Principes pour le fonctionnement des capteurs quantiques – interféromètres et horloges



Principes pour le fonctionnement des capteurs quantiques – interféromètres et horloges


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            <title>Principes pour le fonctionnement des capteurs quantiques – interféromètres et horloges</title></titles>
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	    <date dateType="Created">Mon 12 Feb 2018</date>
	    <date dateType="Updated">Mon 12 Feb 2018</date>
            <date dateType="Submitted">Sun 10 Feb 2019</date>
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Principes pour le fonctionnement des capteurs quantiques – interféromètres et horloges A. Landragin 1 Arnaud Landragin Basic principle of an atomic clock / atomic frequency standard OSCILLATOR (quartz, laser, …) frequency ν : Unstable Inaccurate ν ν ν0 E2 E1 h ν0 = E2 –E1 ATOM / ION REFERENCE ν0 ν SERVO LOOP correction frequency ν : Stable Accurate = ν0 CLOCK SIGNAL 2 1 Arnaud Landragin Applications of atomic clocks Fundamental metrology : Atomic time scales, Definition of SI units for time and frequency 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 Worldwide networks synchronisation Telecommunications, financial datation… Geodesic chronometry Variation of the Earth geoid: 10-18 ⬄ 1 cm Repeater laser station Bidirectional amplifier Brillouin amplifier Braunschweig, Germany 100 km Fiber noise cancellation Fiber noise cancellation Repeater laser station Repeater laser station Clock laser Clock laser fs frequency comb fs frequency comb Paris, France Optical lattice Transfer laser Transfer laser Optical lattice Strasbourg, France Figure 1 | Schematic of the clock comparison. The strontium lattice clocks are located at the national metrology institutes SYRTE and PTB in Paris and Braunschweig, respectively. The course and lay-out of the fibre link sections to Strasbourg (705 km from Paris, 710 km from Braunschweig) are indicated on the map. Additionally, the individual setups consisting of a clock laser, optical lattice, fs frequency comb, transfer laser and stabilized link are shown schematically. In Strasbourg, the frequency difference between the transfer lasers is measured. For details see the main text and Methods. Country border data available at under a Creative Commons Attribution-ShareAlike 3.0 Unported. Full terms at Table 1 | Uncertainty budget. Clock uncertainty Sr lattice clock Paris Sr lattice clock Braunschweig NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12443 ARTICLE Arnaud Landragin Steps to build the clock signal Quantum state preparation Atomic source Oscillator Clock signal detection ν0 ν proba Optical pumping photon Fluorescence Interrogation Coherent transition 2 1 2 1 e 2 1 e 2 1 2 1 2 1 Arnaud Landragin Basic interrogation schemes : the Ramsey interrogation ✓ The Ramsey scheme = two interactions separated by a free evolution time Ramsey fringes pattern (matter waves interferometry) The central linewidth is proportional to 1/2T The envelop width is proportional to 1/TRabi time Interrogation signal 1/TRabi T TRabi TRabi Central fringe Coherent transition = 2⇡. f.T Arnaud Landragin Frequency delivered by a real atomic clock ν = ν0 [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/ν0 à Frequency (in)accuracy : Uncertainty on the value of the frequency offset ε Arnaud Landragin The white frequency noise meas y N N S 1 / 1 ) ( 0 ν ν τ σ Δ ∝ Clock signal linewidth : ! Cold / slow atoms ! Trapping ion interrogat 1 T ∝ Δυ Resonance frequency : à Increase the frequency (optical clocks) Clock signal to noise ratio : ! Try to eliminate instrumental noises ! Quantum limit : number atoms N S ∝ / Number of elementary measurements during the integration time τ Arnaud Landragin A major limitation of short term stability à Periodic measurement (fc) of the oscillator frequency vs atomic frequency à Bandpass of the servo loop << fc à Aliasing of oscillator noise at harmonics n.fc (stroboscopic effect) Degradation of short term frequency stability (Dick effect) Use very high spectral purity oscillators : - RF cryogenic oscillators (RF clock) - Lasers pre-stabilized on ultra high finesse cavities (optical clock) W hite frequency noise Flicker floor Fondamental limite: Quantum projection noise Arnaud Landragin Frequency accuracy and systematics 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) Systematics / frequency shifts have an impact both on long term stability (insufficient control) and on accuracy (insufficient knowledge) Arnaud Landragin A large family of atomic clocks Frequency performances Size Laboratory RF/optical