1. 1 Martin L. Perl (martin@slac.stanford.edu) SLAC National Accelerator Laboratory 5 in collaboration with Holger Mueller Physics Department, University California-Berkeley Just published as arXiv 1001- 4061 Beginning an Experiment to Explore the Detection of Dark Energy on Earth Using Atom Interferometry

2. 2 The majority of astronomers and physicists accept the reality of dark energy but also believe it can only be studied indirectly through observation of the structure and motions of galaxies This talk describes the beginning of an experimental investigation of whether it is possible to directly detect dark energy on earth using atom interferometry through the presence of dark energy density.

3. 3 Outline of Presentation 1.Atom interferometry 2. Conventional beliefs about the nature of dark energy. 3. Comparison of dark energy density with energy density of a weak electric field. 4. The terrestrial gravitational force field and a possible dark energy force. 5.Preliminary considerations on how well we can null out g. 6. Our assumptions about the properties of dark energy that make the experiment feasible. 7. Brief description of experimental method.

4. 4 1. Atom Interferometry The Nobel Prize in Physics 1997 The Royal Swedish Academy of Sciences awarded the 1997 Nobel Prize in Physics jointly to Steven Chu, Claude Cohen-Tannoudji and William D. Phillips for their developments of methods to cool and trap atoms with laser light.

5. 5 Optical Interferometer Analogy  wavelength of light = 500 nm n air =air index =1.0003   (initial)   (initial)   final)   (final)    1 (final)   1 (inital) = 2  Ln ai r / L    2 (final)  –   2 (inital) = 2  L /  1   2 = 2  L(n air -1) / air vacuum For L=0.1 m  = 377 rad Perhaps read  to 10 -3 rad

6. 6 Basic Equation 1 for Atom interferometry  atom = e i(2  x/ –  t +  ) = wavelength  = h/momentum = h/mv  phase Cesium mass m=2.21x10 -25 kg Use Cesium velocity=v=1 m/s = 3.0 10 -9 m = 3.0 nm Compare to visible light wavelength of 400 to 800 nm

7. 7 Basic Equation 2 for Atom interferometry Change of phase of atomic wave function called  x 2   = (2  /hv) ƒ U(x) dx x 1 When atom moves from x 1 to x 2 through potential U(x)

8. 8 Basic Equation 3 for Atom interferometry   atom = e i(2  x1/ –  t +   )  2atom = e i(2  x2/ –  t +  2 ) When x1 =x2 |    2 | 2 = 2(1+cos(    -     hen for x1  x 2 one obtains a 1+cos interference pattern

9. 9 A Atoms per second detected Transverse position of atom detector n n/2 0   gratings Atom Interferometer

10. 10   (initial)   (initial)   final)   (final) L E=electric field no field Li atom energy changes by U = -2    E 2 polarizability = 24. x 10 -30 m 3  1 =2  UL/hv  2 =0 Hence  =2  UL/hv For L=0.1 m  = 13 rad Atom Interferometer (electric force) Lithium atoms velocity=1000m/s

11. 11 An early demonstration: D. W.Keith et al., Phys. Rev. Lett. 66, 2693 (1991) From Pritchard MIT Group

12. 12 2. Present beliefs about the nature of dark energy

13. 13 Magnitude of dark energy density: Counting mass as energy via E=Mc 2,the average density of all energy is the critical energy  crit = 9 x10 -10 J/m 3  mass  0.3 x  crit = 2.7 x10 -10 J/m 3  dark energy  0.7 x  crit = 6.3 x10 -10 J/m 3 Use  DE to denote  dark energy

14. 14  DE  6.3 x10 -10 J/m 3 is a very small energy density but as shown in the next section we work with smaller electric field densities in the laboratory  DE is taken to be at least approximately uniformly distributed in space

15. 15 3. Comparison of dark energy density with energy density of a weak electric field.

16. 16  DE  6.3  10 -10 Joules/m 3 Compare to electric field of E=1 volt/m using  E = electric field energy density. Then  E =  0 E 2 / 2=4.4 x 10 -12 J/m 3 This is easily detected and measured. Thus we work with fields whose energy densities are much less than  DE

17. 17 Of course, it is easy to sense tiny electromagnetic fields using electronic devices such as field effect transistors or superconducting quantum interference devices (SQUIDs).

18. 18 Obvious reasons for difficulty or perhaps impossibility of working with dark energy fields: Cannot turn dark energy on and off. Cannot find a zero dark energy field for reference. In some hypothesis about dark energy, it may not exert a force on any material object beyond the gravitational force of its mass equivalent.

19. 19 4. The terrestrial gravitational force field and a possible dark energy force.

20. 20 Phase change of atoms depends upon the forces on the atom. We know nothing about whether or not dark energy exerts such a force, call it g DE, units of force/mass. The gravitational force per unit mass on earth is g = 9.8 m/s 2 Atom interferometry studies have reached a sensitivity of much better than 10 -9 g in measurements of g and found no anomaly. It is probably safe to say that there is no evidence for g DE at the level of 10 -9 g. Therefore g DE < 10 -9 m/s 2 using our assumptions about the properties of dark energy enumerated later.

21. 21 5. Preliminary considerations on how well we can null out g. Based on preliminary considerations we believe we can null out g to a precision perhaps as small as 10 -17. This sets the smallest g DE that we can investigate at 10 -16 m/s 2.

22. 22 6. Our assumptions about the properties of dark energy that make the experiment feasible. A dark energy force, F DE exists, other than the gravitational force equivalent of  DE, F DE is sufficiently local and thus  DE is sufficiently non-uniform so that F DE varies over a length of the order of a meter. F DE acts on atoms leading to a potential energy V DE The ratio g DE /g is large enough for g DE to be detected in this experiment by nulling signals from g.

23. 23 7. Brief description of experimental method.

24. 24 Effects of electric and magnetic forces are nulled by shielding and be using atoms (Cs for example) in quantum states which are not sensitive to the linear Zeeman and Stark effects. The gravitational force is nulled by using two identical atom interferometers.

25. 25 D C A B O T L H vertIcalvertIcal g U up U down  CB = 2  L U up / hv  DA = 2  L U down / hv Since U up – U down = Hg  T =  CB  -  DA = 2  LH g/ hv Interferometer in vertical plane

26. 26 Atomic fountain vertical plan atom interferometer developed mostly by Chu-Kasavich Stanford Group. Also Nu Yu Group at JPL. K-Y. Chung et al., Phys. Rev., D80, 016002 (2009), my colleague is one of the authors.

27. 27 D C A B O T L H U0U0 U0U0  CB = 2  L U 0 / hv  DA = 2  L U 0 / hv Since U up – U down = 0  T = 0 Interferometer in horizontal plane My recent idea is to use horizontal interferometer, but…

28. 28 Double interferometer to be used

29. 29 Detecting dark energy density

30. 30 Present direct support from a Stanford University fund and indirect support from SLAC via laboratory space, utilities, computing facilities and office services. I am about to prepare grant requests to AFOSR: Air Force Office Of Scientific Research ONR: Office of Naval Research DARPA: Defense Advanced Research Projects Agency