Atom Interferometry and Precision Tests in Gravitational Physics

Transcription

1 Atom Interferometry and Precision Tests in Gravitational Physics Lecture III Precision measurements of gravity Determination of the gravitational constant G Experiments on gravity at small spatial scale Tests of the equivalence principle Towards gravitational waves detection with atom interferometry Main references - A. D. Cronin, J. Schmiedmayer, D. E. Pritchard, Optics and interferometry with atoms and molecules, Rev. Mod. Phys. 81, 1051 (2009). - C. Cohen-Tannoudji, D. Guery-Odelin, Advances in Atomic Physics: An Overview, World Scientific (2011) - Lectures at the E. Fermi School on Atom Interferometry, Varenna (2013) G. M. Tino, M. A. Kasevich (eds). Atom Interferometry. Proc. International School of Physics Enrico Fermi, Course CLXXXVIII, Varenna 2013, SIF and IOS (2014).

2 (1 Gal = 1 cm/s 2 1 µgal 10-9 g) from A. Peters, E. Fermi School on Atom Interferometry, Varenna 2013

3 from A. Peters, E. Fermi School on Atom Interferometry, Varenna 2013

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5 Stanford atom gravimeter Resolution: 3x10-9 g after 1 minute Absolute accuracy: Δg/g<3x10-9 A. Peters, K.Y. Chung and S. Chu, Nature 400, 849 (1999)

6 from A. Peters, E. Fermi School on Atom Interferometry, Varenna 2013

7 from A. Peters, E. Fermi School on Atom Interferometry, Varenna 2013

8 from A. Peters, E. Fermi School on Atom Interferometry, Varenna 2013

9 from A. Landragin, E. Fermi School on Atom Interferometry, Varenna 2013

10 Stability of the gravimeter Comparison with state of the art falling corner cube gravimeter FG5 (measurement in Walferdange - Luxembourg) Earth quake Time evolution Standard Allan deviation 10-1/2 1 6!Gal/"! / s Atomic gravimeter better immune to vibrations than FG5X Long term stability 0.2!Gal From A. Landragin, 2014

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13 Precision gravity measurement at µm scale with Bloch oscillations of Sr atoms in an optical lattice ν = m g λ /2 h G. Ferrari, N. Poli, F. Sorrentino, G. M. Tino, Long-Lived Bloch Oscillations with Bosonic Sr Atoms and Application to Gravity Measurement at the Micrometer Scale, Phys. Rev. Lett. 97, (2006) G.M. Tino, School on Ultracold Atoms Precision Les Houches, September 2014 G.M. Tino, E. and Fermi SchoolMeasurements, on Atom Interferometry, Varenna, July 2013

14 Stanford/Yale gravity gradiometer from M.A. Kasevich M.J. Snadden et al., Phys. Rev. Lett. 81, 971 (1998)

15 Firenze gravity-gradiometer Source masses and support Laser and optical system F. Sorrentino, Q. Bodart, L. Cacciapuoti, Y.-H. Lien, M. Prevedelli, G. Rosi, L. Salvi, and G. M. Tino, Sensitivity limits of a Raman atom interferometer as a gravity gradiometer, Phys. Rev. A 89, (2014)

16 compact From M. Kasevich, Stanford University Talk at the International Workshop on Advances in Precision Tests and Experimental Gravitation in Space, Firenze, September 2006

17 isense Integrated Quantum Sensors

18 Measurement of the Newtonian gravitational constant G by atom interferometry

19 Measurements of the Newtonian gravitational constant G Cavendish 1798 G = (80) m 3 kg -1 s -2 [ ] P.J. Mohr, B. N. Taylor, and D. B. Newell, CODATA recommended values of the fundamental physical constants: 2010, Rev. Mod. Phys., Vol. 84, No. 4, (2012) Quinn 2001 G.M. Tino, School on Ultracold G.M. Tino, Atoms E. and Fermi Precision School Measurements, on Atom Interferometry, Les Houches, Varenna, September July

