Applications of Atom Interferometry to Fundamental Physics on Earth and in Space

Applications of Atom Interferometry to Fundamental Physics on Earth and in Space

• Atomic clocks• Atomic clocks

Christian J. BordéChristian J. Bordé

• Gyros, accelerometers, gravimeters• Gyros, accelerometers, gravimeters

• General Relativity• General Relativity

- Measurement of the fine structure constant

- Test of the equivalence principle

- Lense-Thirring effect

ERICE 2001

MATTER-WAVE BEAM SPLITTER THROUGH A SCATTERING PROCESS

A(MA, EA, pA)+ B(MB, EB, pB) C(MC, EC, pC)+ D(MD, ED, pD)

g A(x) [ B(x)

C(x)]

D(x)

Veff(x)

S-MATRIX ( ED +EC -EB -EA ) ( pD +pC -pB -pA )

+ CLOSED PATHS IN SPACE OR IN SPACE-TIME

A

A

A

A

C D

B

AA

D

C

C

C

B

B

B

ERICE 2001

MOMENTUM

E(p)

p

atomslope=v

photonslope=c

rest mass

ENERGY

Mc2

h

h / h dB/

h dB

KERICE 2001

E(p)

p//

h

h /

Recoil energy 22 2/ Mh

ERICE 2001

E(p)

p

ERICE 2001

FIRST-ORDER EXCITED STATE AMPLITUDE

/)'()()(

)1( '1

),(

ttpEkpEi

t

abe

dti

trb

...)(2

)(

)()()(

)(

222

22,,

pE

ck

pE

cpkpEkpE

cpEpE baba

/)'()()()(

2/3

3)1( 001

0)',(

2'

1),( ttpEkpEirrki

ba

t

pabeetkV

kddt

itrb

)0(/)(

2/3

3

2

pae

pd

tpErpi a

)(2/3

31)',(

2rrki

ba etkVkd

),()0(

0trap

),()1(

0trbp

REINTERPRETATION OF RAMSEY FRINGES

),(v

),('

2),(

)0(v/)(vv4/v)(

)0()'(vv)(vv

)(4)()1(

0

1222

0

11

1

22

0

traeeew

i

traedte

eedkw

eitrb

pxxkikwtkzi

bax

pttkkitttkki

xxikkw

xtkzi

bap

xzbaxzba

xxzbaxxzba

x

x

xxzba kk vv2

xzba xxkie v/)(v 1

..),(),( v/)(v)*1()1( 12

00ccetrbtrb xzba xxki

pp

))(t-trrtratra pp 00)*0()0( v(),(),(:limitClassical

00

RAMSEY FRINGES WITH TWO SPATIALLY SEPARATED FIELD ZONES

ba b

a a b

ERICE 2001

FOUNTAIN CLOCK

2

xz

2

1

v/)v(

gT

kk ba

a

a

b

b k

ERICE 2001

Atom InterferometerLaser beams

Atom

beam

ERICE 2001

Laser Cooling of Atoms

reduction of systematic errorshigher interaction times: Tdrift µs ... ms towards 1-10

snew atom sources such as atom lasers (Bose-Einstein condensates)

“working horse“ of laser cooling: Magneto-optical trap (MOT)

MOT

density n 1011 cm-3

temperature T 100 K size x 1mm

BEC

1014 cm-3

10 nK10-100 m

Optical clocks with cold atoms

use the “working horse” of laser cooling: Magneto-optical trap (MOT)

In the future new atom sources such as atom lasers

ERICE 2001

Time-domain Ramsey-Bordé interferences with cold Ca atoms

Time-domain Ramsey-Bordé interferences with cold Ca atoms

ERICE 2001

Femtosecond lasers as frequency comb generators

Time domain:

Frequency domain:

ceo measurement e.g.: ceo = 2(m) - (2m)

ERICE 2001

Experimental Setup

J. Stenger, T. Binnewies, G. Wilpers, F. Riehle, H.R. Telle, J.K. Ranka, R.S. Windeler, A.J. Stentz, private communication

J. Stenger, T. Binnewies, G. Wilpers, F. Riehle, H.R. Telle, J.K. Ranka, R.S. Windeler, A.J. Stentz, private communication

fCa-Servo & Counting

frep-Servo

PLL Counter

FVC

CEO-Counting

Ti:Sa

LBO

100 MHz ( H - maser /

Cs-clock controlled)

455 986 240 MHz from Ca-Standard(via fiber)

