Contrôle d'états quantiques dans des cavités (QUantum State COntrol IN CAvities) – QUSCO-INCA

The goal of this proposal is to demonstrate active quantum feedback procedures to generate and/or protect specific quantum states of a trapped field. Instead of initially preparing a given state and passively observing its evolution under the effect of the coupling to the environment, we will perform on it repetitive QND measurements and use the outcomes of these measurements to influence its subsequent evolution in order to steer it towards a predetermined state. The microwave field, trapped in one or two high-Q superconducting cavities, will be repeatedly monitored by non-resonant Rydberg atoms crossing the apparatus one at a time. A Ramsey atomic interferometer will be used to measure the phase-shift produced by the quantum field on the atomic dipoles, from which the photon number will be inferred. The complete measurement requires many probe atoms, but each one provides partial information which can be used to steer the field quantum state in a desired direction by acting on controlled variables of the field between two consecutive probes. The controlled variables will be of two different types. In one kind of experiment, we will inject small coherent fields in the cavity, with adjustable amplitude and phase. In this way, the cavity field will undergo incremental translations in its phase space with steps whose magnitude and direction will depend on previous QND measurements. Alternatively, we will use resonant Rydberg atoms, sandwiched between the off-resonant probe ones, in order to add or subtract deterministically a single photon in the cavity. These methods will be applied to the preparation and protection of Fock states and Schrödinger cat states. The latter are superpositions of two coherent states of opposite phases which can be generated in a cavity by having a single non-resonant atom interact with an initially prepared coherent field. Feedback procedures will also be applied to improve the QND measurement scheme itself. In its present version, the Ramsey interferometer settings are adjusted in a predetermined way and several tens of atoms are required to pin-down the photon number. We will demonstrate a much more efficient method in which we will modify the interferometer settings after each atom, conditioning them to the results of all the previous measurements. In this way, we will obtain from each atom one bit of the photon number and pin down the field intensity with a number of atoms of the order of the logarithm of the upper bound of the photon number. The method will be applied to a field trapped in a cavity, then extended to fields delocalized in two identical cavities. We will start by preparing in the cavities a 'Schrödinger cat' state in which a coherent field will be in a superposition of states belonging to the two cavities and then measure by the optimal QND method the photon number in the cavities. We will in this way obtain a 'NOON state', superposition of N photons all trapped in one or the other cavity. In order to realize these experiments, we must be able to extract information from the field in a QND way at a rate as fast as possible, so that the feedback could be implemented efficiently. This will require a sub-Poissonian pulsed source of atoms, which prepares regularly atoms one by one, with a negligible probability of misfiring or delivering two atoms or more per pulse. This deterministic 'atom-gun' will be based on the repeated excitation of a small sample of cold atoms in an auxiliary optical cavity, using a photon emission by this cavity as a signal heralding the preparation of a single atom in a specific atomic ground hyperfine state. This atom will then be extracted by a laser push and prepared in a Rydberg circular state before entering the high-Q superconducting cavity. This selective scheme will be an essential tool for efficient quantum feedback operation. Another major experimental advance will concern the computer-assisted implementation of the feedback procedures. In the present stage of the experiment, the field and the atoms are manipulated by operations pre-programmed by a computer. These sequences are synchronized with the atomic preparation pulses so that each atom and the cavity field can be addressed individually in a timely manner. For implementing active feedback, one important extra condition must be fulfilled: the atomic and field manipulations must be conditioned to the actual results of previous measurements. The computer driving the experiment must thus be able, after registering the result of a measurement in real time, to compute the adequate response and to apply it to the system. This requires the use of large computational power and the development of appropriate software. By performing quantum feedback on a field mode, a simple well-controlled system, we will learn more about the quantum-classical frontier and perform essential steps towards controlling the quantum world for practical applications.