RDECOM. Optimal pulse schemes for high-precision atom interferometry U.S.ARMY. Michael Goerz 1, Paul Kunz 1, Mark Kasevich 2, Vladimir Malinovsky 1

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1 U.S.ARMY U.S. ARMY RDCOM AH.L RSARCH LABORATORY Optimal pulse schemes for high-precision atom interferometry Michael Goerz 1, Paul Kunz 1, Mark Kasevich 2, Vladimir Malinovsky 1 1 U.S. Army Research Lab, 2 Stanford University 23 August 218

2 optical interferometer: beamsplitter beamsplitter 1/9

3 optical interferometer: beamsplitter beamsplitter 1/9

4 optical interferometer: beamsplitter beamsplitter atom interferometer: atoms have mass and internal structure couple to more external perturbations (gravity) 1/9

5 optical interferometer: beamsplitter beamsplitter mirror? beamsplitter? atom interferometer: atoms have mass and internal structure couple to more external perturbations (gravity) 1/9

6 +4nk +2nk 1-2nk - 4nk.. - 6nk laser cou pies between electronic states: absorbs photon momentum 2/9

7 1 m atomic fountain at Stanford: ultracold 87 Rb atomic cloud +4hk +2hk 1-2hk - 4hk.. - 6hk. laser cou pies between electronic states: absorbs photon momentum "!g ' ' C.Q t= 2T +-' "cii Cl. 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, 53 (215) 2/9

8 1 m atomic fountain at Stanford: ultracold 87 Rb atomic cloud +4hk +2hk 1-2hk - 4hk.. - 6hk. laser cou pies between electronic states: absorbs photon momentum "!g ' ' C.Q t = 2T +-' "cii Cl. 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, 53 (215) 2/9

9 Army applications: ultra-precise measurement of acceleration / gravity inertia navigation: submarines, autonomous vehicles -not jammable! gyroscopes gravity gradient sensors weapons system control geospatial mapping drone or sate ite based detection of underground structures 3/9

10 1 m atomic fountain: sensitivity 1-13 g/ -/Hz AOSense (21) 1-6 g/-/rz state of the art 1-9 g/-/rz 4/9

11 1 m atomic fountain: sensitivity 1-13 g/ -/Hz factors: signal to noise ratio large momentum transfer AOSense (21) 1-6 g/-/rz state of the art 1-9 g/-/rz 4/9

12 Apply optimal control to atom optics pulses =} increase fide ity =} robustness against fluctuations 5/9

13 T Time 2T 6/9

14 Time 2T 6/9

15 +41ik +21ik o +61ik ik C -41ik.. ;e (/) -61ik a. Time T 2T 6/9

16 +41ik +21ik o +61ik ik C -41ik.. ;e (/) -61ik a. Time T 2T 6/9

17 +41ik +21ik o +61ik ik C :;:; - 41ik.. -61ik a. "ui Time T 2T train of pulses rapid adiabatic passage: tune th rough laser frequency at constant amplitude 6/9

18 a,_ 1 Vl '- : ik.. +41ik a.- +21ik -~ -.c: 8 o N 6 ::, 4-21ik C C: :;:; -41ik Q) 2 "ui.. Time -61ik a. T -2 2T time (1/w,}. train of pulses rapid adiabatic passage: tune th rough laser frequency at constant amplitude 6/9

19 ~~lr , :5 3 a.-.a 4 ~ 2-2 oo.i.i..i"tc 5~.,._~~&..l----'-::"~.._., J_.,.._j time (1/w,} +41ik +21ik o -21ik -41ik +61ik..... C :;:; (/) -61ik a. Time T 2T e QJ 1-1 ~ ~ 1-2 co co 1-3 :5 1- a. 4 rapid adiabatic passage a. 1-s ~% ~~ 7nb,l,.,,_,l,.,,_,,.,,_'::-:::'~,,, ~ 9% 95,, /C 1 % 15% 11% pulse amplitude 6/9

20 a,_ 1 Vl '- :5 3 a.- - ~ -.c: N 8 6 ::, 4 C: Q) compress +4/ik +2/ik o -2/ik -4/ik.. -6/ik a,_ 5 Vl '- :5 3 a.- - ~ -.c: N 8 6 ::, 4 C: Q) time (1/w,) 35 6/9