MS Fiber

FrequencyComb

Generator

PLL

Counter

PM

PD

PD

OC

PZTs

SESAM

-

PZT

Method: Count Ca beatCount ceo

phase-lock frep

ERICE 2001

Interféromètres atomiques

Jets

atomiquesFaisceaux

laser

E(p)

p

E(p)

p

RECOIL DOUBLING

22 / Mch : splittingrecoil ERICE 2001

21HYPER

Measurements of with Atom Interferometers

frequency shift due to the photon recoil in a Ramsey-Bordé interferometer

atmk

2

2

1

determined by HYPERHYPERmeasured in ground-based experiments, e.g. ion traps

atp

at

e

p

m

h

m

m

m

m

c

R

22

accuracy 210-10 210-10 510-9

~h/m

HYPER-precision cold atom interferometry

in space

BNM-LPTF ( A. Clairon, P. Wolf, Paris)ENS-LKB (C. Salomon, Paris)IAMP (K. Danzmann, Hanover)IQO (W. Ertmer & E.M. Rasel, C.Jentsch, Hanover)IOTA (P. Bouyer, Paris)LHA (N. Dimarcq, A. Landragin , Paris)LGCR (P. Tourrenc, Paris)LPL (C. Bordé, Paris & Hanover)PTB (J. Helmcke, Braunschweig)RAL (M.K. Sandford, R. Bingham, M. Caldwell, B.Kent,

Chilton, Didcot)Queen Mary and Westfield College (I. Percival, London)University Trento (S. Vitale, Trento)University Ulm (W. Schleich, Ulm)University Konstanz (C.Lämmerzahl, Konstanz)

The HYPERHYPER Core Team:

GRAVITOELECTRIC AND GRAVITOMAGNETIC INTERACTIONS:THE USUAL PICTURE

Two entries: 1 - Field equations- R.L. Forward, General Relativity for the Experimentalist (1961)- Braginsky, Caves & Thorne, Laboratory experiments to test relativistic gravity (1977)

t

b

cgGg

t

g

cc

uGbb

t

hchcghcb

chVchAmce

1 2,4 .,

416 ,0 .

2,

2/,,

0022

200

2

2 - Motion equation and Schroedinger equation

0022

2

1

2

1hmceVhmcAep

mH

- DeWitt, Superconductors and gravitational drag (1966)

- G. Papini, Particle wave functions in weak gravitational fields (1967)

bgdt

d

c

vv

Atom Interferometers as Gravito-Inertial

Sensors: Analogy between gravitation and electromagnetism

1 0000 hg g

T T ’ T

Laser beams

Atoms

Metric tensor

Newtonian potential

Gravitoelectric field

gUhc

2/002

e.m.22

00 ~/.2/2 VcxgcUh

ERICE 2001

Atom Interferometers as Gravito-Inertial Sensors: I - Gravitoelectric field case

Laser beams

Atoms

g

2/1

002hMcdt

Gravitational phase shift:

k

T T ’ T

with light: Einstein red shiftwith neutrons: COW experiment (1975)with atoms: Kasevich and Chu (1991)

Phaseshift

Circulation of potential

Ratio of gravitoelectric flux to quantum of flux

Mass independent (time)2

)'(. TTTgk

2/./ 00

2

hxdtdM

c

ERICE 2001

32

Atom Interferometric Gravimeter

• Performances:– Resolution: 3x10-9 g after 1 minute

– Absolute accuracy: g/g<3x10-9

• From A. Peters, K.Y. Chung and S. Chu ERICE 2001

35ERICE 2001

Gradiometer with cold atomic clouds

Yale university

Sensitivity: 3.10-8 s-2/Hz

30 E/Hz

Potential on earth:

1E/Hz

Atoms

Atoms

MirrorR

aman lasers

~1m

Laser beams

Atoms

Atom Interferometers as Gravito-Inertial Sensors: Analogy between gravitation and electromagnetism

Metric tensor

Gravitomagnetic field

Pure inertial rotation

e.m.0 ~ Ahh i

cxh /

chc 22

ERICE 2001

Laser beams

Atoms

dtphc

.

1

with light: Sagnac (1913)with neutrons: Werner et al.(1979)with atoms: Riehle et al. (1991)

Atom Interferometers as Gravito-Inertial Sensors: II - Gravitomagnetic field case

Phaseshift

Circulation of potential

Ratio of gravitomagnetic flux to quantum of flux

Mc

AchcSd

Mc /

.2curl.

/

1 2

Sagnac phase shift:

ERICE 2001

44

Atomic Beam Gyroscope

Sensitivity:

6.10-10 rad.s-1/Hz

(Yale University)

Magnetic shield

Cs oven

Wave packetmanipulation

Atomic beams

Statepreparation

Lasercooling

Detection

Rotation rate (x10-5) rad/s-10 -5 0 5 10 15 20

Nor

mal

ized

sig

nal

-1

0

1

Interference fringes

ERICE 2001

45

COLD CESIUM ATOM SENSOR

GYROSCOPEInterferometer’s area : ~ 10 mm²expected sensitivity: 10-8 rad.s-1 /Hzfirst signal expected for spring 2001

ACCELEROMETERexpected sensitivity: 10-8 m.s-2 /Hz

One RAMAN beam

3 temporal pulses

~ 3 0

cm

MOT

Detection

Collaboration between severallaboratories in Paris:

