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arXiv:1203.1920 · Physical Review Letters

Field Locked to a Fock State by Quantum Feedback with Single Photon Corrections

X. Zhou, I. Dotsenko, Bruno Peaudecerf, T. Rybarczyk, C. Sayrin, S. Gleyzes, J. M. Raimond, M. Brune, S. Haroche

Published Jun 15, 2012• 126 citations
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Abstract

Fock states with photon numbers n up to 7 are prepared on demand in a microwave superconducting cavity by a quantum feedback procedure that reverses decoherence-induced quantum jumps. Circular Rydberg atoms are used as quantum nondemolition sensors or as single-photon emitter or absorber actuators. The quantum nature of these actuators matches the correction of single-photon quantum jumps due to relaxation. The flexibility of this method is suited to the generation of arbitrary sequences of Fock states.

DOI
10.1103/physrevlett.108.243602

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Fock states with photon numbers n up to 7 are prepared on demand in a microwave superconducting cavity by a quantum feedback procedure that reverses decoherence-induced quantum jumps. Circular Rydberg atoms are used as quantum nondemolition sensors or as single-photon emitter or absorber actuators. The quantum nature of these actuators matches the correction of single-photon quantum jumps due to relaxation. The flexibility of this method is suited to the generation of arbitrary sequences of Fock states.
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 perform quantum non-demolition (QND) photon counting on a microwave field trapped in a very high Q superconducting cavity, employing circular Rydberg atoms as non-absorbing light probes. Beyond realizing fundamental tests of quantum measurement theory, we use this QND method to prepare non-classical Fock and Schrodinger cat states of the field and to reconstruct their Wigner functions. Monitoring the evolution of these functions provides a direct observation of the decoherence process. Quantum feedback procedures will enable us to steer the field towards target states and to protect them against decoherence.
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.
We explore experimentally the fundamental projective properties of a quantum measurement and their application in the control of a system's evolution. We perform quantum non-demolition (QND) photon counting on a microwave field trapped in a very-high- Q superconducting cavity, employing circular Rydberg atoms as non-absorbing probes of light. By repeated measurement of the cavity field we demonstrated the freeze of its initially coherent evolution, illustrating the back action of the photon number measurement on the field's phase. On the contrary, by utilizing a weak QND measurement in combination with the control injection of coherent pulses, we plan to force the field to deterministically evolve towards any target photon-number state. This quantum feedback procedure will enable us to prepare and protect photon-number states against decoherence.