Feedback control of atomic coherent spin states

Transcription

1 Feedback control of atomic coherent spin states Andrea Bertoldi Institut d Optique, France RG Colloquium Hannover 13/12/2012

2 Feedback control h(t) Constant flow is required to keep time P = r H2O g h(t) Granular nature of sand solves the problem RG Colloquium Hannover 13/12/2012 1

3 Water clock Ktesibios of Aleandria 250 BC Float: sensor (measurement) and actuator (correction) RG Colloquium Hannover 13/12/2012 2

4 Outline Classical and quantum measurements projection, weak vs strong, SQL Feedback control of a quantum system weak regime vs projecting regime Feedback control of CSS stabiliation of quantum state against synthetic noise Atom Phase Lock atomic clock with LO phase-locked to atomic spin RG Colloquium Hannover 13/12/2012 3

5 Classical measurement Property of nature with a given numerical value 7 < < 8 - uncertainty - infinite precision - no disturbance Improvement using statistics: = (n 8 *8 + n 9 *9) / N - 1 d scales as N RG Colloquium Hannover 13/12/2012 4

6 Quantum measurement Measurement: generation of a value from a process! (distribution of possible values, action on the system ) A measurement always causes the system to jump into an eigenstate of the dynamical variable that is being measured he principles of quantum mechanics, P.A.M. Dirac (1958) RG Colloquium Hannover 13/12/2012 5

7 Projective measurement: Stern Gerlach in B out 1 2 meas & wf collapse Output position correlated to spin projection via B or Effect of Heisenberg uncertainty principle in in out out 1 2 RG Colloquium Hannover 13/12/2012 6

8 Quantum Non Demolition measurements QND measurement M: [M,H] = 0 Eigenstates of the observable are also stationary states second measurement gives same result Braginsky et al., Science 209, 547 (1980) QND measurement has no effect on an eigenstate, but collapses an initial superposition state RG Colloquium Hannover 13/12/2012 7

9 Weak measurements decrease time integral of B out out out partial information retrieval partial projection control of the coupling strength RG Colloquium Hannover 13/12/2012 8

10 Feedback control: classical vs quantum case CL: measurement (does not alter system) + correction Q: measurement (invasive, partially projects) + correction Preparation of photon number states S. Haroche Nature 477, 73 (2012) Stabilied Rabi oscillations I. Siddiqi Nature 490, 77 (2012) RG Colloquium Hannover 13/12/2012 9

11 Feedback control of atomic Coherent Spin State wo Level System = y pseudospin on Bloch sphere Spin: - population ratio (observable) - phase between two states e i = y ensemble of elementary systems with same internal state Maimal coherence, CSS Uncertainty given by SQL ( N) RG Colloquium Hannover 13/12/

12 Feedback control of atomic Coherent Spin State Decoherence sources: uncoherent vs coherent e.g. spontaneous emission e.g. stray magnetic field measure N -N QND, commutes with H RG Colloquium Hannover 13/12/

13 Eperimental setup 5 2 P 3/2 F =3 F =2 F =1 F =0 5 2 S 1/2 F=2 F=1 87 Rb D nm (dipole trap) Finesse ~ 1700 power enhancement ~ 200 butterfly configuration New J. Phys. 13, (2011) RG Colloquium Hannover 13/12/

14 Eperimental setup integral OD All optical BEC in the resonator distance (m) Imaging cavity transversal modes ( 2010 ) Lett. 35, 3769 Opt. Optical trapping in higher modes EM 00 EM 10 EM 20 EM 10 EM 20 RG Colloquium Hannover 13/12/

15 Eperimental setup 5 2 P 3/2 F =3 N 2 F =2 F =1 F =0 N S 1/2 F=2 measure N 2 - N 1 (J ): - inde of refraction depends on internal state - measure phase shift on probe beam - need phase reference F=1 LS atoms 10 K RG Colloquium Hannover 13/12/

16 Eperimental setup 5 2 P 3/2 F =3 F =2 F =1 F = S 1/2 F=2 Frequency modulation spectroscopy F=1 - strong carrier (phase reference) - weak sidebands (atomic signals) - difference on the photodiode Rb D 2 line - very short probe pulses (50 ns 2 s) RG Colloquium Hannover 13/12/

17 Eperimental setup 5 2 P 3/2 F =3 F =2 F =1 F =0 5 2 S 1/2 F=2 87 Rb D 2 line F=1 Prepare CSS on the equatorial plane (N 1 =N 2 ) Carrier frequency set to have phase shift from atoms in F=1 equal to phase shift from atoms in F=2 RG Colloquium Hannover 13/12/

18 Coherent spin manipulation 5 2 P 3/2 F =3 F =2 F =1 F =0 F=2 5 2 S 1/ GH F=1 Coherent manipulation of the spin on the Bloch sphere using resonant microwave pulses 87 Rb D 2 line RG Colloquium Hannover 13/12/

19 Feedback control of CSS Eperimental sequence: prepare CSS (optical pumping) CSS on the equator binary random collective rotation statistical miture correction weak measurement (determine hemisphere, no disturbance) RG Colloquium Hannover 13/12/

20 Residual coherence after binary RCR CSS pure state mied state from binary RCR coherence + = 50 % 50 % RG Colloquium Hannover 13/12/

21 Weak measurement: trade off accuracy destructivity N 2 1. Measurement of J as a Kraus operator M P m 0 2 1/ 2 e 1 J 4 m M M m m m 0 2 p s 2. Probability to get the right hemisphere P m 0 0 dm erf 2J sin N 1 3. Coherence after correction N ph p 1 p cos e out s s 2 Eperiment: = / 4 out = p s ep(-n ph ) spontaneous emission RG Colloquium Hannover 13/12/