20 Measurements of the Newtonian gravitational constant G NIST-82 torsion balance TR&D-96 torsion balance LANL-97 torsion balance CODATA 1998 UWash-00 BIPM-01 UWup-02 torsion balance torsion balance simple pendulum CODATA 2002 MSL-03 HUST-05 UZur-06 torsion balance torsion balance beam balance CODATA 2006 HUST-09 JILA-10 torsion balance simple pendulum CODATA 2010 BIPM-13 torsion balance THIS WORK atom interferometry G (10-11 m 3 kg -1 s -2 )

21 Terry Quinn. Measuring big G, NATURE VOL /28 DECEMBER 2000 G.M. Tino, School on Ultracold G.M. Tino, Atoms E. and Fermi Precision School Measurements, on Atom Interferometry, Les Houches, Varenna, September July

22 Why atoms? Extremely small size Well known and reproducible properties Quantum systems Precision gravity measurement by atom interferometry Potential immunity from stray fields effects Different states, isotopes,

23 MAGIA (MISURA ACCURATA di G MEDIANTE INTERFEROMETRIA ATOMICA) Measure g by atom interferometry Add source mass Measure change of g am g Precision measurement of G

24 MAGIA (MISURA ACCURATA di G MEDIANTE INTERFEROMETRIA ATOMICA) Measure g by atom interferometry Add source masses Measure change of g am g Precision measurement of G Test of Newtonian law G.M. Tino, School on Ultracold G.M. Tino, Atoms E. and Fermi Precision School Measurements, on Atom Interferometry, Les Houches, Varenna, September July

25 MAGIA: atom gravimeter + source mass Sensitivity 10-9 g/shot 500 kg tungsten mass Peak mass acceleration a G 10-7 g one shot ΔG/G shots ΔG/G 10-4

26 MAGIA apparatus Manipulate 87Rb atoms Transport light Long interaction times Gravitational field LASER SYSTEM OPTICAL FIBERS Ti VACUUM SYSTEM W SOURCE MASSES L. Cacciapuoti, M. de Angelis, M. Fattori, G. Lamporesi, T. Petelski, M. Prevedelli, J. Stuhler, G.M. Tino, Analog+digital phase and frequency detector for phase locking of diode lasers, Rev. Scient. Instr. 76, (2005) G. Lamporesi, A. Bertoldi, A. Cecchetti, B. Dulach, M. Fattori, A. Malengo,, S. Pettorruso, M. Prevedelli, G.M. Tino, Source Masses and Positioning System for an Accurate Measurement of G, Rev. Scient. Instr. 78, (2007)

27 MAGIA apparatus Laser system 6 frequency stabilized ECDL 780 nm (Reference, Cooling 2D-MOT, Cooling 3D-MOT, Repumper master, Raman master, Raman slave) 3 optically injected diode 780 nm (Repumper 2D-MOT, Repumper 3D-MOT, Probe) 4 Tapered 780 nm (Cooling 2D-MOT, Cooling 3D-MOT, Raman master, Raman ~20 AOMs ~20 PM optical fibres Active stabilization loops Intensity of 3D-MOT Cooling up and down laser beams, master and slave Raman laser beams and Probe laser tilt of Raman retro-reflection mirror Earth rotation compensation with tilt-tip Raman mirror Vacuum system 2D-MOT chamber, steel, 10-7 torr Rb pressure main chambers and interferometer tube, titanium, ~10-10 torr Electronic control system real-time system for analog I/O and TTL signals, <5 μs jitter ~20 shutter drivers ~10 DDS for AOM and OPLL driving 6 low-noise coil drivers Laboratory environment temperature stability 0.1 C humidity stability 5%

28 Double launch and juggling TRAPPING/COOLING N=5 x 10 8 T=2 µk z LAUNCH JUGGLING sample 1 rapid double launch! 30 cm sample 0 sample 2 t 28

29 Triple velocity selection Goal: reduce background of thermal atoms from off-resonant scattering during VS pulse Initial state after launch: F=2, unpolarized, 2.5 µk (3.5 v rec ) Raman + blow-away pulses Final state: F=1, m F =0, v z =v rec /3

