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Martin L. Perl ( martin@slac.stanford) SLAC National Accelerator Laboratory 5

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

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Martin L. Perl ( martin@slac.stanford) SLAC National Accelerator Laboratory 5

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  1. Beginning an Experiment to Explore the Detection of Dark Energy on Earth Using Atom Interferometry 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

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

  5. Optical Interferometer Analogy l=wavelength of light = 500 nm nair =air index =1.0003 L f1(initial) f1final) air vacuum f2(final) f2(initial) Df1 =f1(final) - f1(inital) = 2pLnai r/ l Df2 =f2(final) -– f2(inital) = 2pL / l Df =Df1- Df2= 2pL(nair-1) / l For L=0.1 m Df = 377 rad Perhaps read Df to 10-3 rad

  6. Basic Equation 1 for • Atom interferometry • Yatom =ei(2px/l –wt + f) • = wavelength= h/momentum = h/mv f = 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. Basic Equation 2 for Atom interferometry Change of phase of atomic wave function called Df x2 Df= (2p/hv) ƒU(x) dx x1 When atom moves from x1 to x2 through potential U(x)

  8. Basic Equation 3 for Atom interferometry Y1atom = ei(2px1/l –wt + f1) Y2atom= ei(2px2/l –wt + f2) When x1 =x2 |y1 + y2|2 = 2(1+cos(f1- f2)) Then for x1¹ x2 one obtains a 1+cos interference pattern

  9. Atom Interferometer f1 f2 gratings n Atoms per second detected n/2 0 Transverse position of atom detector A

  10. Atom Interferometer (electric force) Lithium atoms velocity=1000m/s L f1(initial) f1final) E=electric field no field f2(final) f2(initial) Li atom energy changes by U = -2pe0aE2 polarizability = 24. x 10-30 m3 Df2 =0 Df1 =2pUL/hv HenceDf =2pUL/hv For L=0.1 m Df= 13 rad

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

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

  13. Magnitude of dark energy density: Counting mass as energy via E=Mc2 ,the average density of all energy is the critical energy rcrit =9 x10-10 J/m3 rmass» 0.3 x rcrit= 2.7 x10-10 J/m3 rdark energy» 0.7 x rcrit= 6.3 x10-10 J/m3 Use rDE to denote rdark energy

  14. rDE » 6.3 x10-10 J/m3 is a very small energy density but as shown in the next section we work with smaller electric field densities in the laboratory rDE is taken to be at least approximately uniformly distributed in space

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

  16. rDE» 6.3 ´ 10-10 Joules/m3 Compare to electric field of E=1 volt/m using rE=electric field energy density. Then rE = e0E2/2=4.4 x 10-12 J/m3 This is easily detected and measured. Thus we work with fields whose energy densities are much less than rDE

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

  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 gDE , units of force/mass. • The gravitational force per unit mass on earth • is g = 9.8 m/s2 • 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 gDEat the level of 10 -9 g. • Therefore gDE < 10 -9 m/s2 using our assumptions • about the properties of dark energy enumerated later.

  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 gDE that we can investigate at 10-16 m/s2.

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

  23. 7. Brief description of experimental method.

  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. L C Uup T B H g Udown O vertIcal A D DfCB = 2pL Uup / hv DfDA = 2pL Udown / hv Since Uup – Udown = Hg DfT = DfCB- DfDA = 2pLH g/ hv Interferometer in vertical plane

  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. L C T B H O A D Interferometer in horizontal plane U0 U0 DfCB = 2pL U0 / hv DfDA = 2pL U0 / hv Since Uup – Udown = 0 DfT = 0 My recent idea is to use horizontal interferometer, but…

  28. Double interferometer to be used

  29. Detecting dark energy density

  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

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