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UNCLASSIFIED
U.S. ARMY
RDECOM AH.L RESEARCH LABORATORY
U.S.ARMY
Optimal pulse schemes for high-precision atom interferometry
Michael Goerz1 , Paul Kunz1, Mark Kasevich2
, Vladimir Malinovsky1
1 U.S. Army Research Lab, 2 Stanford University
23 August 2018 UNCLASSIFIED
UNCLASSIFIED Optimal pulse schemes for atom interferometry
optical interferometer:
beamsplitter
beamsplitter
Michael Goerz ([email protected]) UNCLASSIFIED 1/9
UNCLASSIFIED Optimal pulse schemes for atom interferometry
optical interferometer:
beamsplitter
beamsplitter
Michael Goerz ([email protected]) UNCLASSIFIED 1/9
optical interferometer:
beamsplitter
Michael Goerz ([email protected])
UNCLASSIFIED Optimal pulse schemes for atom interferometry
beamsplitter
atom interferometer:
atoms have mass and internal structure • couple to more external perturbations
(gravity)
UNCLASSIFIED 1/9
optical interferometer:
beamsplitter
mirror? beamsplitter?
Michael Goerz ([email protected])
UNCLASSIFIED Optimal pulse schemes for atom interferometry
beamsplitter
atom interferometer:
atoms have mass and internal structure • couple to more external perturbations
(gravity)
UNCLASSIFIED 1/9
+4nk +2nk I
I 01
I - 2nk I
- 4nk I . .
- 6nk ·
laser cou pies between electronic states: absorbs photon momentum
Michael Goerz ([email protected])
UNCLASSIFIED Optimal pulse schemes for atom interferometry
UNCLASSIFIED 2/9
+4hk +2hk I
I 01
I - 2hk I
- 4hk I ..
- 6hk .
laser cou pies between electronic states: absorbs photon momentum
Michael Goerz ([email protected])
UNCLASSIFIED Optimal pulse schemes for atom interferometry
10 m atomic fountain at Stanford: ultracold 87 Rb atomic cloud
" !g ' ' C .Q +-'
t= 2T "cii 0
Cl.
UNCLASSIFIED
0 T 2T
n/2 (n/2-1}1t (n/2-1)1t 1t (n/2-1}1t (n/2-1)1t 1t/2
Kovachi et al. Nature 528, 530 (2015)
2/9
+4hk +2hk I
I 01
I - 2hk I
- 4hk I ..
- 6hk .
laser cou pies between electronic states: absorbs photon momentum
Michael Goerz ([email protected])
UNCLASSIFIED Optimal pulse schemes for atom interferometry
10 m atomic fountain at Stanford: ultracold 87 Rb atomic cloud
" !g ' ' C .Q +-'
t = 2T "cii 0
Cl.
UNCLASSIFIED
0 T 2T
_ U, l,ll,..__ ,,l ,l ll,l , ,t,lU,'u'---
n/2 (n/2-1}1t (n/2-1)1t 7t (n/2-1}1t (n/2-1)1t n/2
Kovachi et al. Nature 528, 530 (2015)
2/9
UNCLASSIFIED
Michael Goerz ([email protected]) UNCLASSIFIED
Optimal pulse schemes for atom interferometry
Army applications: ultra-precise measurement
of acceleration / gravity
• inertia I navigation:
submarines, autonomous vehicles -not jammable!
• gyroscopes
• gravity gradient sensors
• weapons system control
• geospatial mapping
• drone or sate I I ite based
detection of underground structures
3/9
Michael Goerz ([email protected])
UNCLASSIFIED Optimal pulse schemes for atom interferometry
10 m atomic fountain: sensitivity 10- 13 g/ -/Hz
UNCLASSIFIED
AOSense (2010) 10- 6 g/-/Rz state of the art 10- 9 g/-/Rz
4/9
Michael Goerz ([email protected])
UNCLASSIFIED Optimal pulse schemes for atom interferometry
10 m atomic fountain: sensitivity 10- 13 g/ -/Hz
factors:
• signal to noise ratio
• large momentum transfer
UNCLASSIFIED
AOSense (2010) 10- 6 g/-/Rz state of the art 10- 9 g/-/Rz
4/9
UNCLASSIFIED Optimal pulse schemes for atom interferometry
Apply optimal control to atom optics pulses
=} increase fide I ity
=} robustness against fluctuations
Michael Goerz ([email protected]) UNCLASSIFIED 5/9
UNCLASSIFIED Optimal pulse schemes for atom interferometry
Time T 2T
Michael Goerz ([email protected]) UNCLASSIFIED 6/9
UNCLASSIFIED Optimal pulse schemes for atom interferometry
Time
2T
Michael Goerz ([email protected]) UNCLASSIFIED 6/9
UNCLASSIFIED Optimal pulse schemes for atom interferometry
+61ik ..
+41ik I .
