5d relativistic optics for matter and antimatter interferometry
DESCRIPTION
5D relativistic optics for matter and antimatter interferometry. Christian J. Bordé LPL & SYRTE. http://christian.j.borde.free.fr. OUTLINE OF THE LECTURE Introduction to atom interferometry with labelled internal states Application to hydrogen - PowerPoint PPT PresentationTRANSCRIPT
5D relativistic opticsfor matter and antimatter
interferometry.
Christian J. BordéLPL & SYRTE
Christian J. BordéLPL & SYRTE
http://christian.j.borde.free.fr
http://christian.j.borde.free.fr/
OUTLINE OF THE LECTURE
1.Introduction to atom interferometry with labelled
internal states
2.Application to hydrogen
3.5D Relativistic atom/antiatom interferometry
4.Theory of gravimeters and clocks and test of the
EEP
[65] T. J. Phillips (1997)
Ch. J. Bordé, Atomic clocks and inertial sensors
π/2 Pulses
Atoms
a
bLaser beams
π/2 Pulses
Atoms
a
bLaser beams
Bordé-Ramsey interferometersLaser beams
Atom
beam
SF6 1981
MOLECULAR INTERFEROMETRY
First atom-wave gyro: Riehle et al. 1991
Aharonov-Casher phase shift
From Laser Spectroscopy X, 1991
Laser Spectroscopy XI1993
BORDÉ-RAMSEY INTERFEROMETERS
Multiple wave interferometerAltitude
g
a
Time
b
a
b
a
bb
b
b
a
a
a
b
b
a
a
a
b
b
a
Multiple wave interferometerAltitude
g
a
Time
b
a
b
a
bb
b
b
a
a
a
b
b
a
a
a
b
b
a
23 January 2010 Royal Society
MOMENTUM
E(p)
p
Mass
ENERGY
1905
2 2 2 2 2/p p E c p m c
2 4 2 2( )E p m c p c
( / , , , )x y zp E c p p p ( / , , , )x y zp E c p p p g p
mc
E
p
ˆ ( / , , , , )x y zp E c p p p m c ˆ 0 , 1 , 2 , 3 , 4
ˆˆ 0p p
E(p)
p//
ab
mac2
mbc2
cs
x
tˆ ( , , , , )x c t x y z c
02222 d xd tcd s
02222ˆ
ˆ d sd xd tcd xd x
ˆˆ2ˆˆ
ˆˆ
0
1, 1, 1, 1, 1
d G dx dx
G
ˆ ( , , , , )x c t x y z c ˆ ( / , , , , )x y zp E c p p p mc 4
ˆˆ
4 4 4 21 +
g G AG
G A G A A
Generalization in the presence of interactions
2 2g p q A p q A m c
ˆˆˆˆ 0G p p
ˆ ( , , , , )x c t x y z c ˆ ( / , , , , )x y zp E c p p p mc
4ˆˆ
4 4 4 21 +
g G AG
G A G A A
Generalization in the presence of interactions
2 2g p q A p q A m c
ˆˆˆˆ 0G p p
ˆˆ2ˆˆ 0d G d x d x
ˆˆ2 2ˆˆˆ 0m c G p p
2 0
5 D e q u a tion s o f m o tion
d
*ˆ ˆˆ
ˆˆ ˆ
ˆ
Lp m x
x
*ˆˆ
ˆˆˆ ˆ ˆ
2
mL G x x
0 * 0 *ˆp m x m c *
4 4 *ˆ ˆ
mp m x
m
* 2*
00ˆ2i i i
m cp g m g
5D OPTICAL PATH
( 4 )ˆ ˆ0ˆ
ˆ0 00 0
j jGE d l
h p d x c d t d xc GG
00
ˆ0ˆ0ˆˆˆˆ
ˆˆˆˆ
)4(
ˆ
ˆ
G
GGGf
dxdxfdl
ji
jiji
jiji
0 04 Gc
E
h
ˆ 0 ˆˆ
ˆˆ
ˆˆ5 D e ikon a l e q u a tion ( , 0 ,1, 2 , 3, 4 ):
0 G
GENERAL FORMULA FOR THE PHASE SHIFT OF AN ATOM/PHOTON INTERFEROMETER
(0)
(5) (5)( , , , ), ; ( , , , ),x y zk k k k q x y z c ctc c
(5) (5)
1
( . ) ( )N
j j jj
k q
+ end terms , , , , / 2D D D Dp p q q
Bordé-Ramsey interferometersLaser beams
Atom
beam
Tcmmm abb /)2(2 2**2
*1
211
22*1 kpcmcm bb 2
1122*
2 kpcmcm bb
21
22* pcmcm aa
Bordé-Ramsey interferometersLaser beams
Atom
beam
Tcmmm abb /)2(2 2**2
*1
211
22*1 kpcmcm bb 2
1122*
2 kpcmcm bb
21
22* pcmcm aa
Tcmmm abb /)2(2 2**2
*1
Atomic Gravimeter
ecap
Seta
nidrooc
z
Time coordinate t
T T'z0 v0
v0' z1 v1
z1' v1'
z2' v2'
z2 v2
arm I
arm II
1 0 0( )( / ) ( )vz A T z g B T * * *
1 0 0/ ( )( / ) ( ) / /p m C T z g D T p m k m
//)()/)(( *001 gmpTBgzTAz
0 jjdxp
0 1 1 2 22 ( ' ) / 2 ( ' ) / 2kz k z z k z z
2 2 2 2 22 2
' '2 ' 0
2 2
z zmc p k p
2'2
2 1 1 0 2 2
0 *
0
( ' ) ( ' ) / 2
sinh ' 2sinh v2
1 cosh ' 2cosh
k z z z z k z z
k kT T T
m
gT T T z
Exact phase shift for the atom gravimeter
which can be written to first-order in with T=T’
2 2 20 0*
7v
12 2
kkgT k T gT T z
m
Reference: Ch. J. B., Theoretical tools for atom optics and interferometry, C.R. Acad. Sci. Paris, 2, Série IV, p. 509-530, 2001
0 1 1 2 22 ( ' ) / 2 ( ' ) / 2kz k z z k z z
2g
I
mkgT
m
Tcmmm abb /)2(2 2**2
*1
Conclusions5D theoretical framework well-adapted to matter/antimatter interferometry
Unified treatment of clocks and gravito-inertial sensors
Single formula for the various contributions to the phase shifts including effects involving the electric charge and dipole moments: scalar and vector AB effect, AC and HMW shiftsleading to a complete test of charge conjugation
This framework has required an explicit introduction of mass and proper time as associated dynamical variables and conjugate quantum mechanical observables Related controversial matters: gravitational red shift of de Broglie-Compton clocks, clocks versus anticlocks …