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Localization-delocalization wavepacket transition in Pythagorean aperiodic potentials.

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We demonstrate a novel composite optical lattice with tunable periodicity. This structure enables the observation of eigenmode transitions and can visualize Pythagorean triples.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Optics
  • Materials Science

Background:

  • Optical lattices are crucial for simulating quantum systems.
  • Controlling lattice periodicity is key to manipulating quantum states.
  • Composite lattices offer complex potential landscapes for quantum studies.

Purpose of the Study:

  • To introduce a novel composite optical lattice formed by two rotated square patterns.
  • To investigate the continuous transformation between incommensurate and periodic structures.
  • To explore the localization-delocalization transition of eigenmodes in these lattices.

Main Methods:

  • Creation of a composite optical lattice by rotating two square patterns.
  • Mathematical analysis of lattice periodicity based on rotation angles and Pythagorean triples.
  • Numerical simulation of linear eigenmodes and their behavior under varying lattice parameters.

Main Results:

  • Lattice periodicity is achieved for specific rotation angles related to Pythagorean triples (cos θ = a/c, sin θ = b/c).
  • Linear eigenmodes are extended for Pythagorean triple lattices.
  • A localization-delocalization transition of eigenmodes is observed for intermediate rotation angles, controllable by sublattice strength.

Conclusions:

  • The composite optical lattice provides a versatile platform for studying quantum phenomena.
  • The sharp delocalization of eigenmodes can serve as a method for visualizing Pythagorean triples.
  • The observed effects are general and applicable to other lattice geometries, such as hexagonal lattices.