Diffusive Limit of Non-Markovian Quantum Jumps.

Area of Science:

• Quantum Physics
• Quantum Information Theory
• Statistical Mechanics

Background:

• Stochastic descriptions of open quantum systems are crucial for understanding complex quantum dynamics.
• Existing models often face limitations in accurately capturing non-Markovian effects.
• Resolving long-standing problems in these descriptions is essential for advancing quantum technologies.

Purpose of the Study:

• To establish classical stochastic processes for non-Markovian quantum state diffusion and non-Markovian quantum jumps.
• To explore the diffusive limit of non-Markovian quantum jumps in both projective and standard Hilbert spaces.
• To introduce a novel diffusive unraveling, termed non-Markovian quantum diffusion, and simplify existing methods.

Main Methods:

• Derivation of classical stochastic processes corresponding to quantum dynamics.
• Analysis of diffusive limits in Hilbert and projective Hilbert spaces.
• Application of kernel smoothing techniques to simplify non-Markovian quantum jump and diffusion models.

Main Results:

• Identified classical stochastic processes for non-Markovian quantum state diffusion and quantum jumps.
• Demonstrated that the diffusive limit on projective Hilbert space unifies non-Markovian quantum jumps and state diffusion.
• Introduced non-Markovian quantum diffusion as a distinct process arising from the Hilbert space limit.
• Kernel smoothing significantly simplifies the application of non-Markovian quantum jumps and diffusion.

Conclusions:

• The study provides a unified framework for stochastic descriptions of non-Markovian open quantum systems.
• Introduced novel methods and simplified existing ones, enhancing their practical applicability.
• Demonstrated the utility of these methods through the analysis of a driven dissipative two-level atom.