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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
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Four-Dimensional Quantum Hall Effect with Ultracold Atoms.

H M Price1, O Zilberberg2, T Ozawa1

  • 1INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, I-38123 Povo, Italy.

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

We propose a realistic method to detect the 4D quantum Hall effect in ultracold atoms. This research identifies quantized current responses and proposes experimental protocols to extract topological numbers for exploring higher-dimensional topological phases.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Physics
  • Atomic Physics

Background:

  • The quantum Hall effect describes topological phenomena in 2D electron systems.
  • Exploring topological phases in higher dimensions remains a significant challenge.
  • Ultracold atoms in optical lattices offer a controllable platform for simulating complex quantum systems.

Purpose of the Study:

  • To propose a realistic experimental scheme for detecting the four-dimensional (4D) quantum Hall effect.
  • To investigate the quantized current responses and topological properties of a 4D system.
  • To establish methods for extracting topological invariants in higher dimensions.

Main Methods:

  • Utilizing ultracold atoms arranged in a 3D optical lattice.
  • Inducing synthetic motion along a fourth dimension via controlled internal state transitions.
  • Employing semiclassical analysis to determine linear and nonlinear quantized current responses.
  • Proposing experimental protocols based on current or center-of-mass-drift measurements.

Main Results:

  • Identification of linear and nonlinear quantized current responses in the 4D model.
  • Relating the observed responses to the topology of the Bloch bands.
  • Development of protocols to extract the topological second Chern number.
  • Demonstration of a feasible pathway to higher-dimensional topological physics.

Conclusions:

  • The proposed scheme provides a realistic route for detecting the 4D quantum Hall effect.
  • This work opens avenues for exploring novel topological phases in synthetic higher dimensions.
  • Experimental verification of these concepts will advance the field of topological matter.