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arXiv:0905.0114 · Physical Review A

Quantum feedback by discrete quantum nondemolition measurements: Towards on-demand generation of photon-number states

I. Dotsenko, Mazyar Mirrahimi, M. Brune, S. Haroche, J. M. Raimond, Pierre Rouchon

Published Jul 9, 2009• 74 citations
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Abstract

We propose a quantum feedback scheme for the preparation and protection of photon-number states of light trapped in a high-$Q$ microwave cavity. A quantum nondemolition measurement of the cavity field provides information on the photon-number distribution. The feedback loop is closed by injecting into the cavity a coherent pulse adjusted to increase the probability of the target photon number. The efficiency and reliability of the closed-loop state stabilization is assessed by quantum Monte Carlo simulations. We show that, in realistic experimental conditions, the Fock states are efficiently produced and protected against decoherence.

DOI
10.1103/physreva.80.013805

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We propose a quantum feedback scheme for the preparation and protection of photon-number states of light trapped in a high-QQQ microwave cavity. A quantum nondemolition measurement of the cavity field provides information on the photon-number distribution. The feedback loop is closed by injecting into the cavity a coherent pulse adjusted to increase the probability of the target photon number. The efficiency and reliability of the closed-loop state stabilization is assessed by quantum Monte Carlo simulations. We show that, in realistic experimental conditions, the Fock states are efficiently produced and protected against decoherence.
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 increase 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. I.
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 increase 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.
The ubiquitous decoherence phenomenon is responsible for the lack of quantum superpositions at the macroscopic scale. It is increasingly difficult to isolate a quantum system from its environment when its size increases. Making use of the weird quantum properties of mesoscopic quantum states thus requires efficient means to combat decoherence. One option is real-time quantum feedback. It features the components of a conventional feedback: measurement of the system's state (sensor), analysis (controller), and feedback action (actuator) aiming to the target state. The random back-action of the measurements by the sensor makes quantum feedback much more difficult than its classical counterpart. Mesoscopic photon number (Fock) states feature a decoherence rate proportional to the photon number. They are thus a simple example of a fragile quantum resource. We demonstrated recently two quantum feedback schemes continuously stabilizing Fock state of a microwave field in a high-quality cavity. Sensitive atoms, crossing the field one at a time, are used as quantum nondemolition (QND) probes of its photon number. The feedback actuator is either a classical source [Sayrin et al., Nature (London) 477, 73 (2011)] or individual resonant atoms emitting or absorbing one photon each [Zhou et al., Phys. Rev. Lett. 108, 243602 (2012)]. Both schemes detect the quantum jumps of the photon number and efficiently correct their adverse effects, preparing and preserving a fragile quantum resource. We present an in-depth analysis of our methods, which sheds light onto the fundamental difficulties encountered in quantum feedback, in particular concerning the state estimation algorithm, and onto the ways to circumvent them. These results open the way to informationally optimal QND measurements or to the stabilization of mesoscopic field state superpositions. More generally, they can be cast in a variety of contexts to loosen the tight constraints set by decoherence in quantum metrology and quantum information processing.
We implement a permanent quantum feedback procedure. It prepares on-demand and stabilizes photon-number states in a high-quality superconducting microwave cavity. The feedback uses sensitive circular atoms to probe the cavity field in a Quantum Non Demolition way. This information is used by a controller and an actuator to feed small coherent amplitudes into the cavity, leading it deterministically towards the target state with a high fidelity. Quantum jumps of the photon number are detected and their effect is then actively compensated, protecting this fragile quantum resource against decoherence.
We propose a feedback scheme for preparation of photon number states in a microwave cavity. Quantum Non-Demolition (QND) measurements of the cavity field and a control signal consisting of a microwave pulse injected into the cavity are used to drive the system towards a desired target photon number state. Unlike previous work, we do not use the Galerkin approximation of truncating the infinite-dimensional system Hilbert space into a finite-dimensional subspace. We use an (unbounded) strict Lyapunov function and prove that a feedback scheme that minimizes the expectation value of the Lyapunov function at each time step stabilizes the system at the desired photon number state with (a pre-specified) arbitrarily high probability. Simulations of this scheme demonstrate that we improve the performance of the controller by reducing “leakage” to high photon numbers.