Compensation of gravity gradients and rotations in precision atom interferometry

Transcription

1 Compensation of gravity gradients and rotations in precision atom interferometry Albert Roura partly based on Phys. Rev. Lett. 118, (2017) Vienna, 11 April 2018

2 Motivation

3 Tests of universality of free fall (UFF) Central to Einstein s equivalence principle. Tests of UFF with macroscopic masses: free fall, lunar laser ranging (LLR) G torsion balance (Ëotvös) AB =2 g A g B g A + g B

4 Measurement of Newton s gravitational constant G By far the less accurately determined of all fundamental constants (using macroscopic masses). NIST-82 TR&D-96 LANL-97 Torsion balance Torsion balance Torsion balance CODATA 1998 UWash-00 Torsion balance BIPM-01 Torsion balance UWup-02 Simple pendulum CODATA 2002 MSL-03 Torsion balance HUST-05 Torsion balance UZur-06 Beam balance CODATA 2006 HUST-09 Torsion balance JILA-10 Simple pendulum CODATA 2010 Rosi et al., Nature 510, 518 (2014) BIPM-13 This work Torsion balance Atom interferometry G (10 11 m 3 kg 1 s 2 )

5 Earth observations: mapping Earth s gravitational field Gravity gradiometry from space (spatial resoultion & 100 km) Observing time evolution of mass distribution with applications to geophysics, hydrology, oceanography... Example: ground water depletion and stressed aquifers NASA GRACE Mission

6 Atom interferometry can make a significant contribution in all these cases BUT Gravity gradients (and rotations) pose a major challenge due to the dependence on the initial position and velocity of the atomic wave packets.

7 Outline 1. Motivation 2. Precise gravitational measurements with atom interferometry: - atom-interferometry-based gravimeters - long-time interferometry (& microgravity platforms) 3. Challenges in UFF tests due to gravity gradients 4. Overcoming loss of contrast and initial co-location problem 5. Compensation of large rotation rates

8 Precise gravitational measurements with atom interferometry (AI)

9 AI-based gravimeters z /2 /2 k 2 k 2 g 2 i g 1 i k 1 k 1 T T t N g1 /(N g1 + N g2 ) k e = k 1 k = k e gt 2 0 p 2 p 3 p

10 The evolution of the wave packets can be decomposed into two independent aspects: expansion dynamics of a centered wave packet central position and momentum which follow classical trajectories including the kicks from the laser pulses

11 AI-based gravimeters z /2 /2 k 2 k 2 g 2 i g 1 i k 1 k 1 T T t N g1 /(N g1 + N g2 ) k e = k 1 k = k e gt 2 0 p 2 p 3 p

12 PRL 112, (2014) P H Y S I C A L R E V I E W L E T T E R S week ending 23 MAY 2014 Quantum Test of the Universality of Free Fall D. Schlippert, 1 J. Hartwig, 1 H. Albers, 1 L. L. Richardson, 1 C. Schubert, 1 A. Roura, 2 W. P. Schleich, 2,3 W. Ertmer, 1 and E. M. Rasel 1* 1 - simultaneous differential measurement - common mirror effect of vibration noise highly suppressed 87 Rb 39 K - Eötvös parameter: Rb,K < improved bounds for dilaton models and SME - Future plans for dedicated space mission: AB

13 Gradiometry and measurements of G Corner Cube 2 Upper Gravimeter + - Balanced Detection - differential measurement - common-mode noise suppression Raman Beams k 2 - determination of the gravity gradient k 1 zz U g 2 g 1 z 2 z 1 Pb movement - changing position of well-characterized source mass measurement of G 1 Trapping Beams Lower Gravimeter + - G/G Rosi et al., Nature 510, 518 (2014) Fixler et al., Science 315, 74 (2007)

14 Long-time interferometry Higher sensitivity long-time interferometry = k e a T 2 Natural compact set-ups in microgravity platforms (freely falling frame) Challenges: growing size of atom cloud BECs, atomic lensing rotations gravity gradients (effects grow cubically with time)

15 Microgravity platforms g 10 5 g 10 6 g drop tower in Bremen (> 500 drops) sounding rocket (23 Jan 2017) International Space Station (2018) QUANTUS (5-10 s) MAIUS (6 min) CAL / BECCAL (several years)

16 Long-time interferometry Higher sensitivity long-time interferometry = k e a T 2 Natural compact set-ups in microgravity platforms (freely falling frame) Challenges: growing size of atom cloud BECs, atomic lensing rotations gravity gradients (effects grow cubically with time)

17 Long-time interferometry Higher sensitivity long-time interferometry = k e a T 2 Natural compact set-ups in microgravity platforms (freely falling frame) Challenges: growing size of atom cloud BECs, atomic lensing rotations gravity gradients (effects grow cubically with time)

