Gravity measurements with atom interferometry

Transcription

1 Gravity measurements with atom interferometry F. Sorrentino Dipartimento di Fisica & LENS, Università di Firenze & INFN with support from

2 Outline AI differential gravity measurements in space An example on ground: the MAGIA experiment

3 Atom interferometry sensors (I) Virtual sensitivity improvement of several orders of magnitude over optical interferometers. However, such advantage is currently reduced by small particle flux (10 10 for alkali, for H) small separation of matter-wave paths (few photon recoils). Nevertheless, AI sensors already compete with optical counterparts. Already achieved: inertial sensing (acceleration, gravity gradient, rotations) measurement of fundamental constants (G,!). In progress/proposed: tests of GR (EP, Lense-Thirring, limits on PPN parameters); test of Newton s 1/r 2 law at short length scale; atom neutrality; GW detection. Moreover, large progress are foreseen in the next future (LMT beam splitters, high flux atomic sources, sub-shot noise detection schemes, etc.)

4 Atom interferometry sensors (II) AI inertial sensors feature very good long term stability and control over systematic effects Differential configurations allow for very large CMRR of vibrations Based on quantum atom-light interaction, which can be precisely modeled The possible choice of different internal/external quantum states, as well as of different isotopic species, provides knobs to isolate, model and minimize several possible noise sources

5 AI measurements in space = kgt 2 Terrestrial AIs achieve differential gravity accuracy approaching ~10-11 g with T~0.1 s In space ~10-15 g or better is foreseen with T>>1s Main issues to address for AI experiments in space: TRL (lot of work in progress) Motivation for space (on ground, large T requires long free-fall distance) Understanding noise and error sources (test bench experiments on ground)

6 The MAGIA apparatus

7 Space Atom Interferometers

8 TRL of AI

9 AI WEP test: kinematic requirements (I)

10 AI WEP test: kinematic requirements (II)

11 AI WEP test: kinematic requirements (III)

12 MAGIA Misura Accurata di G mediante Interferometria Atomica

13 MAGIA Misura Accurata di G mediante Interferometria Atomica Measure g by atom interferometry g

14 MAGIA Misura Accurata di G mediante Interferometria Atomica Measure g by atom interferometry Add source masses Measure change of g a M g

15 Motivation Cavendish 1798 Zang 2009 F. Sorrentino, Q2C5 12/10/12 Gravity measurements...

16 Using atomic probes Point-like test masses in free fall virtually insensitive to stray fields well know and reproducible properties different states, isotopes precision measurements by atom interferometry

17 Raman interferometry in a 87 Rb atomic fountain z(t) 2 R2k R2k R2k T T 2 R1k R1k R1k Phase di erence between the paths: = k c [z(0)]2z(t )] + e k e = k 1 k 2 with z(t) = gt 2 /2+v 0 t + z 0 & e =0 = k e gt 2 t Final population: N a = N/2(1 + cos[ ]) T = 150 ms 2 = 10 6 g S/N=1000 Sensitivity 10 9 g/shot A. Peters et al., Nature 400, 849 (1999)

18 Atom gravimeter + source masses Sensitivity 10 9 g/shot one shot G/G Kg tungsten mass Peak mass acceleration a g 10 7 g shots G/G 10 4

19 MAGIA: experimental procedure launch two clouds of Rb atoms apply Raman pulses with masses in position 1 detect atoms selectively repeat several times fit the differential phase shift between the two clouds move masses to position 2 and repeat subtract differential phase for pos. 1 and 2 ( φ ( z ) φ + φ ( z, t )) ( φ ( z ) + φ + φ ( z, t )) φ φ I 1 II 1 φ I 2 φ II 2 = = φ ( z g g g g 1 2 φ ( z SM 1 2 ) ) + φ φ Sys SM SM SM SM + φ + φ Sys Sys Sys Sys I I II II ( φ1 φ2 ) ( φ1 φ2 ) = 4φ + φ ( Δz, Δt) ( z ( z 1 2 1, t, t 2 I I II ) II )

20 Raman 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)

21 MAGIA: first results G = (11) (3) m 3 kg 1 s 2 G. Lamporesi et al., Phys. Rev. Lett 100, (2008)

22 G measurement at Stanford G = (27) (21) x m3 kg-1 s-2 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) F. Sorrentino, Q2C5 12/10/12 Gravity measurements...

