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Statistical Transmutation in Floquet Driven Optical Lattices.

Tigran A Sedrakyan1,2, Victor M Galitski3,4, Alex Kamenev1

  • 1William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA.

Physical Review Letters
|November 21, 2015
PubMed
Summary
This summary is machine-generated.

Interacting bosons in a driven 2D optical lattice can mimic fermionic behavior, a phenomenon achieved through Floquet band engineering and Chern-Simons flux attachment, offering new insights into quantum statistics.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Ultracold atoms

Background:

  • Interacting bosons in optical lattices are a key platform for studying quantum phenomena.
  • The Tonks-Girardeau regime in one dimension demonstrates fermionic behavior in bosons.
  • Periodically driven quantum systems (Floquet systems) offer novel ways to engineer effective Hamiltonians.

Purpose of the Study:

  • To investigate the possibility of realizing fermionic statistics for interacting bosons in a two-dimensional (2D) optical lattice.
  • To explore the role of Floquet engineering in achieving statistical transmutation.
  • To identify experimental probes for detecting this emergent fermionic behavior.

Main Methods:

  • Theoretical modeling of interacting bosons in a periodically driven 2D optical lattice.
  • Analysis of the Floquet band structure, specifically the emergence of a 'moat' shape.
  • Application of the Chern-Simons flux attachment technique to induce statistical transmutation.
  • Calculation of the velocity distribution of released bosons.

Main Results:

  • Interacting bosons in a driven 2D optical lattice can effectively exhibit fermionic statistics.
  • The Floquet band develops a characteristic 'moat' shape, indicating a degeneracy in kinetic energy.
  • Statistical transmutation is achieved via a mechanism analogous to Chern-Simons flux attachment.
  • The velocity distribution of released bosons serves as a sensitive probe for the emergent fermionic state.

Conclusions:

  • It is possible to engineer fermionic statistics for interacting bosons in 2D driven optical lattices.
  • The 'moat' shaped Floquet band and flux attachment are key to this statistical transmutation.
  • Experimental measurements of boson velocity distributions can confirm the presence of fermionic quasiparticles.