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

5in collaboration with

Holger MuellerPhysics Department, University California-Berkeley

Just published as arXiv 1001- 4061

Beginning an Experimentto Explore the Detection of

Dark Energy on Earth Using Atom Interferometry

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The majority of astronomers and physicistsaccept the reality of dark energy but alsobelieve it can only be studied indirectlythrough observation of the structure and motions of galaxies

This talk describes the beginning of an experimental investigation of whetherit is possible to directly detect darkenergy on earth using atom interferometrythrough the presence of dark energy density.

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Outline of Presentation1. Atom interferometry

2. Conventional beliefs about the nature ofdark 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 wecan null out g.

6. Our assumptions about the properties ofdark energy that make the experimentfeasible.

7. Brief description of experimental method.

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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 methodsto cool and trap atoms with laser light.

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Optical Interferometer Analogy

wavelength of light = 500 nmnair =air index =1.0003

(initial)

(initial)

final)

(final)

1(final) 1(inital) = 2Lnai r/

L

2(final) –2(inital) = 2L /

12= 2L(nair-1) /

airvacuum

For L=0.1 m = 377 rad

Perhaps read to 10-3 rad

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Basic Equation 1 for Atom interferometry

atom =ei(2x/ –t + )

= wavelength= h/momentum = h/mv

phase

Cesium mass m=2.21x10-25 kgUse Cesium velocity=v=1 m/s

= 3.0 10-9 m = 3.0 nm

Compare to visible light wavelengthof 400 to 800 nm

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Basic Equation 2 for Atom interferometry

Change of phase of atomicwave function called

x2

= (2/hv) ƒ U(x) dx x1

When atom moves from x1 to x2

through potential U(x)

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Basic Equation 3 for Atom interferometry

atom = ei(2x1/ –t + )

2atom = ei(2x2/ –t + 2

)

When x1 =x2

|2|2 = 2(1+cos(-

hen for x1x2 one obtainsa 1+cos interference pattern

9A

Atoms perseconddetected

Transverse position of atom detector

n

n/2

0

gratings

Atom Interferometer

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(initial)

(initial)

final)

(final)

L

E=electric fieldno field

Li atom energy changes by U = -2E2

polarizability = 24. x 10-30 m3

1 =2UL/hv 2 =0

Hence =2UL/hv

For L=0.1 m

= 13 rad

Atom Interferometer (electric force)

Lithium atomsvelocity=1000m/s

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An early demonstration: D. W.Keith et al.,Phys. Rev. Lett. 66, 2693 (1991)

From Pritchard MIT Group

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2. Present beliefs about the nature of dark energy

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Magnitude of dark energydensity:

Counting mass as energy viaE=Mc2 ,the average density ofall energy is the critical energy

crit = 9 x10-10 J/m3

mass 0.3 x crit= 2.7 x10-10 J/m3

dark energy 0.7 x crit= 6.3 x10-10 J/m3

Use DE to denote dark energy

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DE 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

DE is taken to be at leastapproximately uniformly distributed in space

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3. Comparison of darkenergy density withenergy density of aweak electric field.

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DE 6.3 10-10 Joules/m3

Compare to electric field of E=1 volt/m

using E = electric field energy density.

Then

E = 0E2/2=4.4 x 10-12 J/m3

This is easily detected and measured. Thuswe work with fields whose energy densities are much less than DE

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Of course, it is easy to sense tinyelectromagnetic fields using electronicdevices such as field effect transistorsor superconducting quantuminterference devices (SQUIDs).

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Obvious reasons for difficulty or perhaps impossibility of workingwith 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.

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

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•Phase change of atoms depends upon the forces onthe 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 earthis g = 9.8 m/s2

•Atom interferometry studies have reached asensitivity of much better than 10 -9 g inmeasurements of g and found no anomaly.

•It is probably safe to say that there is no evidencefor gDE at the level of 10 -9 g.

•Therefore gDE < 10 -9 m/s2 using our assumptions about the properties of dark energy enumerated later.

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5. Preliminary considerations on how well we can null out g.

Based on preliminary considerations we believewe can null out g to a precision perhaps as smallas 10-17. This sets the smallest gDE that wecan investigate at 10-16 m/s2.

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6. Our assumptions about the properties ofdark energy that make the experiment feasible.

A dark energy force, FDE exists, other than the gravitational force equivalent of DE,

FDE is sufficiently local and thus DE 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 gDE to be detected in this experiment by nulling signals from g.

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7. Brief description of experimental method.

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• 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.

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D

C

A

B

O

T

L

H

vertIcal

g

Uup

Udown

CB = 2L Uup / hv

DA = 2L Udown / hv

Since Uup – Udown = Hg

T = CB-DA = 2LH g/ hv

Interferometer in vertical plane

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Atomic fountain vertical planatom interferometer developedmostly by Chu-Kasavich StanfordGroup. Also Nu Yu Group at JPL.

K-Y. Chung et al., Phys. Rev. , D80, 016002 (2009), my colleague is one of the authors.

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D

C

A

B

O

T

L

H

U0

U0

CB = 2L U0 / hv

DA = 2L U0 / hv

Since Uup – Udown = 0

T = 0

Interferometer in horizontal plane

My recent idea is to use horizontal interferometer, but…

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Double interferometer to be used

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Detecting dark energy density

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Present direct support from a Stanford University fund and indirect supportfrom 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