21 a,_ 1 Vl '- :5 3 a.- - ~ -.c: N 8 6 ::, 4 C: Q) compress +4/ik +2/ik o -2/ik -4/ik.. -6/ik a,_ 5 Vl '- :5 3 a.- - ~ -.c: N 8 6 ::, 4 C: Q) time (1/w,) 35 6/9

22 cu_ 1 ll '- :: 3 c.- ~ ~ 8-6 ::, 4 ~ ~ 2-2 1;;,,1,,_..,,,_,,.._,..,..,,,..,,.,..,_,_ so time (1/w,) +4/ik +2/ik o -2/ik -4/ik.. -6/ik time (1/w,) 7/9

23 QJ 5 Vl -;: :5 3 a.- ~;i.a,,_,_..11,..11,1..,1.ii..,_i.i..,i.i,..i,..,,_,_..11,..11,1..,1.ii..,._. 8 +4/ik +2/ik o -2/ik -4/ik.. -6/ik optimize for fidelity.-~..,_.ii.,.11,,..11.,_.ii.,.,_..i,..i..,..i.11,,..ii..i..i.ii time (1/w,) 1 QJ 1-1 QJ.._ ~ 1-2 co C 1-3 co :5 1- a. 4 a. 1-~% 95% 1% 15% 11% pulse amplitude 7/9

24 QJ 5 Vl -;: :5 3 a.- ~ 8 ;i.a,,_,_..11,..11,1..,1.ii..,_i.i..,i.i,..i,..,,_,_..11,..11,1..,1.ii..,._. +4/ik +2/ik o -2/ik -4/ik.. -6/ik optimize for fidelity.-~..,_.ii.,.11,,..11.,_.ii.,.,_..i,..i..,..i.11,,..ii..i..i.ii time (1/w,) 1 QJ 1-1 QJ.._ ~ 1-2 co C 1-3 co :5 1- a. 4 a. 1-~% 95% 1% 15% 11% pulse amplitude 7/9

25 V.i''l!!.9 +61ik. cu_ 5 ll '- +41ik :: 3 c.- +21ik ~ -C N 8 o 6 ::, -21ik C. 4 C :;:; cu 2-41ik "ui.. -61ik a. -2 s time (1/w,) Time T 2T cu rn "'i:: "53 c.- QJ 1-1 QJ.._ ~ ~ 1-2 -C N C 1-3 :::::,. C cu :5 1-4 a. -2 a. 1-~% co co % 1% 15% 11% time (1/w,) pulse amplitude 8/9

26 QJ 5 Vl -;: :5 3 a.- ~:;i.i..iiii.i...11i&.iiii.i..iii.."':....i.. _..i. 8 6 ::, 4 C: QJ _1.--,, : _ +4/ik +2/ik o -2/ik -4/ik.. -61ik 5 QJ_ Vl '- :5 3 a.- -.:i.:: -.c:: N 8 6 ::, 4 C: QJ time (1/w,) 35 1 QJ 1-1 QJ.._ ~ 1-2 co c: 1-3 co :5 1- a. 4 a. 1-~% 95% 1% 15% 11% pulse amplitude 8/9

27 QJ 5 Vl -;: :5 3 a.- ~:;i.i..iiii.i...11i&.iiii.i..iii.."':....i.. _..i. 8 6 ::, 4 C: QJ _1.--,, : _ +4/ik +2/ik o -2/ik -4/ik.. -61ik 5 QJ_ Vl '- :5 3 a.- -.:i.:: -.c:: N 8 6 ::, 4 C: QJ time (1/w,) 35 1 QJ 1-1 QJ.._ ~ 1-2 co c: 1-3 co :5 1- a. 4 a. 1-~% 95% optimized for robustness 1% 15% 11% pulse amplitude 8/9

28 Conclusion relative phase difference: ~ cf> = -2kmaxgT 2 ~g optima control can com press pulses t= 2T by order of magnitude while guarant eeing robustness Army applications: ultra-precise measurement of acceleration / gravity inertia navigation, satellite based gravitational sensing 9/9