Periodic thermodynamics of the parametrically driven harmonic oscillator

Area of Science:

• Quantum Thermodynamics
• Statistical Mechanics
• Driven Quantum Systems

Background:

• Understanding the behavior of quantum systems coupled to thermal environments is crucial.
• Parametrically driven harmonic oscillators are fundamental models in quantum physics.
• Floquet theory describes systems subjected to periodic driving.

Purpose of the Study:

• To determine the quasistationary distribution of Floquet-state occupation probabilities.
• To investigate the influence of a thermal bath's spectral density on system temperature.
• To explore methods for engineering the system's effective temperature and stability.

Main Methods:

• Analysis of a parametrically driven harmonic oscillator coupled to a thermal bath.
• Application of Floquet theory to determine quasienergy states.
• Calculation of quasistationary distribution using detailed balance and Boltzmann statistics.

Main Results:

• The occupation probabilities follow a geometric Boltzmann distribution.
• The system's effective 'quasitemperature' deviates from the bath temperature due to spectral density.
• Demonstrated 'quasithermal engineering' to achieve effective cooling below bath temperature.
• Observed quasithermal instability in a mechanically stable driven system.

Conclusions:

• The spectral density of a thermal bath significantly impacts the effective temperature of driven quantum systems.
• Engineered thermal baths offer pathways to control quantum system properties, including effective temperature.
• Driven systems can exhibit unexpected instabilities, even when classically stable.