30 Raman interferometry

31 Detection In upper chamber, atoms interact with two horizontal laser beams resonant with the F=2 >F =3 transition rectangular shape, 15 mm width 4 mm height intensity ~3.5 I S retro-reflected in upper half (blow-away in lower half) Additional F=1 >F =2 laser beam in the middle to repump atoms in F=2 upper (lower) detector counts atom in F=2 (F=1) Fluorescence collected on two independent photodiodes solid angle ~0.01 sterad transimpedance 1 GOhm, conversion ~5 µv/atom

32 Experimental sequence Trapping N=5x Rb Laser cooling - MOT Cooling T=4 µk Laser cooling - Optical molasses Launch h= cm Moving opt. mol. - Atomic fountain Double launch Selection Interferometer Δt=80 ms Δz=30 cm F=1 m F =0 Δv z =v rec /2 Δφ Juggling Two-photon Raman transition π/2 π π/2 Raman sequence with phase locked lasers Detection N 1, N 2 Fluorescence detection

33 Gravity gradiometer T=5 ms resol. = g/shot T=50 ms resol. = g/shot T=150 ms resol. = g/shot = k e gt 2 G. T. Foster et al., Opt. Lett 27, 951 (2002)

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35 A. Bertoldi G.Lamporesi, L. Cacciapuoti, M. deangelis, M.Fattori, T.Petelski, A. Peters, M. Prevedelli, J. Stuhler, G.M. Tino, Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G, Eur. Phys. J. D 40, 271 (2006) J. B. Fixler, G. T. Foster, J. M. McGuirk and M. A. Kasevich, Atom Interferometer Measurement of the Newtonian Constant of Gravity, Science 315, 74 (2007)

36 Source mass COMPOSITION PROPERTIES REALIZATION INTERMET IT 180 (PLANSEE) W 95.3% Ni 3.2% Cu 1.5% Density 18 kg/m 3 Resistivity 12x10-8 Ωm Amagnetic CTE 5x10-6 K -1 Roughness 3 µm SINTERING T=1500 C - P=1 bar Hot Isostatic Pressing T=1200 C - P=1000 bar MICROSCOPE ANALYSIS ULTRASONIC TEST Before HIP holes: Ø ~ 100 µ m After HIP DENSITY TEST (INRIM, Torino) ρ = kg/m 3 res: 10 mg/m 3 σ ρ = 12 kg/m 3 ( ) Δρ =47 kg/m 3 ( ) G. Lamporesi, A. Bertoldi, A. Cecchetti, B. Dulach, M. Fattori, A. Malengo,, S. Pettorruso, M. Prevedelli, G.M. Tino, Source Masses and Positioning System for an Accurate Measurement of G, Rev. Scient. Instr. 78, (2007)

37 Optimized trajectories atoms Masses separation in the two configurations and atomic clouds initial position have been chosen in order to minimize the dependence on atomic initial parameters and reach the accuracy on G of the interferometer is realized around an acceleration max/min the Earth s gravity gradient must be over-compensated only high density material can be used L E A D T U N G S T E N G.M. Tino, School on Ultracold G.M. Tino, Atoms E. and Fermi Precision School Measurements, on Atom Interferometry, Les Houches, Varenna, September July

38 2007 Results from MAGIA G = (11) (3) m 3 kg -1 s -2 G. Lamporesi, A. Bertoldi, L. Cacciapuoti, M. Prevedelli, G. M. Tino Determination of the Newtonian Gravitational Constant Using Atom Interferometry Phys. Rev. Lett. 100, (2008)

39 MAGIA: From proof-of-principle to the measurement of G Sensitivity 15-fold improvement of the instrument sensitivity from 2008 to 2013 integration time for the target 100 ppm reduced by more than a factor 200 Accuracy systematic uncertainty reduced by a factor ~10 since 2008, mostly due to better characterization of source masses control & mitigation of Coriolis acceleration excellent control of atomic trajectories Data analysis we developed a reliable model accounting for all of the relevant effects gravitational potential generated by source masses along atomic path quantum mechanical phase shift of atomic probes detection efficiency measured data are compared with a Montecarlo simulation

40 Improving the sensitivity Larger number of atoms: 2D-MOT and higher power Raman lasers Lower detection noise: minimize stray light and use ultra-low noise electronics Larger contrast: remove thermal atoms with better velocity selection Lower fluctuations of main experimental parameters...

