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Title: Topological Frequency Conversion in Strongly Driven Quantum Systems

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:
 [1] ;  [2] ;  [3]
  1. Argonne National Lab. (ANL), Argonne, IL (United States); Univ. of California, Santa Barbara, CA (United States)
  2. Institute of Quantum Information and Matter and Department of Physics, Pasadena, CA (United States); California Inst. of Technology (CalTech), Pasadena, CA (United States)
  3. Harvard Univ., Cambridge, MA (United States)
Publication Date:
Grant/Contract Number:
AC02-06CH11357
Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Volume: 7; Journal Issue: 4; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society
Research Org:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
OSTI Identifier:
1399642
Alternate Identifier(s):
OSTI ID: 1400405

Martin, Ivar, Refael, Gil, and Halperin, Bertrand. Topological Frequency Conversion in Strongly Driven Quantum Systems. United States: N. p., 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. 2017. "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},
number = 4,
volume = 7,
place = {United States},
year = {2017},
month = {10}
}

Works referenced in this record:

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

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

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

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

Topological Insulators in Three Dimensions
journal, March 2007