Time-of-Flight Measurements as a Possible Method to Observe Anyonic Statistics

Area of Science:

• Quantum physics
• Ultracold atoms
• Condensed matter physics

Background:

• Fractional quantum Hall states exhibit exotic quasiparticles called anyons.
• Understanding anyonic statistics is crucial for quantum information science.
• Observing these statistics in ultracold atoms presents experimental challenges.

Purpose of the Study:

• To propose a practical experimental method for observing anyonic statistics of quasiholes.
• To provide direct signatures of the statistical phase in fractional quantum Hall states.
• To validate the proposed method with numerical simulations.

Main Methods:

• Utilizing a standard time-of-flight experiment.
• Stably preparing quasihole states by pinning them with localized potentials.
• Measuring the mean square radius of the expanding atomic cloud to infer angular momentum and statistical phase.

Main Results:

• The proposed time-of-flight method provides direct signatures of the anyonic statistical phase.
• Monte Carlo calculations validate the method for realistic particle numbers in ν=1/2 and 1/3 fractional quantum Hall liquids.
• The mean square radius measurement is directly related to the average total angular momentum.

Conclusions:

• A standard time-of-flight experiment is a viable method for observing anyonic statistics in ultracold atom fractional quantum Hall states.
• The proposed technique offers a pathway to experimentally probe fundamental properties of anyons.
• The study opens avenues for exploring quantum Hall liquids of light and non-Abelian anyons.