Localization of wave patterns on classical periodic orbits in a square billiard

Area of Science:

• Quantum mechanics
• Classical mechanics
• Optics and photonics

Background:

• Quantum wave functions and classical trajectories are fundamental concepts in physics.
• Understanding their connection can reveal deeper insights into physical systems.
• Previous studies have explored this link in various systems.

Purpose of the Study:

• To analytically construct the connection between wave functions and classical periodic trajectories in a square billiard.
• To experimentally verify this connection using microcavity lasers.

Main Methods:

• Utilizing the representation of SU(2) coherent states to analytically construct the wave function form.
• Superposing nearly degenerate eigenfunctions to localize wave patterns.
• Studying wave function features through transverse pattern formation in a microcavity laser, drawing analogy between Schrödinger and Helmholtz equations.

Main Results:

• An analytical function form was derived, showing wave patterns localized on classical periodic trajectories.
• Experimental results from a square-shaped microcavity laser demonstrated transverse patterns that closely matched the constructed wave patterns.
• The findings confirm the localization of wave patterns along classical periodic orbits.

Conclusions:

• The study successfully established an analytical link between quantum wave functions and classical periodic trajectories in a square billiard.
• Experimental validation using microcavity lasers supports the theoretical findings.
• This work provides a method for visualizing quantum phenomena through classical analogies.