Real-time quantum feedback prepares and stabilizes photon number states

Feedback loops are at the heart of most classical control procedures. A controller compares the signal measured by a sensor with the target value. It adjusts then an actuator in order to stabilize the signal towards its target. Generalizing this scheme to stabilize a micro-system's quantum state relies on quantum feedback, which must overcome a fundamental difficulty: the measurements by the sensor have a random back-action on the system. An optimal compromise employs weak measurements providing partial information with minimal perturbation. The controller should include the effect of this perturbation in the computation of the actuator's unitary operation bringing the incrementally perturbed state closer to the target. While some aspects of this scenario have been experimentally demonstrated for the control of quantum or classical micro-system variables, continuous feedback loop operations permanently stabilizing quantum systems around a target state have not yet been realized. We have implemented such a real-time stabilizing quantum feedback scheme. It prepares on demand photon number states (Fock states) of a microwave field in a superconducting cavity and subsequently reverses the effects of decoherence-induced field quantum jumps. The sensor is a beam of atoms crossing the cavity which repeatedly performs weak quantum non-demolition measurements of the photon number. The controller is implemented in a real-time computer commanding the injection, between measurements, of adjusted small classical fields in the cavity. The microwave field is a quantum oscillator usable as a quantum memory or as a quantum bus swapping information between atoms. By demonstrating that active control can generate non-classical states of this oscillator and combat their decoherence, this experiment is a significant step towards the implementation of complex quantum information operations.Comment: 12 pages, 4 figure

Application de la méthode de l’« état passé » à la mesure quantique non-destructive du nombre de photons dans une cavité

We experimentally study the evolution of photon-number states of a microwave field stored in a very high finesse Fabry-Perot cavity. To probe the field, we send one by one circular Rydberg atoms which interact dispersively with the cavity mode. Using the Ramsey interferometry technique, we perform a quantum non-demolition measurement of the photon number n. The standard estimate of the field’s state at time t is based on the analysis of all measurements performed before this time. In this manuscript, we present the implementation of the “past quantum state” analysis which uses the complete ensemble of the probes detection results obtained both before and after time t. The past state is a better estimate of the real field state than the density matrix. The almost noiseless reconstructed quantum trajectories make the resolution of quantum jumps of the field more efficient. Furthermore, the past state method allows us to remove the main restriction of our QND measurement related to its interferometric periodicity. We are now able to observe photon number states with n > 8, which were inaccessible with the standard analysis, and measure their decay rates.Nous étudions expérimentalement l’évolution d’états nombre du champ micro-onde contenu dans une cavité Fabry-Perot de grande finesse. Pour sonder le champ, nous envoyons un par un des atomes de Rydberg circulaires qui interagissent de manière dispersive avec le mode du champ. Grâce à un interféromètre atomique de Ramsey, nous mesurons le nombre de photons n de façon non-destructive. L’estimation usuelle de l’état du champ à l’instant t est issue de l’analyse des résultats de mesure obtenus avant t. Dans ce manuscrit, nous présentons la méthode de l’« état passé » qui utilise l’ensemble complet des mesures des sondes avant et après t. L’état passé du champ est une meilleure estimation de l’état réel que ne l’est la matrice densité. La quasi absence de bruit sur les trajectoires quantiques individuelles du champ permet la résolution efficace, à posteriori, des sauts quantiques. De plus, l’état passé permet d’aller au-delà la limite principale de notre mesure QND liée à la périodicité de la mesure interférométrique. Nous pouvons désormais observer des états de Fock avec n > 8, inaccessibles par la méthode d’analyse habituelle, et nous mesurons leurs taux de relaxation