clocks : Fundamental metrology / physics Medium size clocks : Industry, atomic time scales, GNSS, … Miniaturized clocks : Industry, telecoms, … 1 m3 1 dm3 1 cm3 Rb cell clocks CPT cocks Cs beam clocks H-maser (passive and active) Compact cold atomic clocks Arnaud Landragin Horloge à atomes neutres de Sr en réseau ✓ Cas du Sr neutre (record 2.10-18) Optical frequency combs 1.5 µm ultra-stable laser 698 nm ultra-stable laser Sr optical lattice clock Sr optical lattice clock Coherent optical fiber links Fiber-based time and frequency dissemination Present and future applica h LNE-SYRTE atomic clock ensem Telecommunication satellite ccuracy of atomic clocks Different types of atomic clocks Increased accuracy leads to ne Clock-based geodesy: clocks fo Laser stabilization using spectral hole burning 1062.5 nm ultra- stable laser Hg Optical frequency combs 1.5 µm ultra-stable laser 698 nm ultra-stable laser Sr optical lattice clock Sr optical lattice clock Coherent optical fiber links Fiber-based time and frequency dissemination Optical frequency combs 1.5 µm ultra-stable laser em 698 nm ultra-stable laser Sr optical lattice clock Sr optical lattice clock Coherent optical fiber links Fiber-based time and frequency dissemination ✓ Mesures non-destructives dans horloge à réseau optique Sr ➡ Exploiter la non-destructivité classique ● Minimisation de l’impact du bruit du laser d’interrogation ● ➔ Contraintes sur laser ultra-stable relâchée (transportabilité) ● Atteindre le bruit de projection quantique ➡ Démontrer et utiliser non-destructivité quantique ● Génération d’états corrélés pour aller au-delà du bruit de projection quantique: vers la limite d’Heinseberg ● Etats corrélés pour minimiser les effets systématiques Arnaud Landragin Atom interferometry Phase shift 0,0 0,5 1,0 -15-10 -5 0 5 10 0,0 0,5 1,0 Exit port 2 Exit port 1 Δφ: difference of accumulated phase shift along the two arms : 2 wave interferences Exit port 1 Exit port 2 Most of the inertial sensors used two photon Raman transitions lasers Mach-Zehnder type interferometer Arnaud Landragin Atom interferometry as Inertial sensors long term stability and accuracy • Inertial navigation, submarine, satellite, boat… • 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)… • Geophysics ground or onboard Earth’s rotation rate, tidal effects, gravity field mapping … g Arnaud Landragin Simple examples in geophysics ✓ Measurement of (Bouguer) gravity anomaly to detect modifications of mass distribution ✓ Volcanology: 4D mapping of mass distribution evolutions (time/space variations) ✓ Deformation and constraints: ➡ accumulation during seismic cycle... Earthquake in China 2 Mars 20th 2008 (magnitude 7,7) S. Merlet, et al., Metrologia 46, 87–94, (2009) Arnaud Landragin Stimulated Raman transitions 6S1/2 9,2 GHz 6P3/2 852 nm Raman transitions D2 line for Cs Transition between 2 momentum states 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, 10-13 (1989)) Arnaud Landragin Wave-packet manipulation +φef g e g e -φeff Laser phase printed on the atomic wave during a transition Rabi oscillations between Transition probability ΩRabiτ π/2 π and π pulse Atomic mirror π/2 pulse Atomic beam splitter € 1 2 f , p + e, p + !keff eiφ ( ) Arnaud Landragin Interferometer Phase shift Laser : at center of the wave packet φi = k.ri+φl Phase shift contributions along the perturbed trajectories: Action : Propagation of the atomic wave Overlapping at exit of the interferometer Ch.J. Bordé, Metrologia 39, 435-463 (2002) Relative displacements of the referential frame of the center of mass of the atoms/laser (for acc, gradient and rotation...) Arnaud Landragin Acceleration phase shift Constant acceleration ΔΦ = Φ1(t1) – 2Φ2 (t2) + Φ3 (t3) = ∝Z1(t1)-2Z2(t2)+Z3(t3) In the atomic reference frame : Arnaud Landragin Rotation phase shift T T Ω Θ1 = -Ω T Θ3 = +Ω T Atomic frame ΔΦ = −2 ! keff ∧ ! V ( )T2 ⋅ ! Ω ! A = " m T2 ! keff ∧ ! V ( ) ΔΦSAGNAC = 2 E ! A⋅ ! Ω "c2 Sagnac effect Arnaud Landragin 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 106) € ΔΦ = −2 ! keff ∧ ! V ( )T2 ⋅ ! Ω = ! keff .! a .T2 Arnaud Landragin Gravimeter π/2 π/2 π 2D-MOT atom interferometer Raman 2 Detection of |a〉 et |b〉 3D-MOT 108 Rb-atoms in 50 ms Tatoms~2 µK Raman 1 Mirror Interrogation time: 160 ms Cycling frequency: 3 Hz Arnaud Landragin Gravimeter ! ✓ Problem of phase ambiguity for large sensitivity ✓ Isolation platform ✓ Correlation with a mechanical accelerometer (or seismometer) Interrogation time: 160 ms Cycling frequency: 3 Hz Best sensitivity: σg/g = 5.10-9 in 1s Arnaud Landragin Gravimeter 27 days measurement, april-may 2015 1.5 d measurement: 1 nm.s-2 