Lecture 3
Atom Interferometry:
from navigation
to cosmology
E.A. Hinds
Centre for Cold Matter
Imperial College London
Les Houches, 26 Sept. 2014
Why do atoms make good sensors?
Identical
calibrated
Constant
no drift
The moving parts don’t wear out
Quantum interference gives high sensitivity
Two-slit interferometer using atoms
Mlynek Phys. Rev. Lett. 1991
atomic beam
low count rate because
most atoms miss slits
counts/5min
Phase difference f
of quantum waves
makes cos2f fringes
scanning
detector
detector position
A better scheme uses laser light
split
p/2
swap
recombine
p/2
p
2
1
1
Internal atomic states
Raman
Transition
1
2
1
2 sin2F
cos2F 1
sensitive
to gravity
or other forces
just like a
Mach-Zehnder
2
Calculating the interferometer phase
Phase factors
C
2
A
1
1
D
2
along ADB
1) Propagation.
B
1
is the classical action
1
2) Transitions
these just come from the
phase of the light field
if uniform acceleration
Storey and Cohen-Tannoudji J. Phys II France 4, 1999 (1994)
Now
B0
Therefore
C0
D0
A
C
D
B
For a Raman transition
So with counter-propagating beams
The beautiful conclusion:
Sensitivity to acceleration
cos2(F)
Dg
0
p
Kasevich & Chu Appl. Phys. B 1992
Early days
20 measurements/sec.
Comparable with today’s very
best mechanical gravimeters
Scale factor and bias (offset) stability
Best Numbers for AI
Schmidt (2009)
Bias: < 10-10 g
Scale factor: 10-10
ATOM
INTERFEROMETER
There is a trade-off between sampling rate and sensitivity
4×10-9 g/√Hz at 10 Hz
Main limiting factor is optical phase stability
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 ?
state of the art
10-11g bias
10-10g bias
Now add the error
from a bias
straightforward
A submarine might travel for a month without GPS
and still know its position to 300m!
Turning to cosmology ……
scienceblogs.com
Einstein’s field equations give the big picture
Newton’s
constant
stress-energy
tensor for light
and matter
describes the curvature
of space-time
light & matter
decelerate expansion
of universe
After introducing it,
Einstein guessed that L = 0
The famous
cosmological
constant
space-time
metric
tensor
this term
accelerates expansion
of universe
What we know from observation
From NASA
The expansion used to decelerate – due to matter and light (incl. dark matter)
As these became less dense, expansion began to accelerate. Why?
1) L just is nonzero – there’s no reason. (Unsatisfying)
2) We forgot to include something in Tmn that looks like a L
We don’t know what that is, so we say it’s “dark energy”
Composition of the universe
So, we understand 5% of what’s there.
I wonder if we even understand
5% of what there is to understand.
ESA/Planck
Vacuum field as dark energy
A vacuum field does the trick:
This generates a suitable L in Einstein’s equations
L
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
Enter the chameleon field f
Khoury and Weltman PRL 93, 171104 (2004)
Its vacuum value obeys
coupling constants
10-5 eV < L < 10-1 eV
Image: wikispaces.com
10-14 MPlanck < M < 100 MPlanck
In a homogeneous region
and then
matter
density
In the low density of space, f is large – that drives the acceleration.
Copeland review article arXiv:hep-th/0603057v3
“5th force” experiments
virtual
f
A new field f should produce a new force
No force is seen in terrestrial gravity tests
m1
m2
Adelberger et al. Prog. Part. Nucl. Phys. 62, 102 (2009)
But that’s expected! The interaction is suppressed in our dense atmosphere.
So how can we detect f on earth?
The answer is in
Burrage, Copeland and Hinds, arXiv:1408.1409 (2014)
Measure f in a high vacuum chamber
f
f0
a
vacuum
chamber
atom acceleration a
measured forces near a source in vacuum
Baumgärtner et al. PRL 2010
Shih and Parsegian PRA 1974/5
Au/Si atom chip
atomic beam deflection
~100 nm
~200mm
gold cylinder
BEC interferometry to measure g
van der Waals force
Sukenik et al. PRL 1992
Harber et al. PRA 2005
Jenke et al. PRL 2014
bouncing neutron
f measures g
~1mm
atomic beam
gold plates
Casimir-Polder force
~ 6 mm
trapped
BEC
df measures
CP force gradient
~ 20 mm
New limits on chameleon parameters from atom expts.
atom interferometry can easily measure 10-6 g
and
10-9 g is possible
2
a
b
c
10
3
eV
eV
1
Log10
Log10 a g
e
d
0
0
5
R=1 cm
1
2
10
a
640246
14
12
10
8
6
4
2
0
Log10 M Mp
So atom interferometry could reveal new physics all the way to the Planck scale!
Conclusion and Outlook
Force measurements on atoms
with a source mass inside the vacuum
are already sensitive to chameleon fields
In future,
Atom interferometry can improve greatly on this
& will reach up to Planck scale physics
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.