18 Long-time interferometry Higher sensitivity long-time interferometry = k e a T 2 Natural compact set-ups in microgravity platforms (freely falling frame) Challenges: growing size of atom cloud BECs, atomic lensing rotations gravity gradients (effects grow cubically with time)

19 Challenges in UFF tests due to gravity gradients

20 Initial co-location Systematics associated with initial central position & momentum of the two species can a mimic violation of UFF: g zz z 0 + zz v 0 T zz s 2 g g z 0. 1nm v pm/s No limitation in principle, but challenging in practice. Minimum time for verification set by Heisenberg s uncertainty principle. nn p z ~/2 (time required may exceed entire mission lifetime)

21 Loss of contrast Gravity gradients (tidal forces) lead to open interferometers: freely falling frame (Einstein elevator) z k e k e k e 2 1 t I k e k e z = zz T 2 v rec T p =( zz T 2 ) mv rec

22 Relative displacement between interfering wave packets at exit port fringe pattern in density profile loss of contrast z 6= 0, p 6= 0 1 N I N I +N II C =1 C =

23 Overcoming loss of contrast and initial co-location problem

24 Phase shift contribution connected with initial co-location directly related to z, p : = 1 ~ p x 0 +2v 0 T 1 ~ x mv Suitable adjustment of laser wavelength of 2nd pulse z = p =0 z k e + k e k e k e t k e k e + k e k e = zz T 2 /2 k e A. Roura, Phys. Rev. Lett. 118, (2017)

25 Initial co-location as well as loss of contrast are simultaneously taken care of. Required single-photon frequency change: for longer times in space T =5s 14 GHz for moderate times (and higher sufficient 2n = 50 T =1s ) AOMs may be 0.6 GHz Dependence on the mirror position, but highly suppressed in the differential measurement.

26 PRL 118, (2017) P H Y S I C A L R E V I E W L E T T E R S week ending 21 APRIL 2017 Circumventing Heisenberg s Uncertainty Principle in Atom Interferometry Tests of the Equivalence Principle Albert Roura Institut für Quantenphysik, Universität Ulm, Albert-Einstein-Allee 11, Ulm, Germany (Received 26 July 2016; published 17 April 2017) Besides tests of UFF, application to gradiometry measurements: (relaxing coupling of static to initial-position/velocity jitter & bias) mapping of Earth s gravitational field from space accurate measurements of G gravitational antennas

27 Experimental demonstration for gradiometry measurements (Florence): G. D Amico et al., Phys. Rev. Lett. 119, (2017) Atomic fountain experiments in Stanford s 10-meter tower: gravity-gradient compensation scheme successfully implemented very effective in overcoming the initial-colocation problem key ingredient in efforts to test UFF with atom interferometry at level Overstreet et al., Phys. Rev. Lett. (2018)

28 Gradiometry & determination of G One can use the technique to cancel the effect of static gravity gradients in measurement of time-dependent ones. Also for measurements of static gravity gradients insensitive to initial position & velocity: G. Rosi, Metrologia 55, 50 (2018) vanishing gradiometry phase for = c 4 zz T 2 /2 k e G. D Amico et al., Phys. Rev. Lett. 119, (2017) (application to determination of ) G

29 Compensation of large rotation rates

30 Compensation of rotations with a tip-tilt mirror as seen from a non-rotating frame:

31 Tip-tilt mirror leads to change in along the longitudinal direction: k e k e! k 0 e = cos( T ) k e k 0 e It can be compensated with following change for the second pulse: k e (1/2)( T ) 2 k e

32 Compensation of rotations with a tip-tilt mirror as seen from a non-rotating frame: k 0 e k e k 0 e

33 Tip-tilt mirror leads to change in along the longitudinal direction: k e k e! k 0 e = cos( T ) k e k 0 e It can be compensated with following change for the second pulse: k e (1/2)( T ) 2 k e

34 Simultaneous compensation of gravity gradients and large rotation rates: z k e + k e k e k e t k e k e + k e k e = zz T 2 /2 k e (1/2)( T ) 2 k e

35 Quantitative example for BECCAL ISS s angular velocity and gravity gradient: ISS 1.13 mrad/s s 2 required frequency change for T =2.6s: 1.5 GHz (partial cancellation)

36 Conclusion

37 Gradiometry and tests of UFF based on AI can provide a useful complement to those based on macroscopic masses. Gravity gradients pose a great challenge in practice as well as an ultimate limitation from HUP due to: initial co-location of the two species loss of contrast I have presented a novel scheme that can simultaneously overcome both difficulties. It can be combined with a tip-tilt mirror to compensate large rotation rates.

38 Thank you for your attention. Q-SENSE European Union H2020 RISE Project

39 QUANTUS Ulm University Wolfgang Schleich Albert Roura Wolfgang Zeller Stephan Kleinert Matthias Meister Christian Ufrecht Jens Jenewein Sabrina Hartmann