General Linearized Theory of Quantum Fluctuations around Arbitrary Limit Cycles

Area of Science:

• Quantum Optics
• Nonlinear Dynamics
• Many-Body Physics

Background:

• Standard linearization of Gaussian quantum fluctuations is widely used for analyzing quantum-optical systems.
• This method simplifies analysis but struggles with time-dependent classical states, such as those in limit-cycle formation.

Purpose of the Study:

• To develop a new linearization scheme applicable to quantum-optical systems with time-dependent classical states.
• To address the limitations of standard linearization in scenarios like spontaneous limit-cycle formation.

Main Methods:

• Introduced a novel linearization scheme tailored for time-dependent classical states.
• Utilized the driven Van der Pol oscillator as a model system for testing and validation.
• Compared the new method's results with full numerical simulations.

Main Results:

• The new scheme successfully handles situations with time-dependent classical states, including limit-cycle formation.
• The method maintains the simplicity and linear scalability of standard linearization.
• Demonstrated applicability to large, many-body quantum systems.

Conclusions:

• The developed linearization scheme extends the analysis of quantum-optical systems to complex dynamics.
• This approach provides a practical and scalable tool for studying phenomena like spontaneous symmetry breaking in quantum systems.