|set pointattenuatorStabilizing the power of a laser beam via feedback/forwardlaserpump|set pointLoop-shaping: put gain where you need it & close carefully • Higher gain at acoustic, seismic frequencies• Try not to close in a noise bump with inadequate phase marginFilter sensor noise and limit gain to SNR bandwidthlaser|pumptoo muchgainSignal diagram for “general” scenarioConclusions• It’s as important to characterize your noise as to characterize your plant • Plenty of room for theory to help with optimizing and compromisingplantcontrollerprocess noisesensor noiseMeasuring optical phaseϕθθ-ϕLocal oscillatorSignalapproximates canonical phase measurement,given prior knowledge of mean phase and photon numberAdaptive homodyne measurementϕdspLocal oscillatorSignalϕ1ϕ2ϕ3(H. M. Wiseman)…variance within 1% of canonical phase measurement for h n i & 10 photons !Adaptive homodyne feedback algorithms()()∫Φ=vuivdueuIA0()∫Φ−=vuivdueB02*vvvvABvAC +=Mark I: estimate = arg(A); Mark II: estimate = arg(C)()()vAv argˆ=ϕ() ()2ˆπϕ+=Φ vvLocal oscillator phase: ()()()()vvvvACvεεϕ−=1argˆ()vvCBvvvv−−=122ε“optimized” scheme (squeezed states):(D. W. Berry and H. M. Wiseman, PRA 63, 013813 (2000))technical effects?Technical challenges – laser noiseNPRONd:YAGhigh-Qresonator(cavity)τ ~ 16 µsTechnical challenges – loop delayquant-ph/0203143; to appear in JOSA BExperimental implementationClosing the loop…M. Armen, J. Au, J. Stockton, … PRL 89, 133602 (2002)The power of quantum feedbackquantum system Feedback control of quantum dynamicsinput output ControllerModulatoroptical coupling to internal and/or center-of-mass atomic dynamicsCavity QED with cold atoms104Cesium AtomsDetectorMirrorSubstrateMirrorSurfaceProbeLaseryzxCesium AtomsDetectorMirrorSubstrateProbeLaseryzxC. J. HoodSingle-atom spatial trajectories(with J. Ye and H. J. Kimble)• quantum-limited sensitivity, we believe• but how to prove it?Planar magnetic microtraps:Weinstein and Libbrecht (95)Haensch, Hinds, Schmiedmayer, …Intracavity optical lattice:Vernooy, Ye, and Kimble (98)Jessen, Deutch, …Intra-cavity atom traps• quantum-limited broadband measurement + low latency signal processing (HW) • synthesis (bilinear/stochastic/Hamiltonian) & identification methodology (SW)• explore “applications” with demonstrable, unique benefits of real-time QFBReal-time ‘quantum feedback’ controlquantum system input output ControllerModulatorPlanar trapping geometries for integrated cQEDσ−σ+MOTAnti-Helmholtz coilsCu or Macor blockReichel, Hänsel, and Hänsch, PRL 1999300 µmLoading cold atoms into a surface-MOT, MST(B.
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