+21ik I I
o I I
-21ik I C
-41ik 0 ;e
I . . (/)
0
-61ik · a. Time
0 T 2T
Michael Goerz ([email protected]) UNCLASSIFIED 6/9
UNCLASSIFIED Optimal pulse schemes for atom interferometry
+61ik ..
+41ik I .
+21ik I I
o I I
-21ik I C
-41ik 0 ;e
I . . (/)
0
-61ik · a. Time
0 T 2T
Michael Goerz ([email protected]) UNCLASSIFIED 6/9
UNCLASSIFIED Optimal pulse schemes for atom interferometry
+61ik ..
+41ik I .
+21ik I I
o I I
-21ik I C 0
- 41ik :;:;
I . . "ui 0 Time
-61ik · a. T 2T
train of pulses • rapid adiabatic passage: tune th rough laser frequency at constant amplitude
Michael Goerz ([email protected]) UNCLASSIFIED 6/9
UNCLASSIFIED Optimal pulse schemes for atom interferometry
+61ik .. a,_ 1 +41ik
I . Vl '-:5 3 +21ik I a.-
0 I -~ o I .c: 8 N - I E 6 ::, 4 -21ik I C ... 0 C: -41ik :;:; Q) 2 I . . "ui E 0 Time 0 -61ik · a. 0 T 2T E -2
0 50 100 150 200 time (1/w,}
train of pulses • rapid adiabatic passage: tune th rough laser frequency at constant amplitude
Michael Goerz ([email protected]) UNCLASSIFIED 6/9
UNCLASSIFIED
~~lr------------------, :5 3 a.-
E .a 4 ~ 2 § 0
E - 2 oo....i....i.....i..."tc50~.,___._~~...&.....l----'-::"~........_.......,__J_.,___.__._j 100 150 200 time (1/w,}
+41ik +21ik I
I o I
I -21ik I
-41ik
L. e L.
QJ 10- 1 L.
~ ~ 10- 2 co L. ... § 10- 3
... co :5 10-4 a.
Optimal pulse schemes for atom interferometry
+61ik .. I .
C 0
:;:;
I . . (/)
0
-61ik · a. Time
0 T 2T
rapid adiabatic passage
0 a. 10-s ~%..._..._..._~~ .................. 7nb,l,.,,_,l,.,,_,I,.,,_'::-:::'~,__,__,__~
90% 950,,0 100 /C % 105% 110% pulse amplitude
Michael Goerz ([email protected]) UNCLASSIFIED 6/9
a,_ 1 Vl '-:5 3 a.-
- 0 ~ .c: 8 N -E 6 ::, 4 ... C:
2 Q)
E 0 0
E -2 150 200
compress
a,_ 5 Vl '-:5 3 a.-
- 0 ~ .c: 8 N - 6 E ::, 4 ... C: 2 Q)
E 0 0
E - 2 0 5 10 15 20 25 30
time (1/w,)
Michael Goerz ([email protected])
UNCLASSIFIED
+4/ik +2/ik I
I o I
I -2/ik I
-4/ik
35
UNCLASSIFIED
I . . -6/ik ·
Optimal pulse schemes for atom interferometry
6/9
a,_ 1 Vl '-:5 3 a.-
- 0 ~ .c: 8 N -E 6 ::, 4 ... C:
2 Q)
E 0 0
E -2 150 200
compress
a,_ 5 Vl '-:5 3 a.-
- 0 ~ .c: 8 N - 6 E ::, 4 ... C: 2 Q)
E 0 0
E - 2 0 5 10 15 20 25 30
time (1/w,)
Michael Goerz ([email protected])
UNCLASSIFIED
+4/ik +2/ik I
I o I
I -2/ik I
-4/ik
35
UNCLASSIFIED
I . . -6/ik ·
Optimal pulse schemes for atom interferometry
6/9
cu_ 1 Ill '-::I 3 c.-~ 0 ~ 8 -E 6 ::, 4 ~ ~ 2 0 0
UNCLASSIFIED
E -2 1;;,,1,......,......_.....,,......,......_......,......,....._......,.....,..,__,......,.....,......,.......,.....,_...,_ 0 so 100 150 200
time (1/w,)
15 20 25 time (1/w,)
Michael Goerz ([email protected]) UNCLASSIFIED
+4/ik +2/ik I
I o I
I -2/ik I
-4/ik I . .
-6/ik ·
Optimal pulse schemes for atom interferometry
7/9
QJ 5 Vl -;:
:5 3 a.-
0 ~;i....a...,,_,_..1...1,..1...1,...1..,1....i...i.....,_i....i..,i....i,.....i,..,,_,_..1...1,..1...1,...1..,1....i...i..,._....
8
10 20 25 30
UNCLASSIFIED
35
+4/ik +2/ik I
I o I
I -2/ik I
-4/ik
optimize for fidelity L. 10° 0 L. L.
QJ 10- 1 L. QJ .._ ~ 10- 2 co L.
0 .-~ ....... ....,_.i...i.,.1...1,,..1...1....,_.i...i.,....,_..i...,.....i..,.....i....1...1,,..i...i.....i........i....i...i.. ......
