Principes pour le fonctionnement des capteurs quantiques interféromètres et horloges. A. Landragin

Transcription

1 Principes pour le fonctionnement des capteurs quantiques interféromètres et horloges A. Landragin 1

2 Basic principle of an atomic clock / atomic frequency standard correction OSCILLATOR (quartz, laser, ) ν frequency ν : = ν 0 Unstable Stable SERVO LOOP Inaccurate Accurate ATOM / ION REFERENCE 2 1 ν 0 E 2 E 1 ν ν 0 ν h ν 0 = E 2 E 1 CLOCK SIGNAL

3 Applications of atomic clocks Fundamental metrology : Atomic time scales, Definition of SI units for time and frequency Worldwide networks synchronisation Telecommunications, financial datation Positioning : à 1 ns = 30 cm - Many GNSS : GPS (USA), GLONASS (Russia), GALILEO (Europe), BEIDOU/COMPASS (China), GINSS (India) Tests of fundamental laws of physics : General Relativity tests : - Search for a possible drift of fundamental constants - Search for a possible violation of gravitational red-shift law Geodesic chronometry Variation of the Earth geoid: cm Paris, France Transfer laser fs frequency comb Optical lattice Fiber noise cancellation Clock laser Repeater laser station Bidirectional amplifier Braunschweig, Germany Brillouin amplifier 100 km Clock laser Optical lattice Fiber noise cancellation Transfer fs laser frequency comb Strasbourg, France Repeater Repeater laser laser station station

4 Steps to build the clock signal Atomic source Quantum state preparation Interrogation Oscillator Clock signal detection proba ν 0 ν e e photon Optical pumping 1 Coherent transition 1 Fluorescence

5 Basic interrogation schemes : the Ramsey interrogation The Ramsey scheme = two interactions separated by a free evolution time Interrogation signal =2. f.t Coherent transition time T Rabi Ramsey fringes pattern (matter waves interferometry) The central linewidth is proportional to 1/2T The envelop width is proportional to 1/T Rabi T T Rabi 1/T Rabi Central fringe

6 Frequency delivered by a real atomic clock ν = ν 0 [1 + ε + y(t)] Real clock frequency Ideal clock frequency Frequency offset Frequency noise à Frequency (in)stability : Amplitude of frequency fluctuations δν or their relative value y(t) = δν/ν 0 à Frequency (in)accuracy : Uncertainty on the value of the frequency offset ε

7 The white frequency noise σ Clock signal linewidth : y ( τ ) Δν ν 0 S 1 / N 1 N meas Number of elementary measurements during the integration time τ Δυ 1 Tinterrogation Resonance frequency :! Cold / slow atoms! Trapping à Increase the frequency (optical clocks) Clock signal to noise ratio :! Try to eliminate instrumental noises! Quantum limit : S / N atoms number

8 A major limitation of short term stability à Periodic measurement (f c ) of the oscillator frequency vs atomic frequency à Bandpass of the servo loop << f c à Aliasing of oscillator noise at harmonics n.f c (stroboscopic effect) Degradation of short term frequency stability (Dick effect) White frequency noise Use very high spectral purity oscillators : Flicker floor - RF cryogenic oscillators (RF clock) - Lasers pre-stabilized on ultra high finesse cavities (optical clock) Fondamental limite: Quantum projection noise

9 Frequency accuracy and systematics Systematics / frequency shifts have an impact both on long term stability (insufficient control) and on accuracy (insufficient knowledge) à Frequency shifts induced by : External electro-magnetic fields Collisions Blackbody shift Doppler effect: cold atom (fountain) trapped atom (Neutral atom lattice clocks and Ion clocks ) + Relativistic frequency shifts: red shift from the Earth s gravity (occuring when comparing the frequencies of clocks operating in different frames)

10 A large family of atomic clocks Frequency performances Medium size clocks : Industry, atomic time scales, GNSS, Rb cell clocks CPT cocks Laboratory RF/optical clocks : Fundamental metrology / physics Cs beam clocks H-maser (passive and active) Compact cold atomic clocks Miniaturized clocks : Industry, telecoms, Size 1 cm 3 1 dm 3 1 m 3

11 em Present and future applica Horloge à atomes neutres de Sr en réseau Sr optical lattice clock Optical frequency combs Optical frequency combs Optical frequency Cas du Sr neutre (record ) combs Sr optical lattice clock 698 nm ultra-stable laser ccuracy of atomic clocks types 698 nm Different ultra-stable laser of atomic clocks 698 nm ultra-stable laser Increased accuracy leads to ne Clock-based geodesy: clocks fo Sr optical lattice clock 1.5 µm ultra-stable laser Sr optical lattice clock 1.5 µm ultra-stable laser Sr optical lattice clock 1.5 µm ultra-stable laser h Sr optical lattice clock Mesures non-destructives dans horloge à réseau optique Sr Coherent optical fiber links Coherent optical fiber links Coherent optical fiber links Exploiter la non-destructivité classique Minimisation de l impact du bruit du laser d interrogation Contraintes sur laser ultra-stable relâchée (transportabilité) Fiber-based time Atteindreand le frequency bruit de projection quantique Fiber-based time LNE-SYRTE atomic clock ensem dissemination Hg and frequency Telecommunication satellite Laser quantique stabilization using Fiber-based time Démontrer et utiliser non-destructivité dissemination spectral hole burning and frequency corrélés pour aller au-delà du bruit Génération d états dissemination de projection quantique: vers la limite d Heinseberg Etats corrélés pour minimiser les effets systématiques nm ultrastable laser

