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 02.09.2011   Карта сайта     Language По-русски По-английски
Новые материалы
Электротехника и обработка материалов
Статистика публикаций


Real-time quantum feedback prepares and stabilizes photon number states

Journal name:






Date published:

(01 September 2011)





Published online

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.

Figures at a glance


  1. Figure 1: Scheme of the quantum feedback set-up.

    An atomic Ramsey interferometer (auxiliary cavities R1 and R2) sandwiches the superconducting Fabry–Perot cavity C resonant at 51GHz and cooled to 0.8K (the mean number of blackbody photons is 0.05). The pulsed classical source S′ induces π/2 pulses resonant with the |gright fenceright arrow|eright fence transition in R1 and R2 (with relative phase φr) on the velocity-selected (250ms−1) Rydberg atom qubits (purple circles) prepared by laser excitation (blue arrow) from a rubidium atomic beam (green arrow) in B. The field-ionization detector D measures the qubits in the e/g basis with a 35% detection efficiency and an error rate of a few per cent (Supplementary Methods). The actuator S feeds cavity C by diffraction on the mirror edges. The controller K (a CPU-based ADwin Pro-II system) collects information from D to determine the real translation amplitude α applied by S. It sets the S-pulse duration through a PIN diode switch A (63-μs pulse for |α| = 0.1) as well as a 180° phase-shifter Φ controlling the sign of α.

  2. Figure 2: Individual quantum feedback trajectories.

    Two feedback runs lasting 164ms (2,000 loop iterations) stabilizing |nt = 2right fence (left column) and |nt = 3right fence (right column). The phase-shift per photon, φ0 = 0.256π, allows controller K to discriminate n values between 0 and 7. For nt = 2, the Ramsey phase is φr = −0.44rad, corresponding to nearly equal e and g detection probabilities when n = 2. For nt = 3, two Ramsey phases φr,1 = −0.44rad and φr,2 = −1.24rad are alternatively used, corresponding to equal e and g probabilities when n = 2 and n = 3, respectively. a, Sequences of qubit detection outcomes. The detection results are shown as blue downward bars for g and red upward bars for e. Two-atom detections in the same state appear as double-length bars. b, Estimated distance between the target and the actual state. c, Applied α-corrections (shown on a log scale as sgn(α)log|α|). d, Photon number probabilities estimated by K: P(n = nt) is in green, P(n<nt) in red, P(n>nt) in blue. e, Field density operators ρ in the Fock-state basis estimated by K at four different times marked by arrows.

  3. Figure 3: Photon number histograms following quantum feedback iterations.

    Plots a, b, c and d correspond to the target photon number states nt = 1, 2, 3 and 4, respectively. The red histograms correspond to about 3,900 trajectories stopped when P(nt) has reached the threshold value (0.8) for three successive iterations. These histograms describe the field at the time when the controller K has certified the ‘success’ of the quantum feedback procedure. The blue histograms correspond to 4,000 trajectories stopped at a fixed time (164ms) and describe the feedback procedure steady-state. These histograms are reconstructed by a method independent of the feedback estimator. After interrupting the feedback, we record ten additional QND qubit samples (~2detected atoms) with a Ramsey interferometer phase φr chosen in sequence among 4 values (φr = 1.17, 0.36, −0.44 and −1.24rad). From these additional qubit detections, we reconstruct the final PQND(n) distribution for each ensemble of trajectories by a maximum likelihood algorithm. Statistical error of the reconstructed PQND(n) for different target states is about 0.01–0.02 for n = nt and nt±1, and it is significantly smaller than 0.01 for other photon numbers (see Supplementary Methods). The green histograms give the initial coherent state photon number distributions (a similar reconstruction was performed with a fixed time stop immediately after initial field injection).

  4. Figure 4: Performance of the quantum feedback procedure.

    a, Time evolution of the fraction of individual field trajectories, Cfr(t), that have reached the fidelity threshold (0.8) while converging towards |nt = 3right fence in quantum feedback sequences (smooth line) and in passive QND ‘trials’ (stepped line). Statistics performed over 4,000 and 2,131 trajectories, respectively. The same Ramsey phase settings as in Fig. 2 have been used for both feedback and QND sequences. b, Recovery from a quantum jump: the lower plot shows probabilities (n,t) estimated by K and averaged over 2,561 trajectories, following the preparation at t = 0 of the Fock state |n = 2right fence by a QND measurement of an initial coherent state (colour code shown at right for the different values of n). The Ramsey phase settings are the same as in Fig. 2 for nt = 3.The initial field density matrix of the field estimation algorithm is diagonal and corresponds to the red histogram in Fig. 3c. The experiment thus simulates the reaction of the quantum feedback procedure to a |3right fenceright arrow|2right fence quantum jump occurring at t = 0, after the field has converged to the target. The upper plot in b shows the variation of the average modulus of the injection amplitude . Initially zero, grows rapidly to a maximum while the quantum jump is reversed. The controller finally quiets and returns to its average steady-state value.

Дизайн и программирование N-Studio 
  • Chen Wev   honorary member of ISSC science council

  • Harton Vladislav Vadim  honorary member of ISSC science council

  • Lichtenstain Alexandr Iosif  honorary member of ISSC science council

  • Novikov Dimirtii Leonid  honorary member of ISSC science council

  • Yakushev Mikhail Vasilii  honorary member of ISSC science council

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