Lecture 3 Atom Interferometry: from navigation to cosmology Les Houches, 26 Sept. 2014 E.A. Hinds...
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Transcript of Lecture 3 Atom Interferometry: from navigation to cosmology Les Houches, 26 Sept. 2014 E.A. Hinds...
Lecture 3
Atom Interferometry:from navigation
to cosmology
Les Houches, 26 Sept. 2014
E.A. Hinds Centre for Cold Matter
Imperial College London
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 atomsMlynek Phys. Rev. Lett. 1991
atomic beamscanning detector
detector position
coun
ts/5
min
low count rate because most atoms miss slits
Phase difference f of quantum wavesmakes cos2f fringes
p/2 p p/2
A better scheme uses laser light
1
2
1
1
2 1
2
Internal atomic statessplit swap recombine
12
just like a Mach-Zehnder
cos2Fsin2F
RamanTransition
sensitiveto gravityor other forces
Calculating the interferometer phase
11
2 1
2
1
A
C
D B
Phase factors along ADB
Storey and Cohen-Tannoudji J. Phys II France 4, 1999 (1994)
these just come from the phase of the light field
1) Propagation.
2) Transitions
if uniform acceleration
is the classical action
Now
Therefore
ACD
B
C0
D0
B0
For a Raman transition
So with counter-propagating beams
The beautiful conclusion:
Kasevich & Chu Appl. Phys. B 1992
20 measurements/sec.
Early days
Comparable with today’s verybest mechanical gravimeters
ATOMINTERFEROMETER
Scale factor and bias (offset) stability
Main limiting factor is optical phase stability
Schmidt (2009)
There is a trade-off between sampling rate and sensitivity
4×10-9 g/√Hz at 10 Hz
Best Numbers for AI
Bias: < 10-10 gScale factor: 10-10
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 ?
straightforward
state of the art
10-10g bias
10-11g biasNow add the error
from a bias
A submarine might travel for a month without GPSand still know its position to 300m!
Einstein’s field equations give the big picture
describes the curvatureof space-time
stress-energy tensor for lightand matter
space-timemetric tensor
Newton’sconstant
The famouscosmologicalconstant
this termaccelerates expansion
of universe
light & matterdecelerate expansion
of universe
After introducing it, Einstein guessed that L = 0
From NASA
What we know from observation
1) L just is nonzero – there’s no reason. (Unsatisfying)
2) We forgot to include something in T mn that looks like a L
We don’t know what that is, so we say it’s “dark energy”
The expansion used to decelerate – due to matter and light (incl. dark matter)
As these became less dense, expansion began to accelerate. Why?
Composition of the universe
ESA/Planck
I wonder if we even understand 5% of what there is to understand.
So, we understand 5% of what’s there.
A vacuum field does the trick:
Vacuum field as dark energy
L
This generates a suitable L in Einstein’s equations
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
Its vacuum value obeys
In a homogeneous region
and then matterdensity
In the low density of space, f is large – that drives the acceleration.
10-14 MPlanck < M < 100 MPlanck
coupling constants
10-5 eV < L < 10-1 eV
Enter the chameleon field f
Image: wikispaces.com
Khoury and Weltman PRL 93, 171104 (2004)
“5th force” experiments
So how can we detect f on earth?
Burrage, Copeland and Hinds, arXiv:1408.1409 (2014)
The answer is in
A new field f should produce a new force
m1 m2
virtualf
Adelberger et al. Prog. Part. Nucl. Phys. 62, 102 (2009)
No force is seen in terrestrial gravity tests
But that’s expected! The interaction is suppressed in our dense atmosphere.
measured forces near a source in vacuumShih and Parsegian PRA 1974/5
van der Waals force
atomic beam deflection
gold cylinder
~100 nm ~200mm
Au/Si atom chip
BEC interferometry to measure g
Baumgärtner et al. PRL 2010
Casimir-Polder force
~1mm
Sukenik et al. PRL 1992
atomic beam
gold plates ~ 20 mm
bouncing neutronf measures g
Jenke et al. PRL 2014
~ 6 mm
trapped BEC
df measuresCP force gradient
Harber et al. PRA 2005
New limits on chameleon parameters from atom expts.
So atom interferometry could reveal new physics all the way to the Planck scale!
a
R=1 cm
atom interferometry can easily measure 10-6 g
and10-9 g is possible
Conclusion and Outlook
In future, Atom interferometry can improve greatly on
this & will reach up to Planck scale physics
Force measurements on atomswith a source mass inside the vacuum
are already sensitive to chameleon fields
Measurements on the humble atom or moleculecan 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.