Real time imaging of quantum and thermal fluctuations: the case of a two-level system

TL;DR

This paper investigates the real-time behavior of quantum and thermal fluctuations in a two-level system, revealing how quantum jumps can be statistically characterized using stochastic analysis and classical analogies.

Contribution

It provides a novel stochastic analysis framework for understanding quantum jumps and transition times in a two-level system under continuous measurement.

Findings

Quantum trajectories resemble classical noisy particle motion.

Transition times follow a specific statistical distribution.

Quantum jumps are characterized by large multiplicative noise.

Abstract

A quantum system in contact with a heat bath undergoes quantum transitions between energy levels upon absorption or emission of energy quanta by the bath. These transitions remain virtual unless the energy of the system is measured repeatedly, even continuously in time. Isolating the two indispensable mechanisms in competition, we describe in a synthetic way the main physical features of thermally activated quantum jumps. Using classical tools of stochastic analysis, we compute in the case of a two-level system the complete statistics of jumps and transition times in the limit when the typical measurement time is small compared to the thermal relaxation time. The emerging picture is that quantum trajectories are similar to those of a classical particle in a noisy environment, subject to transitions a la Kramer in a multi-well landscape, but with a large multiplicative noise.