23 Interim progress Corresponding to a statistical uncertainty of 400 ppm on G F. Sorrentino et al., New J. Phys. 12, (2010)

24 Sensitivity to experimental parameters

25 Short-term sensitivity Current sensitivity to differential acceleration: 5x10-9 1s

26 Long term sensitivity Active intensity control of cooling and probe laser beams; tilt stabilization of Raman retro-reflecting mirror Coriolis compensation with tip-tilt mirror Allan variance on gravity gradient measurement ~ s, corresponding to 5x10-11 g (5x improvement from 2011)

27 MAGIA current status Sensitivity to differential gravity: 5*10-9 g / Hz Sensitivity in G measurements: 300 ppm in 12 hours

28 MAGIA: recent progresses 2010 differential acceleration sensitivity: 2*10-8 g / Hz sensitivity in G measurement: 400 ppm in 120 hrs 2012 differential acceleration sensitivity: 5*10-9 g / Hz sensitivity in G measurement: 300 ppm in 12 hrs

29 G measurement reproducibility "# = ( ± 0.08) mrad corresponding to 150 ppm on G

30 MAGIA error budget

31 Atomic trajectories (I) Vertical coordinates of clouds know 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

32 Atomic trajectories (II) Transverse velocities are found in the range of a few mm/s These are due to small tilt (~1 mrad) of the atomic fountain Corresponding AI phase shift due to Coriolis acceleration ~40 mrad, i. e g For a Coriolis shift below 10-4 on G, launching direction should change less than 2 µrad on average when moving the sources masses

33 Coriolis compensation (I) Tip-tilt mirror steering the retro-reflected Raman beam to compensate for the Earth rotation Already shown to improve contrast in AI with LMT beam splitters In MAGIA, contrast drop due to Coriolis is minimal, but still detectable thanks to the large SNR S.-Y. Lan et al., PRL 108, (2012)

34 Coriolis compensation (II) Besides ellipse contrast, Coriolis acceleration affects AI noise as well because of dispersion of atomic transverse velocities Earth rotation 10%: rather easy via contrast 1%: requires a decent compass (tip-tilt absolute orientation within 1 ) and careful calibration of PZT 0.1%: quite challenging: need very good absolute orientation and rotation rate 0.01%: crazy

35 Coriolis compensation (III) If we reduce the frame rotation by a factor 10 with a tip-tilt Raman retro-reflecting mirror, we still need to control the C/F launching direction changes to better than 20 µrad Double stage compensation: ellipse phase shift vs. rotation rate is proportional to the transverse atomic velocity difference In MAGIA we measure transverse velocity components with a precision of a few tens of µm/s When comparing for the two configurations of source masses, we determine C/F transverse velocity changes to be lower than 6 µm/s Sensitivity to transverse velocity differences scales with T 2 : in Q-WEP or STE-QUEST it can easily get down to ~10nm/s "# = ( /- 0.2) mrad (comp.)$ $ $ "# = ( /- 0.2) mrad (non comp) difference < 0.28 mrad => "v E-O < 6 µm/s

36 g measurement with two clouds Using a dual-cloud Raman interferometer for g measurements Simultaneous interferometers allow g measurements in the presence of larger phase noise because of twice larger range for phase retrieval

37 g measurement with two clouds Using a dual-cloud Raman interferometer for g measurements Simultaneous interferometers allow g measurements in the presence of larger phase noise because of twice larger range for phase retrieval suppressed conversion of amplitude noise into phase noise at the edges of the fringe F. Sorrentino et al., Appl. Phys. Lett. 101, (2012) Somewhat similar to using a mechanical accelerometer to correct the phase shift from seismic noise, see J. Le Gouët et al., Appl. Phys B 92, 133 (2008)

38 Free falling vs trapped atoms Light-pulse (Raman or Bragg) atom interferometry highest precision and highest accuracy so far demonstrated atomic wave-function evolves in the absence of external fields AI in optical lattices No free fall or free expansion Small intrinsic size of the sensor but... perturbation by laser field

39 Bloch oscillations of 88Sr Bloch frequency B = (3) Hz damping time = 12 s 8000 photon recoils in 7 s gmeas = (5) ms 1 G. Ferrari et al., PRL 97, (2006) F. Sorrentino, Q2C5 12/10/12 Gravity measurements...

40 Resonant tunneling V. V. Ivanov et al., PRL 100, (2008) F. Sorrentino, Q2C5 12/10/12 g/g Gravity measurements...

41 Absolute measurement of g with Sr N. Poli, et al., Phys. Rev. Lett. 106, (2011) M. Tarallo et al., Phys. Rev. A 88, (2012)

42 Conclusions MAGIA: statistical & systematic errors at the 100 ppm level Double-stage reduction of Coriolis induced systematics compensation of Earth rotation with tip-tilt mirror by contrast maximization measurement of transverse velocity difference components from phase shift vs rotation rate plots well suited for Q-WEP and STE-QUEST Measuring g with two atomic clouds w/o seismic attenuation may be useful to measure extra acceleration in Q-WEP and STE- QUEST Gravity sensor with Sr atoms in optical lattice No free fall or free expansion absolute gravity 10-7 g, will be soon improved by a factor 10 with stabilized lattice laser coming soon: differential gravity measurement with 88 Sr and 87 Sr Optical atomic clock and gravity sensor in the same device

43 Our team Guglielmo M. Tino s group web page: Post-doc positions available! F. Sorrentino, Q2C5 12/10/12 Gravity measurements...