41 MAGIA: increasing sensitivity Current sensitivity to differential acceleration: 3x10-9 1s (=QPN for 4x10 5 atoms) [1] G. Lamporesi et al., Phys. Rev. Lett 100, (2008) [2] F. Sorrentino et al., New J. Phys. 12, (2010) [3] F. Sorrentino et al., Phys. Rev. A 89, (2014)

42 MAGIA: Sensitivity Repetition period of experimental cycle: 1.9 s Number of points per ellipse: 720 (23 min) Number of launched atoms: ~10 9 per cloud Number of detected atoms: ~4x10 5 per cloud Sensitivity to ellipse angle: ~ 9 mrad/shot Sensitivity to differential gravity: 3x10-9 g / Hz Sensitivity in G measurements: 5.7x10-2 / Hz Integration time to G at 10-4 : 100 hours

43 MAGIA: Systematics Precise characterization of source masses (weight, density homogeneity, shape, position) Precise characterization of atomic trajectories Calibration of relative detection efficiency in the two interferometer outputs Removal of k-independent biases (Zeeman shift) Removal of k-dependent biases (Coriolis acceleration)

44 Sensitivity to experimental parameters We acquire a value of G every 2t ell 1 hour fluctuations of ellipse angle, bias and contrast will limit the sensitivity only if they occur over time scales shorter than t ell reproducibility and accuracy on G are only limited by fluctuations of differential ellipse angle We constantly monitor the most relevant experimental parameters cooling, probe, repumper, Raman laser intensity current in magnetic coils (MOT, compensation, bias) temperatures external magnetic fields We experimentally determine the sensitivity of ellipse contrast, bias and angle ellipse angle is measured for the two configuration of source masses calculate average and differential ellipse angle

45 Atomic trajectories Given the curvature of gravitational potential, density distribution of atomic clouds must be centered on the symmetry axis of the source masses, and known within 1 mm in order to keep systematic error on G below 10-4 Vertical coordinates of clouds are measured within 0.1 mm from TOF + double diffraction Transverse density distribution measured by 2D scanning of a thin portion of Raman laser beams (barycenter and width measured within 0.1 mm) T = 0 ms T = 62.5 ms T = 125 ms

46 Use of k-reversal to improve systematics Interferometer phase is affected by systematic shifts, which can be sorted into k eff -dependent: Coriolis (dominating), wave-front distortions, two-photon light shift (negligible in our case) k eff -independent: magnetic gradients, one-photon light shift Alternating measurements with k eff directed upward and downwards allows to cancel out systematic errors from k eff -independent terms; e.g. tiny changes in magnetic fields when moving the source masses Need good overlap of trajectories for direct-k eff and reverse-k eff interferometers A. Louchet-Chauvet et al., The influence of transverse motion within an atomic gravimeter, New J. Phys. 13, (2011)

47 Measurement protocol Ellipse phase is the sum of gravitationally induced phase, the k eff -independent spurious shift and the k eff -dependent spurious phase shift: For each configuration of source masses, we acquire two (interleaved) ellipses with direct and reversed k eff We combine the four ellipse angles the differential phase shift contains the gravitational effect of source masses plus twice the Close-Far change of k eff -dependent terms the other linear combination provides a measurement of twice the Close-Far change of independent phase shift

