Séminaire Mathématiques et Systèmes :
Année 2008 - Année 2009 - Année 2010 - Année 2011 - Année 2012
Janvier : Jeudi 12 janvier 2012 de 14h00-16h00 |
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1. Lieu :
Mines ParisTech, Bd Saint-Michel
salle L-218.2. Descriptif :
PREMIER EXPOSÉ: 14h00-15h00
Orateur: Igor Dotsenko (Laboratoire Kastler Brossel, ENS, igor.dotsenko@lkb.ens.fr)
Titre: Real-time quantum feedback prepares and stabilizes photon number states
Résumé: Feedback loops are central to most classical control procedures. A controller compares the signal measured by a sensor (system output) with the target value or set-point. It then adjusts an actuator (system input) to stabilize the signal around the target value. Generalizing this scheme to stabilize a micro-system’s quantum state relies on quantum feedback, which must overcome a fundamental difficulty: the sensor measurements cause a random back-action on the system. An optimal compromise uses weak measurements, providing partial information with minimal perturbation. The controller should include the effect of this perturbation in the computation of the actuator’s operation, which brings the incrementally perturbed state closer to the target. Although some aspects of this scenario have been experimentally demonstrated for the control of quantum or classical micro-system variables, continuous feedback loop operations that permanently stabilize quantum systems around a target state have not yet been realized. Here 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 nondemolition measurements of the photon number. The controller is implemented in a real-time computer commanding the actuator, which injects adjusted small classical fields into the cavity between measurements.The microwave field is a quantum oscillator usable as a quantum memory or as a quantum bus swapping information between atoms. Our experiment demonstrates that active control can generate non-classical states of this oscillator and combat their decoherence and is a significant step towards the implementation of complex quantum information operations.
DEUXIEME EXPOSÉ: 15h00-15h30
Orateur: Hadis Amini (CAS/INRIA, hadis.amini@mines-paristech.fr)
Titre: Feedback stabilization of discrete-time quantum systems
Résumé: This presentation is devoted to the mathematical methods underlying the LKB quantum feedback experiment stabilizing photon-number states. This controlled system is governed by a discrete-time nonlinear Markov process. In open-loop, this Markov process admits a set of martingales and stationary pure states. These open-loop martingales are exploited to design an adapted Lyapunov feedback law that globally stabilizes the system towards a chosen target state among these stationary pure states. Using a predictive quantum filter, the proposed feedback scheme is proved to be convergent even in the presence of delays and imperfect measurements.
TROISIEME EXPOSÉ: 15h30-16h
Orateur: Zaki Leghtas (INRIA/CAS, zaki.leghtas@inria.fr)
Titre: Stabilization by reservoir engineering of quantum systems: stabilizing entangled light with atoms
Résumé: Stabilization by reservoir engineering has the advantage, in comparison with feedback, to be fully insensitive to measurement errors and delays. We describe here a recent proposal where an entangled state of a microwave field in a superconducting cavity is stabilized. This is achieved by coupling the microwave field to a stream of atoms. By carefully engineering this coupling, the microwave field state converges asymptotically towards a single predefined entangled state, whatever its initial condition is. The preparation and stabilization of such entangled states may have interesting applications to high precision metrology and quantum information processing.