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Real-time quantum feedback prepares and stabilizes photon number states

Abstract

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 feedback1,2,3, which must overcome a fundamental difficulty: the sensor measurements cause a random back-action on the system. An optimal compromise uses weak measurements4,5, 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 quantum6,7,8,9 or classical10,11 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 scheme12 following a method inspired by ref. 13. 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 jumps14,15,16. The sensor is a beam of atoms crossing the cavity, which repeatedly performs weak quantum non-demolition measurements of the photon number14. 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 memory17 or as a quantum bus swapping information between atoms18. Our experiment demonstrates that active control can generate non-classical states of this oscillator and combat their decoherence15,16, and is a significant step towards the implementation of complex quantum information operations.

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Figure 1: Scheme of the quantum feedback set-up.
Figure 2: Individual quantum feedback trajectories.
Figure 3: Photon number histograms following quantum feedback iterations.
Figure 4: Performance of the quantum feedback procedure.

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Acknowledgements

This work was supported by the Agence Nationale de la Recherche (ANR) under the projects QUSCO-INCA, EPOQ2 and CQUID, and by the EU under the IP project AQUTE and ERC project DECLIC.

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Affiliations

Authors

Contributions

C.S. and I.D. contributed equally to this work. Experimental work was carried out by C.S., I.D., X.Z., B.P., T.R., S.G., M.B., J.-M.R. and S.H., with major contributions from C.S., I.D. and X.Z.; P.R., M.M. and H.A. contributed to the design and optimization of the feedback control.

Corresponding author

Correspondence to Serge Haroche.

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Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data 1-5, Supplementary Figures 1- 7 with legends and additional references. (PDF 1034 kb)

Supplementary Movie 1

Quantum feedback trajectory stabilizing a 2-photon state - the movie shows the evolution of the density matrix estimated by the controller during the feedback trajectory presented in the left panel of Fig. 2. The movie also features the evolution of the photon-number distribution for photon numbers from 0 to 7. Each movie frame corresponds to 2 feedback iterations. (MOV 2905 kb)

Supplementary Movie 2

Quantum feedback trajectory stabilizing a 3-photon state - the movie shows the evolution of the density matrix estimated by the controller during the feedback trajectory presented in the right panel of Fig. 2. The movie also features the evolution of the photon-number distribution for photon numbers from 0 to 7. Each movie frame corresponds to 2 feedback iterations. (MOV 3123 kb)

Supplementary Movie 3

Open-loop quantum feedback trajectory - if no control injection is applied, the initial coherent field is rapidly converted into a mixture of photon number states. It then relaxes to vacuum while undergoing a series of quantum jumps (MOV 2817 kb)

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Sayrin, C., Dotsenko, I., Zhou, X. et al. Real-time quantum feedback prepares and stabilizes photon number states. Nature 477, 73–77 (2011). https://doi.org/10.1038/nature10376

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