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We developed a quantum phase reduction theory for nonlinear oscillators using quantum trajectory theory. This method reveals how continuous measurement affects oscillator phase dynamics and response curves.

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Area of Science:

  • Quantum mechanics
  • Nonlinear dynamics
  • Quantum optics

Background:

  • Phase reduction theory is crucial for understanding oscillator dynamics.
  • Classical phase reduction methods are limited for quantum systems.
  • Quantum trajectory theory offers a framework for open quantum systems.

Purpose of the Study:

  • To establish a general framework for phase reduction of quantum nonlinear oscillators.
  • To define limit-cycle trajectories and phase using stochastic Schrödinger equations.
  • To investigate the impact of continuous measurement on quantum oscillator phase dynamics.

Main Methods:

  • Employing quantum trajectory theory to define quantum limit cycles and phase.
  • Utilizing stochastic Schrödinger equations for phase evolution.
  • Calculating quantum phase response curves via unitary transformations and Lie algebra generators.

Main Results:

  • Continuous measurement induces observable phase clusters in quantum oscillators.
  • Measurement alters the phase response curves of quantum oscillators.
  • The observable clusters accurately capture individual quantum oscillator phase dynamics.

Conclusions:

  • The developed framework provides a novel approach to analyzing quantum oscillator dynamics.
  • This method offers insights into quantum phase dynamics beyond classical analogues.
  • Applicable to finite-level quantum systems, advancing quantum control and simulation.