We demonstrate how simultaneously operated 39K–87Rb interferometers exhibiting a high level of correlation can be used to make competitive tests of the university of free fall. This work provides an overview of our experimental apparatus and data analysis procedure, including a detailed study of systematic effects. With a total interrogation time of ms in a compact apparatus, we reach a statistical uncertainty on the measurement of the Eötvös parameter of after s of integration. The main limitations of our measurements arise from a combination of wavefront aberrations, the quadratic Zeeman effect in 39K, parasitic interferometers in 87Rb, and the velocity sensitivity of our detection system. These systematic errors limit the accuracy of our measurement to . We discuss prospects for improvements using ultracold atoms at extended interrogation times.
References
1.
T.
Damour
, F.
Piazza
, and G.
Veneziano
, Phys. Rev. D
66
, 046007
(2002
).2.
C. M.
Will
, Living Rev. Relativ.
9
, 3
(2006
).3.
T.
Damour
, Classical Quantum Gravity
29
, 184001
(2012
).4.
M. A.
Hohensee
, H.
Müller
, and R. B.
Wiringa
, Phys. Rev. Lett.
111
, 151102
(2013
).5.
J. G.
Williams
, S. G.
Turyshev
, and D. H.
Boggs
, Phys. Rev. Lett.
93
, 261101
(2004
).6.
S.
Schlamminger
, K.-Y.
Choi
, T. A.
Wagner
, J. H.
Gundlach
, and E. G.
Adelberger
, Phys. Rev. Lett.
100
, 041101
(2008
).7.
P.
Touboul
, G.
Métris
, M.
Rodrigues
, Y.
André
, Q.
Baghi
, J.
Bergé
, D.
Boulanger
, S.
Bremer
, P.
Carle
et al., Phys. Rev. Lett.
119
, 231101
(2017
).8.
B.
Battelier
, J.
Bergé
, A.
Bertoldi
, L.
Blanchet
, K.
Bongs
, P.
Bouyer
, C.
Braxmaier
, D.
Calonico
, P.
Fayet
et al., “Exploring the foundations of the universe with space tests of the equivalence principle
,” arXiv:1908.11785 (2019
).9.
L.
Zhou
, C.
He
, S.-T.
Yan
, X.
Chen
, D.-F.
Gao
, W.-T.
Duan
, Y.-H.
Ji
, R.-D.
Xu
, B.
Tang
et al., Phys. Rev. A
104
, 022822
(2021
).10.
P.
Asenbaum
, C.
Overstreet
, M.
Kim
, J.
Curti
, and M. A.
Kasevich
, Phys. Rev. Lett.
125
, 191101
(2020
).11.
H.
Albers
, A.
Herbst
, L. L.
Richardson
, H.
Heine
, D.
Nath
, J.
Hartwig
, C.
Schubert
, C.
Vogt
, M.
Woltmann
et al., Eur. Phys. J. D
74
, 145
(2020
).12.
D.
Schlippert
, J.
Hartwig
, H.
Albers
, L. L.
Richardson
, C.
Schubert
, A.
Roura
, W. P.
Schleich
, W.
Ertmer
, and E. M.
Rasel
, Phys. Rev. Lett.
112
, 203002
(2014
).13.
B.
Barrett
, L.
Antoni-Micollier
, L.
Chichet
, B.
Battelier
, T.
Lévèque
, A.
Landragin
, and P.
Bouyer
, Nat. Commun.
7
, 13786
(2016
).14.
J.
Hartwig
, S.
Abend
, C.
Schubert
, D.
Schlippert
, H.
Ahlers
, K.
Posso-Trujillo
, N.
Gaaloul
, W.
Ertmer
, and E. M.
Rasel
, New J. Phys.
17
, 035011
(2015
).15.
G.
Condon
, M.
Rabault
, B.
Barrett
, L.
Chichet
, R.
Arguel
, H.
Eneriz-Imaz
, D.
Naik
, A.
Bertoldi
, B.
Battelier
et al., Phys. Rev. Lett.
123
, 240402
(2019
).16.
B.
Barrett
, L.
Antoni-Micollier
, L.