22 Coherence recovery vs probe intensity Cycle: 1. CSS preparation on equators 2. Binary RCR 3. Weak measurement of J 4. Correction 5. Measurement residual coherence / 2 / 2 Best pulse: photons Feedback increases coherence from to 0.993(1)!! RG Colloquium Hannover 13/12/

23 Binary RCR Check: 1. measurement of p s (sign of RCR and correction recorded and treated off-line) 2. effect of variable intensity probe (Ramsey interferometry) prep /2 /2 3. multiplication of the two decoherence sources consistent with measured residual coherence out = p s ep(-n ph ) RG Colloquium Hannover 13/12/

24 More comple scenarios: 1. repeated binary RCRs N times /2 /4 /4 CSS preparation CSS on the equator RCR WM MCU correction RG Colloquium Hannover 13/12/

25 More comple scenarios: 1. repeated binary RCRs number of iterations Only direction of spin vector, no length! Feedback slows down spin diffusion - Eperimental points recording direction RCR and correction (analysis off-line) - Curves calculated (no feedback) or obtained from success probability (evolving with time because of spontaneous emission and OD light shift) RG Colloquium Hannover 13/12/

26 More comple scenarios: 1. repeated binary RCRs Residual coherence vs time obtained only multiplying effects of decoherence sources - success probability for hemisphere determination - spontaneous emission (by Ramsey interferometry) - differential light shift from Optical Dipole rap (by Ramsey interferometry) without feedback with feedback RG Colloquium Hannover 13/12/

27 More comple scenarios: 2. analog RCRs CSS on the equator analog RCR mied state flat distribution on [-/2,/2] weak measurement (determine J, low disturbance) correction task of the WM more demanding: not only hemisphere but noise angle! probe pulse photons RG Colloquium Hannover 13/12/

28 More comple scenarios: 2. analog RCRs / 2 direct measurement of the residual coherence out = 0.964(5) / repetitions of the eperimental sequence - angle evaluated off-line from RCR and correction angle residual coherence 0.63(3), consistent with 2/ residual coherence: 0.979(2) spin spread 0.979(1) spontaneous emission = 0.958(2) 0.964(5) direct measurement of the residual coherence RG Colloquium Hannover 13/12/

29 Realistic application: timekeeping? Basic demonstration: classical control process preserves quantum state against decoherence toy model Atomic clocks precise timekeeping using frequency lock NPL NIS PB RG Colloquium Hannover 13/12/

30 Atomic clocks quart LO periodical comparison relative dephasing & correction atomic reference F=2 5 2 S 1/ GH hyperfine structure 87 Rb F=1 o increase precision higher frequency (from -wave to optical reference) RG Colloquium Hannover 13/12/

31 Atomic clocks Ramsey interferometry CSS initialiation /2 0 free precession time /2 90 map equatorial plane on vertical destructive measurement fb on LO = n Longer better estimate frequency error BU phase drift must be </2 Need better oscillator cryogenic sapphire oscillator high finesse optical cavity RG Colloquium Hannover 13/12/

32 Atomic Phase Lock /2 0 free precession time /2 90 /2-90 /2 90 CSS initialiation weak measurement After interrogation, state back into the interferometer!! Effective longer interrogation time eff = N (till coherence finite) Interval for operations << bring to PHASE LOCK N Shiga and M akeuchi New J. Physics 14, (2012) RG Colloquium Hannover 13/12/

33 Atomic Phase Lock Atomic Clock prep prep /2 /2 /2 /2 w d start always from start Atomic Phase Lock prep /2 /2 /2 /2 /2 /2 w d start defined by previous measurement Correlation between measurements 1/N RG Colloquium Hannover 13/12/

34 Atomic Phase Lock Atomic Clock prep prep /2 /2 /2 /2 w w AC 1 SNR AC cyc t Atomic Phase Lock prep /2 /2 /2 /2 /2 /2 w w APL 1 SNR APL cyc t Comparison SQL and APL neglecting Dick effect must consider different SNR RG Colloquium Hannover 13/12/

35 Continuous phase measurement 1. Sawtooth phase evolution to LO 2. repeat weak measurement of the relative phase phase corrected for decoherence induced by spontaneous emission phase measured phase sawtooth on LO time (ms) RG Colloquium Hannover 13/12/

36 Phase lock of the LO to the atomic state Phase lock with repeated phase jump on the LO time (ms) Phase lock with frequency shift on the LO Locking of a macroscopic device on a quantum state! RG Colloquium Hannover 13/12/

37 Outlook 1. Phase-Lock an oscillator with 1/f frequency noise to atomic resonance 2. Demonstrate better than 1/ N scaling 3. Compare Atomic clock / Atom Phase Lock 4. Use partially projective measurements Atomic Phase Lock prep /2 /2 /2 /2 /2 /2 w w APL 1 SNR APL cyc t RG Colloquium Hannover 13/12/

38 Conclusions Quantum measurement & feedback, QND & weak measurements Feedback control of a CSS using Weak Measurements rade-off between information retrieval and destructivity fon binary RCR More comple scenarios Repeated binary RCRs Analog RCR number of iterations Improve timekeeping using Atomic Phase Lock prep RG Colloquium Hannover 13/12/2012 /2 /2 /2 /2 /2 /2

39 People Philippe Bouyer Arnaud Landragin A.B. Ralf Kohlhaas Etienne Cantin homas Vanderbruggen (ICFO Barcelona) Simon Bernon (Univ. übingen) RG Colloquium Hannover 13/12/2012