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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°