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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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References

  1. Wiseman, H. M. Quantum theory of continuous feedback. Phys. Rev. A 49, 2133–2150 (1994)

    Article  ADS  CAS  Google Scholar 

  2. Doherty, A. C., Habib, S., Jacobs, K., Mabuchi, H. & Tan, S. M. Quantum feedback control and classical control theory. Phys. Rev. A 62, 012105 (2000)

    Article  ADS  Google Scholar 

  3. Wiseman, H. M. & Milburn, G. J. Quantum Measurement and Control (Cambridge Univ. Press, 2009)

    Book  Google Scholar 

  4. Aharonov, Y. & Vaidman, L. Properties of a quantum system during the time interval between two measurements. Phys. Rev. A 41, 11–20 (1990)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  5. Peres, A. & Wootters, W. K. Optimal detection of quantum information. Phys. Rev. Lett. 66, 1119–1122 (1991)

    Article  ADS  CAS  Google Scholar 

  6. Nelson, R. J., Weinstein, Y., Cory, D. & Lloyd, S. Experimental demonstration of fully coherent quantum feedback. Phys. Rev. Lett. 85, 3045–3048 (2000)

    Article  ADS  CAS  Google Scholar 

  7. Smith, W. P., Reiner, J. E., Orozco, L. A., Kuhr, S. & Wiseman, H. M. Capture and release of a conditional state of a cavity QED system by quantum feedback. Phys. Rev. Lett. 89, 133601 (2002)

    Article  ADS  CAS  Google Scholar 

  8. Cook, R. L., Martin, P. J. & Geremia, J. M. Optical coherent state discrimination using a closed-loop quantum measurement. Nature 446, 774–777 (2007)

    Article  ADS  CAS  Google Scholar 

  9. Gillett, G. G. et al. Experimental feedback control of quantum systems using weak measurements. Phys. Rev. Lett. 104, 080503 (2010)

    Article  ADS  CAS  Google Scholar 

  10. Bushev, P. et al. Feedback cooling of a single trapped ion. Phys. Rev. Lett. 96, 043003 (2006)

    Article  ADS  Google Scholar 

  11. Kubanek, A. et al. Photon-by-photon feedback control of a single-atom trajectory. Nature 462, 898–901 (2009)

    Article  ADS  CAS  Google Scholar 

  12. Dotsenko, I. et al. Quantum feedback by discrete quantum nondemolition measurements: Towards on-demand generation of photon-number states. Phys. Rev. A 80, 013805 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  13. Geremia, J. M. Deterministic and nondestructively verifiable preparation of photon number states. Phys. Rev. Lett. 97, 073601 (2006)

    Article  ADS  CAS  Google Scholar 

  14. Guerlin, C. et al. Progressive field-state collapse and quantum non-demolition photon counting. Nature 448, 889–893 (2007)

    Article  ADS  CAS  Google Scholar 

  15. Brune, M. et al. Process tomography of field damping and measurement of Fock state lifetimes by quantum nondemolition photon counting in a cavity. Phys. Rev. Lett. 101, 240402 (2008)

    Article  ADS  CAS  Google Scholar 

  16. Wang, H. et al. Measurement of the decay of Fock states in a superconducting quantum circuit. Phys. Rev. Lett. 101, 240401 (2008)

    Article  ADS  CAS  Google Scholar 

  17. Maître, X. et al. Quantum memory with a single photon in a cavity. Phys. Rev. Lett. 79, 769–772 (1997)

    Article  ADS  Google Scholar 

  18. Raimond, J. M., Brune, M. & Haroche, S. Manipulating quantum entanglement with atoms and photons in a cavity. Rev. Mod. Phys. 73, 565–582 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  19. Glauber, R. J. Coherent and incoherent states of the radiation field. Phys. Rev. 131, 2766–2788 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  20. Varcoe, B. T. H., Brattke, S., Weidinger, M. & Walther, H. Preparing pure photon number states of the radiation field. Nature 403, 743–746 (2000)

    Article  ADS  CAS  Google Scholar 

  21. Hofheinz, M. et al. Generation of Fock states in a superconducting quantum circuit. Nature 454, 310–314 (2008)

    Article  ADS  CAS  Google Scholar 

  22. Hofheinz, M. et al. Synthesizing arbitrary quantum states in a superconducting resonator. Nature 459, 546–549 (2009)

    Article  ADS  CAS  Google Scholar 

  23. Haroche, S. & Raimond, J. M. Exploring the Quantum: Atoms, Cavities and Photons (Oxford Univ. Press, 2006)

    Book  Google Scholar 

  24. Khalil, H. K. Nonlinear Systems (Prentice Hall, 2001)

    Google Scholar 

  25. Steane, A. M. Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  26. Lu, C.-Y. et al. Experimental quantum coding against qubit loss error. Proc. Natl Acad. Sci. USA 105, 11050–11054 (2008)

    Article  ADS  CAS  Google Scholar 

  27. Schindler, P. et al. Experimental repetitive quantum error correction. Science 332, 1059–1061 (2011)

    Article  ADS  CAS  Google Scholar 

  28. Knill, E., Laflamme, R., Martinez, R. & Negrevergne, C. Benchmarking quantum computers: the five-qubit error correcting code. Phys. Rev. Lett. 86, 5811–5814 (2001)

    Article  ADS  CAS  Google Scholar 

  29. DiCarlo, L. et al. Preparation and measurement of three-qubit entanglement in a superconducting circuit. Nature 467, 574–578 (2010)

    Article  ADS  CAS  Google Scholar 

  30. Vitali, D., Zippili, S., Tombesi, P. & Raimond, J. M. Decoherence control with fully quantum feedback schemes. J. Mod. Opt. 51, 799–809 (2004)

    Article  ADS  CAS  Google Scholar 

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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.

Author information

Authors and 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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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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