in 10000s (10-10 g) Long term stability: between 2 to 4 nm.s-2 Accuracy: 4.10-9 g Arnaud Landragin 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 Time Cycling time Tc Tc Interrogation time 2T 2T Dead time Dead time Dead time Dead time Signal variation Arnaud Landragin 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): Time Cycling time Tc Tc Interrogation time 2T 2T Dead time Dead time Dead time Dead time Arnaud Landragin 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 Time Cycling time Tc Tc Interrogation time Dead time Dead time Dead time Dead time 2T 2T Arnaud Landragin ➡ Ice experiment in 0-g plane between 87Rb/39K: uses of correlation with standard accelerometer (σvib ≃ 0.05 g rms) ➡ T limited by rotation induces lost of contrats (5°/s) 0.36 a d b e Rb Rb 1 g 1 g K ⎟ F=2〉 population lation 0.34 0.32 0.32 0.30 0.28 0.30 0.28 0.26 0.24 –10 –5 0 5 10 15 –1 ARTICLE 3 matter-wave sensors onboard the Novespace Zero-G aircraft. (a) Basic trajectory c flight which produces 20 s of weightlessness per maneuver. The coordinate systems xyz In an airplane: test of the UFF in O-g FIG. 3. Simultaneous K-Rb interferometer fringes during standard- and m in the ground state |F = 2i for each species is correlated with the vibration-indu ICE experiment (collaboration LP2N, SYRTE and CNES) B. Barrett et al., Nature Communications 7, 13786 (2016) general Lissajous figures he two species are not es collapse into an ellipse differential phase) only atio kC1 (Fig. 3f). This e both interferometers irror vibrations (that is, us shape remains fixed ase span. We achieve rrogation times satisfy y to gravitational accel- e made a direct test of the ightlessness. The relative dium atoms is measured hift for systematic effects rential phase due to a f T2 K aK ! aRb ð Þ; ð4Þ of interferometer scale Raman pulse durations25. roll and slope angles. The fact that aeff 0g is less than g origin from the large variation in the aircraft’s slope angle ove parabola (±45!). From the data shown in Fig. 3d–f, we mea an Eötvös parameter of Z1 g ¼ ( ! 0.5±1.1) " 10! 3 du steady flight. Here the uncertainty is the combined statis (dZstat 1g ¼ 4.9 " 10! 5) and systematic (dZ sys 1g ¼ 1.1 " 10 error—which was limited primarily by direction-independ phase shifts due to the quadratic Zeeman effect. Simil in microgravity we measure Z0 g ¼ (0.9±3.0) " 10! 4, w corresponding statistical (dZstat 0g ¼ 1.9 " 10! 4) and system (dZ sys 0g ¼ 2.3 " 10! 4) errors. Here the increased statistical e is a result of fewer data available in 0 g. However, the system uncertainty improves by a factor of B5 compared w measurements in standard gravity. This is a direct result of reduced sensitivity of the DSD interferometer to direct independent systematic effects. Both measurements are consis with Z ¼ 0. Discussion Although the systematic uncertainty was dominated by techn issues related to time-varying magnetic fields, the sensitivit our measurements was primarily limited by two effects relate the motion of the aircraft—vibrational noise on the re reflection mirror and rotations of the interferometer bea Arnaud Landragin 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 cm2) = 1 2 (g ⇥ ke↵ ).⌦T3 π/2 Pulse π Pulse duration T/2 duration T I. Dutta, et al., Phys. Rev. Lett. 116, 183003 (2016). Arnaud Landragin Mesures continues entre-lassées Z Time π π/2 Trapping Detection Mesures continues: pas de temps mort Arnaud Landragin Mesures continues entre-lassées Z Time π π/2 Trapping Detection Mesures continues Fonctionnement entre- lassé ➡ sensibilité record pour un gyromètre atomique 30 nrad.s-1 .Hz-1/2 Gain : 3 Bruit de détection 10-7 10-8 10-9 10-10 Ecart-type d’Allan de vitesse de rotation 100 101 102 103 104 105 temps d’intégration Arnaud Landragin 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 FIG. 1: (Color online) Wannier-Stark ladder where νB is the Bloch frequency, νHF S the hyperfine transition between the states |g⟩ = ! !52 S1/2, F = 1, mF = 0 " and |e⟩ = ! !52 S1/2, F = 2, mF = 0 " of 87 Rb, m the quantum number corresponding to the lattice sites and Ω∆m the coupling between the wells m and m ± ∆m. With respect to Bloch states which are, in the absence of a linear force, delocalized all along the lattice due to its periodicity [40, 41], the spread of the atomic wavefunction |Wm⟩ depends on the lattice depth. While being well localized in the well m at high depth (U0 ≫ 10 Er), the wavefunction extends across a significant number of wells when reducing the depth below 5 Er [42], where the recoil energy Er is defined by h̄k2 l Arnaud Landragin 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…