Feedback generation of quantum Fock states by discrete QND measures

TL;DR

This paper proposes a feedback control scheme using quantum non-demolition measurements to prepare specific photon number states in a microwave cavity, with proven convergence and demonstrated robustness through simulations.

Contribution

It introduces a novel feedback method for quantum state preparation that combines QND measurements with adaptive control, supported by rigorous convergence proofs and simulation results.

Findings

Feedback scheme successfully converges to target photon states.

Scheme demonstrates robustness under realistic experimental conditions.

Convergence proven using stochastic Lyapunov techniques.

Abstract

A feedback scheme for preparation of photon number states in a microwave cavity is proposed. Quantum Non Demolition (QND) measurement of the cavity field provides information on its actual state. The control consists in injecting into the cavity mode a microwave pulse adjusted to maximize the population of the desired target photon number. In the ideal case (perfect cavity and measures), we present the feedback scheme and its detailed convergence proof through stochastic Lyapunov techniques based on super-martingales and other probabilistic arguments. Quantum Monte-Carlo simulations performed with experimental parameters illustrate convergence and robustness of such feedback scheme.