Reduction of Topological Z Classification in Cold-Atom Systems

Area of Science:

• Condensed Matter Physics
• Quantum Simulation
• Topological Matter

Background:

• Topological systems often exhibit complex classifications, posing challenges for experimental realization and understanding.
• Few experimental platforms exist for studying the reduction of topological classifications, such as Z→Z₄.

Purpose of the Study:

• To demonstrate ultracold dipolar fermions in a two-leg ladder optical lattice as a test bed for topological classification reduction (Z→Z₄).
• To provide experimental methods for accessing and verifying this topological reduction.
• To investigate the behavior of edge modes in the presence of dislocations.

Main Methods:

• Utilizing ultracold dipolar fermions (e.g., ¹⁶⁷Er, ¹⁶¹Dy, ⁵³Cr) in a two-leg ladder optical lattice.
• Employing local radio frequency spectroscopy to observe the destruction of one-particle gapless excitations at the edges.
• Measuring the time-dependent spin expectation value of a superposed state to detect gapless spin excitations.

Main Results:

• Demonstrated solid evidence for the Z→Z₄ topological classification reduction in the dipolar fermion system.
• Confirmed the destruction of one-particle and spin gapless excitations at the edges.
• Observed the recovery of a gapless edge mode around a dislocation, even after the reduction.

Conclusions:

• Ultracold dipolar fermions in optical lattices provide a highly controllable platform for realizing and studying topological classification reduction.
• The proposed experimental techniques allow for direct observation of phenomena related to topological reduction.
• The recovery of edge modes around dislocations offers further evidence for the topological reduction.