12 Atom interferometry Mach-Zehnder type interferometer Exit port 2 Exit port 1 1,0 lasers Exit port 2 Exit port 1 0,5 0,0 1,0 0,5 0, Phase shift Δφ: difference of accumulated phase shift along the two arms : 2 wave interferences Most of the inertial sensors used two photon Raman transitions

13 Atom interferometry as Inertial sensors long term stability and accuracy g Fundamental physics " measurement of α, G, watt balance " test of general relativity: Lense-Thirring effect (gyroscope), STE-QUEST, anomalous gravity (accelerometer), gravitational waves detectors (MIGA) Inertial navigation, submarine, satellite, boat Geophysics ground or onboard Earth s rotation rate, tidal effects, gravity field mapping

14 Simple examples in geophysics Measurement of (Bouguer) gravity anomaly to detect modifications of mass distribution Deformation and constraints: accumulation during seismic cycle... Volcanology: 4D mapping of mass distribution evolutions (time/space variations) Earthquake in China 2 Mars 20 th 2008 (magnitude 7,7) S. Merlet, et al., Metrologia 46, 87 94, (2009)

15 Stimulated Raman transitions Practical interests: Control of the difference of phase of lasers and not in the optical range Detection on the internal state (state labeling: C. Bordé, Phys. Lett. A 140, (1989)) Raman transitions Transition between 2 momentum states 6P 3/2 D 2 line for Cs 852 nm 6S 1/2 9,2 GHz

16 Wave-packet manipulation Transition probability Rabi oscillations between and π/2 π Ω Rabi τ Laser phase printed on the atomic wave during a transition π pulse Atomic mirror π/2 pulse Atomic beam splitter e g +φ ef e g -φ eff ( 12 f, p + e, p +!k eff e iφ )

17 Interferometer Phase shift Phase shift contributions along the perturbed trajectories: Laser : at center of the wave packet φ i = k.r i +φl Action : Propagation of the atomic wave Overlapping at exit of the interferometer Ch.J. Bordé, Metrologia 39, (2002) (for acc, gradient and rotation...) Relative displacements of the referential frame of the center of mass of the atoms/laser

18 Acceleration phase shift Constant acceleration In the atomic reference frame : ΔΦ = Φ 1 (t 1 ) 2Φ 2 (t 2 ) + Φ 3 (t 3 ) = Z1(t1)-2Z2(t2)+Z3(t3)

19 Rotation phase shift Atomic frame T T Θ 1 = -Ω T Ω Θ 3 = +Ω T ΔΦ = 2 ( k! eff V! )T 2 Ω!! A = " m T! 2 k eff V! ( ) Sagnac effect ΔΦ SAGNAC = 2 E A! Ω! "c 2

20 Atom interferometers Accelerometer: mesure the difference of acceleration between the atomic and the laboratory inertial frames depends of the space time area (along the splitting direction) Gyroscope: measure the difference of the rotation rate of the laboratory frame depends of the physical oriented area sensitivity of Cold atoms apparatus: better sensitivity: T but N relatively small (typically 10 6 ) =! k eff.! a.t 2 ΔΦ = 2 ( k! eff V! )T 2 Ω!

21 Gravimeter Raman 1 Raman 2 2D-MOT 3D-MOT 10 8 Rb-atoms in 50 ms T atoms ~2 µk Detection of a et b π/2 π π/2 atom interferometer Mirror Interrogation time: 160 ms Cycling frequency: 3 Hz

22 Gravimeter Problem of phase ambiguity for large sensitivity Isolation platform Correlation with a mechanical accelerometer (or seismometer) Best sensitivity: σg/g = in 1s Interrogation time: 160 ms Cycling frequency: 3 Hz!

