u.s. army rdecom · 2018. 9. 20. · +4hk +2hk i i 01 i -2hk i -4hk i .. -6hk . laser cou pies...

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


beamsplitter

Michael Goerz ([email protected])


beamsplitter

atom interferometer:

atoms have mass and internal structure • couple to more external perturbations

(gravity)

UNCLASSIFIED 1/9


beamsplitter

mirror? beamsplitter?



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



UNCLASSIFIED 2/9

+4hk +2hk I

I 01

I - 2hk I

- 4hk I ..

- 6hk .




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 .




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



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



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


Apply optimal control to atom optics pulses

=} increase fide I ity

=} robustness against fluctuations



Time T 2T



Time

2T



+61ik ..

+41ik I .

+21ik I I

o I I

-21ik I C

-41ik 0 ;e

I . . (/)

0

-61ik · a. Time

0 T 2T



+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



+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


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.


+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


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,)


UNCLASSIFIED

+4/ik +2/ik I

I o I

I -2/ik I

-4/ik

35

UNCLASSIFIED

I . . -6/ik ·


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,)


+4/ik +2/ik I

I o I

I -2/ik I

-4/ik I . .

-6/ik ·


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,)


I . . -6/ik ·

95%


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,)


I . . -6/ik ·

95%



7/9


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


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,)


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%



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,)


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%


optimized for robustness


8/9


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


u.s. army rdecom · 2018. 9. 20. · +4hk +2hk i i 01 i -2hk i -4hk i .. -6hk . laser cou pies...

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