48 Ellipse fitting Optimal number of points to fit an ellipse is estimated by varying the number of points and computing the Allan deviation Since the fit is heavily nonlinear the Allan variance per point drops sharply at first, then it reaches a plateau, and finally rises due to long-term drifts of center and contrast Ellipse angle is more stable than bias and contrast: optimal sensitivity is obtained by choosing the number of points per ellipse within the plateau 0.11 "(n) (rad) !(n) (rad) number of points per ellipse

49 Data analysis Calculation of gravitational potential produced by source masses Calculation of phase shift for a single atom along the symmetry axis Calculation for tilted and off-axis trajectories Monte Carlo simulation of atomic cloud

50 Phase shift for a single atom Integration of the classical action along the solution of Lagrange equation (classical path) Perturbative method: split the Lagrangian into L 0 =mgz and L 1 including all other contributions (Earth gradient and source masses) phase shift due to L 1 is calculated from integration over the unperturbed path, which is given by the solution of Lagrange eq. for L 0 corrections are order L 12 ; the approximation is valid whatever the form of L 1, only requiring L 1 << L 0 We compared this method with Bordé s prescription [1] in the case of the uniform gravity gradient, for which the solution for L 1 +L 0 is known integration of action over classical path agrees with Bordé s method up to II order perturbative method provides correct results up to I order [1] C. Antoine and C. J. Bordé, Exact phase shifts for atom interferometry, Phys. Lett. A 306, 277 (2003)

51 G measurement (July 2013) Relative uncertainty ~ 116 ppm (statistical)

52 (99) x m 3 kg 1 s 2 Relative uncertainty: 150 ppm G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli & G. M. Tino, Precision Measurement of the Newtonian Gravitational Constant Using Cold Atoms NATURE vol. 510, p. 518 (2014)

53 Determination of G NIST-82 torsion balance TR&D-96 torsion balance LANL-97 torsion balance CODATA 1998 UWash-00 BIPM-01 UWup-02 torsion balance torsion balance simple pendulum CODATA 2002 MSL-03 HUST-05 UZur-06 torsion balance torsion balance beam balance CODATA 2006 HUST-09 JILA-10 torsion balance simple pendulum CODATA 2010 BIPM-13 torsion balance THIS WORK atom interferometry G (10-11 m 3 kg -1 s -2 ) G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli & G. M. Tino, Precision Measurement of the Newtonian Gravitational Constant Using Cold Atoms NATURE vol. 510, p. 518 (2014)

54 MAGIA error budget E ect Uncertainty Correction Relative uncertainty to G (ppm) G/G (ppm) Air density 10 % 60 6 Apogee time 30 µs 6 Atomic clouds horizontal size 0.5 mm 24 Atomic clouds vertical size 0.1 mm 56 Atomic clouds horizontal position 1 mm 37 Atomic clouds vertical position 0.1 mm 5 Atoms launch direction change C/F 8 µrad 36 Cylinders density inhomogeneity Cylinders radial position 10 µm 38 Ellipse fitting Size of detection region 1 mm 13 Support platforms mass 10 g 5 Translation stages position 0.5 mm 6 Other e ects <2 1 Systematic uncertainty 92 Statistical uncertainty 116 Total M. Prevedelli, L. Cacciapuoti, G. Rosi, F. Sorrentino and G. M. Tino, Measuring the Newtonian constant of gravitation G with an atomic interferometer, in Newtonian constant of gravitation Theme Issue of Philosophical Transactions A, 372, (2014)

55 From M. Kasevich

56 Project of Measuring G with AI in HUST HUST: Huazhong University of Science & Technology Source masses 24 10Kg spheres Gravitational signal!g = 120µGal Differential gravity sensitivity! "g = 4 s Project target 1

57 Future prospects to improve the measurement of G with atom interferometry Highly homogeneous (lower-density, e.g. silicon) source mass Higher sensitivity atom interferometer Different scheme with better definition of atomic velocities Smaller size of the atomic sensor Atom with lower sensitivity to magnetic fields

58 Possible scheme for MAGIA Advanced Ultracold Sr atoms in optical lattice ν = m g λ /2 h ΔG/G 10-5 ΔG/G 10-6?