Lecture 3 Atom Interferometry: from navigation to cosmology Les Houches, 26 Sept. 2014 E.A. Hinds Centre for Cold Matter Imperial College London.

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:

Sensitivity to accelerationcos2(F)

0 p

Dg

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!

Turning to cosmology ……

scienceblogs.com

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)

Copeland review article arXiv:hep-th/0603057v3

“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.

Measure f in a high vacuum chamber

f

vacuumchamber

atom acceleration a

f

a

f0

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.