8 ... C 10-3 0 ... co :5 10-4 a. 0 a.
10-~0% 5 10 15 20 25 30 35 time (1/w,)
Michael Goerz ([email protected]) UNCLASSIFIED
I . . -6/ik ·
95%
Optimal pulse schemes for atom interferometry
100% 105% 110% pulse amplitude
7/9
QJ 5 Vl -;:
:5 3 a.-
0 ~ ;i....a...,,_,_..1...1,..1...1,...1..,1....i...i.....,_i....i..,i....i,.....i,..,,_,_..1...1,..1...1,...1..,1....i...i..,._....
8
10 20 25 30
UNCLASSIFIED
35
+4/ik +2/ik I
I o I
I -2/ik I
-4/ik
optimize for fidelity L. 10° 0 L. L.
QJ 10- 1 L. QJ .._ ~ 10- 2 co L.
0 .-~ ....... ....,_.i...i.,.1...1,,..1...1....,_.i...i.,....,_..i...,.....i..,.....i....1...1,,..i...i.....i........i....i...i.. ......
8 ... C 10-3 0 ... co :5 10-4 a. 0 a.
10-~0% 5 10 15 20 25 30 35 time (1/w,)
Michael Goerz ([email protected]) UNCLASSIFIED
I . . -6/ik ·
95%
Optimal pulse schemes for atom interferometry
100% 105% 110% pulse amplitude
7/9
UNCLASSIFIED Optimal pulse schemes for atom interferometry
V .i'E'l!!.9 +61ik .
cu_ 5 +41ik
I .. Ill '-::I 3 +21ik I c.-
0 I ~ o I C 8 N - I E 6 -21ik I C ::, 4 0 ....
C -41ik :;:; cu 2 I . . "ui E 0 Time 0 -61ik · a. 0
T 2T E -2 0 s 10 15 20 25 30
time (1/w,)
10° 5 L. cu 0 rn "'i:: L.
"53 L.
QJ 10- 1 c.-L.
0 QJ
~ .._ ~ 10- 2 C
N co - L. ... E C 10- 3 :::::, 0 .... ... C co cu :5 10-4 E 0 a. 0 0 E -2 a.
10-~0% 0 5 10 15 20 25 30 35 95% 100% 105% 110% time (1/w,) pulse amplitude
Michael Goerz ([email protected]) UNCLASSIFIED 8/9
QJ 5 Vl -;:
:5 3 a.-
0 ~:;i....i.....i...i...i...i....i. .......... .1...1...i...&....i...i...i...i....i.....i...i...i.."':....i.._..i. _...1.--,,.1....1..:_ ...............
8
E 6 ::, 4 ... C: QJ 2 E 0 0
E -2 0 5 10
5 QJ_ Vl '-:5 3 a.-
- 0 .:i.:: .c:: 8 N - 6 E ::, 4 ... C: 2 QJ
E 0 0
E - 2 0 5 10 15 20 25 30
time (1/w,)
Michael Goerz ([email protected])
35
UNCLASSIFIED
+4/ik +2/ik I
I o I
I -2/ik I
-4/ik
L. 10° 0 L. L.
QJ 10- 1 L. QJ .._ ~ 10- 2 co L. ... c: 10- 3 0 ... co :5 10-4 a. 0 a.
10-~0%
UNCLASSIFIED
I . . -61ik ·
95%
Optimal pulse schemes for atom interferometry
100% 105% 110% pulse amplitude
8/9
QJ 5 Vl -;:
:5 3 a.-
0 ~:;i....i.....i...i...i...i....i. .......... .1...1...i...&....i...i...i...i....i.....i...i...i.."':....i.._..i. _...1.--,,.1....1..:_ ...............
8
E 6 ::, 4 ... C: QJ 2 E 0 0
E -2 0 5 10
5 QJ_ Vl '-:5 3 a.-
- 0 .:i.:: .c:: 8 N - 6 E ::, 4 ... C: 2 QJ
E 0 0
E - 2 0 5 10 15 20 25 30
time (1/w,)
Michael Goerz ([email protected])
35
UNCLASSIFIED
+4/ik +2/ik I
I o I
I -2/ik I
-4/ik
L. 10° 0 L. L.
QJ 10- 1 L. QJ .._ ~ 10- 2 co L. ... c: 10- 3 0 ... co :5 10-4 a. 0 a.
10-~0%
UNCLASSIFIED
I . . -61ik ·
95%
Optimal pulse schemes for atom interferometry
optimized for robustness
100% 105% 110% pulse amplitude
8/9
UNCLASSIFIED Optimal pulse schemes for atom interferometry
Conclusion
relative phase d ifference:
~ cf> = -2kmaxgT 2
~g • optima I control can com press pulses
t= 2T by order of magnitude while guaranteeing robustness
• Army applications:
ultra-precise measurement of acceleration / gravity
• inertia I navigation,
satellite based gravitational sensing
Michael Goerz ([email protected]) UNCLASSIFIED 9/9