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

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.

17 pages, 1 figure, to be published version

References in corpus (8)

• Progressive field-state collapse and quantum non-demolition photon counting
• Observing single quantum trajectories of a superconducting qubit
• Quantum trajectory approach to circuit QED: Quantum jumps and the Zeno effect
• Existence, uniqueness and approximation of a stochastic Schrödinger equation: the diffusive case
• Are dynamical quantum jumps detector-dependent?
• Open quantum random walks: bi-stability on pure states and ballistically induced diffusion
• Iterated Stochastic Measurements
• A Wave Function approach to dissipative processes

Cited by in corpus (8)

• Spikes in quantum trajectories
• Exponential Stability of Subspaces for Quantum Stochastic Master Equations
• Computing the Rates of Measurement-Induced Quantum Jumps
• KPZ physics and phase transition in a classical single random walker under continuous measurement
• Zooming in on Quantum Trajectories
• Spiking and collapsing in large noise limits of SDEs
• Stochastic spikes and strong noise limits of stochastic differential equations
• Controlling quantum flux through measurement: an idealised example