23 Gravimeter 27 days measurement, april-may d measurement: 1 nm.s -2 in 10000s (10-10 g ) Long term stability: between 2 to 4 nm.s -2 Accuracy: g

24 Aliasing in cold atoms measurements Cycling time Tc: aliasing effect (as Dick effect for clocks) Interrogation pulse sequence 2T: π/2-π-π/2 average measurement during the interrogation Dead times: lost of information, practical limit for Inertial sensors Interrogation time 2T 2T Dead time Dead time Dead time Dead time Signal variation Cycling time Tc Tc Time

25 Dead times Correlation with classical sensor during the measurements Dead times: lost of information => error for navigation Fill the holes: - Hybridization with classical sensor (fusion of data): Interrogation time 2T 2T Dead time Dead time Dead time Dead time Cycling time Tc Tc Time

26 Dead times Correlation with classical sensor during the measurements Dead times: lost of information => error for navigation Fill the holes: - Hybridization with classical sensor (fusion of data) - Continuous measurements Interrogation time 2T 2T Dead time Dead time Dead time Dead time Cycling time Tc Tc Time

27 lation F=2 population general Lissajous figures roll and slope angles. The fact that aeff 0g is less than g origin In an of thein UFF in O-g large variation the aircraft s slope angle ove he two species are airplane: not from thetest es collapse into an ellipse parabola (±45!). From the data shown in Fig. 3d f, we mea ICE experiment (collaboration LP2N, SYRTE and CNES) differential phase) only an Eo tvo s parameter of Z1 g ¼ (! 0.5±1.1) " 10! 3 du 87Rb/39K: uses of correlation with kc1 Ice experiment in 0-gsteady plane between flight. Here the uncertainty is the combined statis atio (Fig. 3f). This sys! 5) stat ¼ 4.9 " 10 and systematic (dz (dz(σ e both interferometers standard accelerometer 0.05 g rms) vib 1g ¼ 1.1 " 10 1g irror vibrations (that is, error which was limited primarily by direction-independ 3 T limited by rotation induces lost of contrats (5 /s) us shape remains fixed phase shifts due to the quadratic Zeeman effect. Simil ase span. We achieve in microgravity we measure Z0 g ¼ (0.9±3.0) " 10! 4, w! 4) and system ¼ 1.9 " 10 rrogation times satisfy corresponding statistical (dzstat 0g sys! 4 (dz0g ¼ 2.3 " 10 ) errors. Here the increased statistical e is a result of fewer data available in 0 g. However, the system y to gravitational accel- uncertainty improves by a factor of B5 compared w gravity. This is a direct result of e made a direct test of the measurements in standard ARTICLE ightlessness. The relative reduced sensitivity of the DSD interferometer to direct measurements are consis 0.36 dium atoms is measured independent systematic effects. Both 1g b a with Z ¼ Rb hift for systematic effects 0.32 rential phase due to a 0.30 Discussion 0.28 Although the systematic uncertainty was dominatedk by techn 0.26 f fields, the10 sensitivit TK ðak! arb Þ; ð4þ issues related to time-varying magnetic our measurements was primarily limited by two effects relate B. Barrett etonboard al., Nature Communications 7,aircraft (2016) matter-wave sensors Novespace Zero-G (a) Basic 0.32 trajectory Rb 1 g d e of interferometer scale thethe motion of the aircraft vibrational noise on the re FIG. 3. Simultaneous K-Rb interferometer fringes during standardand m c flight which produces 20 s of weightlessness per maneuver. The coordinate systems xyz Arnaud Landragin in the ground state F = 2i for each species with the vibration-indu Raman pulse durations. reflection mirror and rotations0.28ofis correlated the interferometer bea

28 4 pulse cold atom gyroscope New generation of gyroscope: with 4 pulses, 2T=800 ms «Pure Gyroscope» => increases the area, not sensitive to DC acceleration Extremely large area in 4 pulse sequence (area up to 11 cm 2 ) duration T π Pulse duration T/2 = 1 2 (g k e ). T 3 π/2 Pulse I. Dutta, et al., Phys. Rev. Lett. 116, (2016).

29 Mesures continues entre-lassées Mesures continues: pas de temps mort Z π π/2 Detection Trapping Time

30 Mesures continues entre-lassées Mesures continues Fonctionnement entrelassé sensibilité record pour un gyromètre atomique Z Ecart-type d Allan de vitesse de rotation Bruit de détection 10-9 π 30 nrad.s -1.Hz -1/ π/ temps d intégration Detection Gain : 3 Trapping Time

31 Interférométrie atomiques Gravimètre et gyromètre : au niveau de l état de l art Accéléromètre embarqué : démonstration de principe de l intérêt pour l inertiel avec une grande stabilité du biais (avion, bateau) Gradiomètre : variation de gravité (mesure de G), intérêt en géophysique sol et embarquée Interféromètres à atomes confinés : augmentation de la durée de mesure nouvelles architectures ingénierie quantique

32 Conclusion Nouvelles applications ou technologie : identifier le besoin réel, convaincre de l intérêt Hybridation Capteurs Quantiques / Capteurs Classiques : horloges, capteurs inertiels technologies classiques optimisées Ressources pour les autres domaines classiques ou quantiques Points forts : capacité à reproduire le même état quantique pour des mesures séparées dans l espace et le temps A développer ou réaliser: intrication sur l état externe, horloges intriquées à distance