LHA/LPTF, LPL, IOTA, LKB

ERICE 2001

HYPERHYPER-precision cold atom interferometry

in space

47HYPER

Atomic Sagnac UnitInterferometer length 60 cm

Atom velocity 20 cm/s

Drift time 3 s

109 atoms/shot

Sensitivity 2x10-12 rad/s

125th Anniversary of the Metre Convention

Area 54 cm2

LENSE-THIRRING FIELD

5

2

21

).(3

4

11

2

1

r

rrr

c

GILT

hc

xx

txtxxd

c

Gtxh

2

1

'

),'(v),'('

4),( 3

3

at rotation earth

Gravitomagneticfield lines

Gravitomagnetic field generated by a massive rotating body:

Field lines ~ to magnetic dipole:

49HYPER

HYPER Lense-Thirring measurement

Signal vs time

Hyper carries two atomic Sagnac interferometers, each of them is sensitive to rotations around one particular axis. The two units will measure the vector components of the gravitomagnetic rotation along the two axes perpendicular to the telescope pointing to a guide star.

TOrbit

0 . 5 1 1 . 5 2

- 2

-

1

1

2

3

10 rad/s-14

-

125th Anniversary of the Metre Convention

50HYPER

The HYPERHYPER Satellite

ASU1

ASU2Star Tracker Pointing

Cold Atom Source

ASU Reference (connected to the Raman Lasers

& to the Star Tracker)

ONERA 2001

AtomicSagnacUnit 1

Atomic SagnacUnit 2

Star Tracker

Raman Lasers Module

Laser Cooling Module

Conclusion

• Expected Overall Performance:

3x10-16rad/s over one

year of integration i.e. a

S/N~100 at twice the orbital

frequency

Resolution: 3x10-12rad/s /Hz

Lense-Thirring Measurement

52HYPER

measurement of the fine-structure constant improved by one or even two orders of magnitude to test QED

latitudinal mapping of the general relativistic gravito-magnetic effect of the Earth(Lense-Thirring-effect)

The HYPERHYPER Mission Goals (1)

~h/m

53HYPER

investigation of decoherence of matter-waves

for the first time cold-atom gyroscopes control a spacecraft

The HYPERHYPER Mission Goals (2)

HYPERHYPER Summary HYPERHYPER will investigate• precision measurement of (h/mat)

• gravito-inertial effects (Lense-Thirring-Effect)

• decoherence (effects of quantum gravity)

• navigation by atom interferometric sensors

ABCD PROPAGATOR

200

0000002

02

0

1'

2200

0020

0

0

0

v2

exp

vvexpv2v2

exp1

)(2

exp)v(exp

'exp'

2exp

1

BAzzX

YiM

BAzzDCziM

BCzDBACziM

X

iMdt

iMBAz

iM

zzpizz

X

YiM

X

t

t

222/1

'')(2)(2

exp'2

AzzzzDB

iMdz

Bi

M

)(),(),(/)()(exp/exp tYtXtzzFtzztipiS clclcl

1'

22 )2/2/(exp)(exp dtgiM

ziM t

t

0000

0000

,vv

,v

DYCXYDCz

BYAXXBAzz

cl

cl

GRAVITOELECTRIC AND GRAVITOMAGNETIC INTERACTIONS:THE USUAL PICTURE

Two entries: 1 - Field equations- R.L. Forward, General Relativity for the Experimentalist (1961)- Braginsky, Caves & Thorne, Laboratory experiments to test relativistic gravity (1977)

t

b

cgGg

t

g

cc

uGbb

t

hchcghcb

chVchAmce

1 2,4 .,

416 ,0 .

2,

2/,,

0022

200

2

2 - Motion equation and Schroedinger equation

0022

2

1

2

1hmceVhmcAep

mH

- DeWitt, Superconductors and gravitational drag (1966)

- G. Papini, Particle wave functions in weak gravitational fields (1967)

bgdt

d

c

vv

The Dirac equation is written as:

i¹h@t = ¡ i¹hc°0° j @j  + mc2°0 + VÂ

with the interaction Hamiltonian

V = ec®¹ A ¹

for electromagnetic interactions

and

V =c4®¹ h¹ ºpº + h:c: =

c4

f ®¹ h¹ º ;pºg+

with p0 = ¡ ®j pj + °0mc and pj = i¹h@j

for gravitational interactions,

hence the correspondence:

eA ¹ Ã !14h¹ ºpº + h:c:

A new analogy between electromagnetic and gravitational interactions

Ecphhc

EAeEcphh

c

EeA /.

2,/.

2000

RELATIVISTIC PHASE SHIFTS

±' = ¡1¹h

Z t

t0dt0

(c2

2E (~p)p¹ h¹ º(~x0 + ~vt0; t0)pº

+°

m(° + 1)

"c2p¹ ~r h¹ º (~x0 + ~vt0; t0)pº

2E 2(~p)£ ~p

#

¢~s

¡c2

"~r £

Ã~h(~x0 + ~vt0; t0)¡

)h (~x0 + ~vt0; t0) ¢

~pcE (~p)

! #

¢~s

)

where ~s is the mean spin vector

~s =X

r;r0¯¤

r;i¯ r0;i¹hw(r)y~aw(r0)=2°