First passage time of laser-driven tunneling.

Area of Science:

• Quantum mechanics
• Statistical physics

Background:

• Quantum tunneling is a phenomenon where particles pass through potential barriers.
• Understanding tunneling rates and passage times is crucial in various physical systems.

Purpose of the Study:

• To introduce and explore the concept of first passage time as a unified framework for quantum tunneling.
• To analytically unify quantum tunneling rate and passage time.
• To demonstrate the applicability and insights of this quantum first passage time approach.

Main Methods:

• Solving the Fokker-Planck and backward Kolmogorov's equations for quantum probability density.
• Applying the first passage time concept to quantum tunneling phenomena.
• Analyzing specific potential settings and wave functions.

Main Results:

• A closed-integral-form analytical unification of tunneling rate and passage time.
• Recovery of Kramers escape rate and lifetime of tunneling quasi-stationary wave packets.
• Derivation of classical passage time for free-particle wave functions and insights into electron barrier traversal time.

Conclusions:

• First passage time provides a meaningful and unified extension to quantum tunneling theory.
• This approach bridges quantum and classical descriptions of particle transport.
• It offers valuable insights into complex quantum phenomena like field-induced ionization.