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Nonlinearity and parity-time (PT) symmetry in periodic potentials create unique nonlinear periodic solutions. These exhibit thresholdless symmetry breaking and stable, asymmetric spectral structures.

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Area of Science:

  • Physics
  • Nonlinear dynamics
  • Quantum mechanics

Background:

  • Parity-time (PT) symmetry in periodic potentials is crucial for understanding wave phenomena.
  • Nonlinear effects can significantly alter the behavior of systems with PT symmetry.

Purpose of the Study:

  • To investigate the peculiar features of nonlinear periodic solutions arising from the interplay between nonlinearity and PT symmetry.
  • To analyze the resulting nonlinear Bloch spectrum and its stability properties.

Main Methods:

  • Theoretical analysis using a two-mode approximation and effective potential theory.
  • Numerical validation of theoretical predictions.

Main Results:

  • Demonstration of thresholdless symmetry breaking.
  • Observation of asymmetric (multi-)loop structures in the nonlinear Bloch spectrum.
  • Persistence of unbroken PT symmetry even after gap closure.
  • Nonmonotonic dependence of PT phase transition on defocusing nonlinearity.
  • Enhanced stability of nonlinear states associated with loop structures.

Conclusions:

  • The interplay of nonlinearity and PT symmetry in periodic potentials leads to novel spectral features.
  • Asymmetric and loop structures in the nonlinear Bloch spectrum are well-explained by theoretical models and validated numerically.
  • These findings offer new insights into the behavior of complex nonlinear systems with PT symmetry.