiro; Vishwanath, Ashvin
  • Physical Review X, Vol. 6, Issue 4
  • DOI: 10.1103/PhysRevX.6.041001

Topological singularities and the general classification of Floquet–Bloch systems
journal, December 2015


Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension
journal, December 2016

  • Lin, Qian; Xiao, Meng; Yuan, Luqi
  • Nature Communications, Vol. 7, Issue 1
  • DOI: 10.1038/ncomms13731

Semiclassical many-mode floquet theory
journal, April 1983


A Floquet model for the many-body localization transition
journal, December 2016


Scattering approach to parametric pumping
journal, October 1998


Berry phase effects on electronic properties
journal, July 2010


Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics
journal, April 2016


Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates
journal, May 2011


Phase structure of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases
journal, June 2016


Phase structure of one-dimensional interacting Floquet systems. II. Symmetry-broken phases
journal, June 2016


Fate of Many-Body Localization Under Periodic Driving
journal, July 2015