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Related Experiment Video

Updated: Aug 16, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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On the Quantization of AB Phase in Nonlinear Systems.

Xi Liu1, Qing-Hai Wang2, Jiangbin Gong2,3

  • 1NUS Graduate School-Integrative Sciences and Engineering Programme (ISEP), National University of Singapore, Singapore 119077, Singapore.

Entropy (Basel, Switzerland)
|December 23, 2022
PubMed
Summary

For Kerr nonlinearity, the Aharonov-Bohm phase jumps by π at the critical point where nonlinear Dirac cones appear and disappear. Other nonlinearities show continuous phase changes.

Keywords:
AB phaseBerry phaseDirac coneadiabatic dynamicspower-law nonlinearityquantization

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Area of Science:

  • Condensed matter physics
  • Nonlinear dynamics
  • Quantum mechanics

Background:

  • Nonlinearity can induce self-intersecting energy bands in momentum space.
  • Nonlinear Dirac cones are an intriguing consequence of such phenomena.

Purpose of the Study:

  • Investigate the Aharonov-Bohm (AB) phase in nonlinear systems.
  • Analyze the impact of power-law nonlinearity on the AB phase around nonlinear Dirac cones.

Main Methods:

  • Utilized the Qi-Wu-Zhang model with power-law nonlinearity.
  • Studied the AB phase via adiabatic paths in momentum space.

Main Results:

  • Kerr nonlinearity leads to a π-jump in the AB phase at critical nonlinearity.
  • This π-quantization occurs when nonlinear Dirac cones emerge or vanish.
  • Other nonlinearities result in a continuous AB phase change with nonlinear strength.

Conclusions:

  • The study reveals unique π-quantization of the AB phase for Kerr nonlinearity.
  • Results offer potential for experimental measurement of power-law nonlinearity.
  • Motivates further research into geometric phases in nonlinear systems.