Arcsine Laws of Light.

Area of Science:

• Quantum optics
• Statistical mechanics
• Extreme value statistics

Background:

• Coherent driving of optical resonators is fundamental in quantum optics.
• Understanding the statistical properties of transmitted light is crucial for device applications.
• Extreme value statistics (EVS) provides tools to analyze rare events.

Purpose of the Study:

• To investigate the statistical distribution of time-integrated light intensity in coherently driven resonators.
• To determine if Lévy's arcsine laws, a key concept in EVS, apply to this system.
• To explore the implications of these statistical laws for optical sensor precision.

Main Methods:

• Theoretical analysis of light transmission in coherently driven resonators.
• Numerical simulations to verify the applicability of arcsine laws under various conditions.
• Comparison with established statistical mechanics principles.

Main Results:

• Time-integrated light intensity follows Lévy's arcsine laws.
• Convergence to the arcsine distribution is algebraic, universal, and robust to non-equilibrium effects.
• Arcsine laws hold even with frequency noise and in nonlinear resonators with non-Gaussian states.
• This indicates weak ergodicity breaking.

Conclusions:

• Lévy's arcsine laws govern light intensity statistics in coherently driven resonators.
• This statistical behavior is robust and independent of system non-equilibrium.
• The observed weak ergodicity breaking offers a pathway to enhance resonant optical sensor precision without energy cost.