1. Lecture 3 Atom Interferometry: from navigation to cosmology Les Houches, 26 Sept. 2014 E.A. Hinds Centre for Cold Matter Imperial College London

2. Why do atoms make good sensors? Identicalcalibrated Constantno drift The moving parts don’t wear out Quantum interference gives high sensitivity

3. Two-slit interferometer using atoms Mlynek Phys. Rev. Lett. 1991 atomic beam scanning detector detector position counts/5min low count rate because most atoms miss slits Phase difference  of quantum waves makes cos 2  fringes

4.  /2  A better scheme uses laser light 1 2 1 1 2 1 2 Internal atomic states splitswaprecombine 1 2 just like a Mach-Zehnder cos 2  sin 2  Raman Transition sensitive to gravity or other forces

5. Calculating the interferometer phase 1 1 21 2 1 A C D B Phase factors along ADB Storey and Cohen-Tannoudji J. Phys II France 4, 1999 (1994) these just come from the phase of the light field 1) Propagation. 2) Transitions if uniform acceleration is the classical action

6. Now Therefore A C D B C0C0 D0D0 B0B0 For a Raman transition So with counter-propagating beams The beautiful conclusion:

7. Sensitivity to acceleration cos 2 (  ) 0  gg

8. Kasevich & Chu Appl. Phys. B 1992 20 measurements/sec. Early days Comparable with today’s very best mechanical gravimeters

9. ATOM INTERFEROMETER Scale factor and bias (offset) stability Main limiting factor is optical phase stability Schmidt (2009) There is a trade-off between sampling rate and sensitivity 4×10 -9 g/√Hz at 10 Hz Best Numbers for AI Bias: < 10 -10 g Scale factor: 10 -10

10. How good is that for navigating submarines? Suppose I set out on a 1D journey with no other errors – just the measurement noise. How long I can go before the position uncertainty is 300m ? straightforward state of the art 10 -10 g bias 10 -11 g bias Now add the error from a bias A submarine might travel for a month without GPS and still know its position to 300m! A submarine might travel for a month without GPS and still know its position to 300m!

11. Turning to cosmology …… scienceblogs.com

12. Einstein’s field equations give the big picture describes the curvature of space-time stress-energy tensor for light and matter space-time metric tensor Newton’s constant The famous cosmological constant this term accelerates expansion of universe light & matter decelerate expansion of universe After introducing it, Einstein guessed that  = 0

13. From NASA What we know from observation 1)  just is nonzero – there’s no reason. (Unsatisfying) 2) We forgot to include something in T  that looks like a  We don’t know what that is, so we say it’s “dark energy” The expansion used to decelerate – due to matter and light (incl. dark matter) As these became less dense, expansion began to accelerate. Why?

14. Composition of the universe ESA/Planck I wonder if we even understand 5% of what there is to understand. So, we understand 5% of what’s there.

15. A vacuum field does the trick: Vacuum field as dark energy  This generates a suitable  in Einstein’s equations For electrons, protons, light etc, the vacuum energy is zero (we are going to ignore the fluctuations) So we need a field with a non-zero vacuum value. Nice review by Copeland et al., arXiv:hep-th/0603057v3

16. Its vacuum value obeys In a homogeneous region and then matter density In the low density of space,  is large – that drives the acceleration. 10 -14 M Planck <  < 10 0 M Planck coupling constants 10 -5 eV <  < 10 -1 eV Enter the chameleon field  Image: wikispaces.com Khoury and Weltman PRL 93, 171104 (2004)

17. Copeland review article arXiv:hep-th/0603057v3

18. “5 th force” experiments So how can we detect  on earth? Burrage, Copeland and Hinds, arXiv:1408.1409 (2014) The answer is in A new field  should produce a new force m1m1 m2m2 virtual  Adelberger et al. Prog. Part. Nucl. Phys. 62, 102 (2009) No force is seen in terrestrial gravity tests But that’s expected! The interaction is suppressed in our dense atmosphere.

19. Measure  in a high vacuum chamber  vacuum chamber atom acceleration a  a 

20. measured forces near a source in vacuum Shih and Parsegian PRA 1974/5 van der Waals force atomic beam deflection gold cylinder ~100 nm ~200  m Au/Si atom chip BEC interferometry to measure g Baumgärtner et al. PRL 2010 Casimir-Polder force ~1  m Sukenik et al. PRL 1992 atomic beam gold plates ~ 20  m bouncing neutron f measures g Jenke et al. PRL 2014 ~ 6  m trapped BEC  f measures CP force gradient Harber et al. PRA 2005

21. New limits on chameleon parameters from atom expts. So atom interferometry could reveal new physics all the way to the Planck scale! a R=1 cm atom interferometry can easily measure 10 -6 g and 10 -9 g is possible

22. Conclusion and Outlook In future, Atom interferometry can improve greatly on this & will reach up to Planck scale physics Force measurements on atoms with a source mass inside the vacuum are already sensitive to chameleon fields Measurements on the humble atom or molecule can shed light on something as huge as the cosmos and can begin to probe the domain of quantum gravity. ….oh, and they are exceedingly good for inertial sensing.