Transcript Detecting dark energy density - SLAC

Beginning an Experiment
to Explore the Detection of
Dark Energy on Earth Using
Atom Interferometry
Martin L. Perl ([email protected])
SLAC National Accelerator Laboratory
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in collaboration with
Holger Mueller
Physics Department, University California-Berkeley
Just published as arXiv 1001- 4061
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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.
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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.
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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 methods
to cool and trap atoms with laser light.
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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
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10-3 rad
Basic Equation 1 for
Atom interferometry
Yatom =ei(2px/l –wt + f)
l= wavelength = h/momentum = h/mv
f = phase
Cesium mass m=2.21x10-25 kg
Use Cesium velocity=v=1 m/s
l= 3.0 10-9 m = 3.0 nm
Compare to visible light wavelength
of 400 to 800 nm
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Basic Equation 2 for
Atom interferometry
Change of phase of atomic
wave function called Df
x2
Df = (2p/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
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 x1 x2 one obtains
a 1+cos interference pattern
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Atom Interferometer
f1
f2
gratings
n
n/2
Atoms per
second
detected
0
Transverse position of atom detector
A
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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
Df1 =2pUL/hv
Df2 =0
Hence Df =2pUL/hv
For L=0.1 m
Df= 13 rad
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From Pritchard MIT Group
An early demonstration: D. W.Keith et al.,
Phys. Rev. Lett. 66, 2693 (1991)
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2. Present beliefs
about the nature of
dark energy
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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
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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
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3. Comparison of dark
energy density with
energy density of a
weak electric field.
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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
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Of course, it is easy to sense tiny
electromagnetic fields using electronic
devices such as field effect transistors
or superconducting quantum
interference devices (SQUIDs).
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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.
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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 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 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 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.
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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,
FDE is 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
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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Interferometer in vertical plane
L
Uup
C
T
B
H
g
Udown O
A
DfCB = 2pL Uup / hv
DfDA = 2pL Udown / hv
D
v
e
r
t
I
c
a
l
Since Uup – Udown = Hg
DfT = DfCB - DfDA = 2pLH g/ hv
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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.
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Interferometer in horizontal plane
L
C
U0
B
T
H
U0
O
A
D
DfCB = 2pL U0 / hv
DfDA = 2pL U0 / hv
Since Uup – Udown = 0
DfT = 0
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 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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