Chichet
, B.
Battelier
, P.-A.
Gominet
, A.
Bertoldi
, P.
Bouyer
, and A.
Landragin
, New J. Phys.
17
, 085010
(2015
).17.
B.
Barrett
, P.-A.
Gominet
, E.
Cantin
, L.
Antoni-Micollier
, A.
Bertoldi
, B.
Battelier
, P.
Bouyer
, J.
Lautier
, and, and A.
Landragin
, “Mobile and remote inertial sensing with atom interferometers
,” in Proceedings of the International School of Physics ‘Enrico Fermi,’ Atom Interferometry
Vol. 188
, edited by G. M.
Tino
and M. A.
Kasevich
(IOS/SIF
, Amsterdam/Bologna
, 2014
), pp. 493
–555
.18.
L.
Antoni-Micollier
, B.
Barrett
, L.
Chichet
, G.
Condon
, B.
Battelier
, A.
Landragin
, and P.
Bouyer
, Phys. Rev. A
96
, 023608
(2017
).19.
The cycle time for each measurement was s, which includes significant dead time resulting from the software that controls the experiment.
20.
G.
Salomon
, L.
Fouché
, P.
Wang
, A.
Aspect
, P.
Bouyer
, and T.
Bourdel
, Europhys. Lett.
104
, 63002
(2013
).21.
The difference in Raman π-pulse efficiencies between the two species is primarily due to the width of their velocity distributions.
22.
P.
Cheinet
, B.
Canuel
, F.
Pereira Dos Santos
, a
Gauguet
, F.
Yver-Leduc
, and A.
Landragin
, IEEE Trans. Instrum. Meas.
57
, 1141
(2008
).23.
S.
Merlet
, J.
Le Gouët
, Q.
Bodart
, A.
Clairon
, A.
Landragin
, F.
Pereira Dos Santos
, and P.
Rouchon
, Metrologia
46
, 87
(2009
).24.
J.
Le Gouët
, T. E.
Mehlstäubler
, J.
Kim
, S.
Merlet
, A.
Clairon
, A.
Landragin
, and F.
Pereira Dos Santos
, Appl. Phys. B
92
, 133
(2008
).25.
We note that this correction has a statistical uncertainty of —limited by our knowledge of the mean acceleration at any time. This error produces artificial noise in the phase offset of each interferometer that changes randomly between data sets. However, this noise is common to the two interferometers and cancels in the measurement of η.
26.
We note that the rejection of vibration noise using the FRAC method is not a limitation on the differential measurement, but places a large uncertainty on individual acceleration measurements due to an imperfect rejection of the MA bias.
This can be solved by filtering out the dc component of the MA.27.
R.
Geiger
, V.
Ménoret
, G.
Stern
, N.
Zahzam
, P.
Cheinet
, B.
Battelier
, A.
Villing
, F.
Moron
, M.
Lours
et al., Nat. Commun.
2
, 474
(2011
).28.
V.
Ménoret
, P.
Vermeulen
, N. L.
Moigne
, S.
Bonvalot
, P.
Bouyer
, A.
Landragin
, and B.
Desruelle
, Sci. Rep.
8
, 12300
(2018
).29.
J.
Stockton
, X.
Wu
, and M. A.
Kasevich
, Phys. Rev. A
76
, 033613
(2007
).30.
M. J.
Snadden
, J. M.
McGuirk
, P.
Bouyer
, K. G.
Haritos
, and M. A.
Kasevich
, Phys. Rev. Lett.
81
, 971
(1998
).31.
G.
Rosi
, F.
Sorrentino
, L.
Cacciapuoti
, M.
Prevedelli
, and G. M.
Tino
, Nature
510
, 518
(2014
).32.
G. W.
Biedermann
, X.
Wu
, L.
Deslauriers
, S.
Roy
, C.
Mahadeswaraswamy
, and M. A.
Kasevich
, Phys. Rev. A
91
, 033629
(2015
).33.
R.
Caldani
, K. X.
Weng
, S.
Merlet
, and F.
Pereira Dos Santos
, Phys. Rev. A
99
, 033601
(2019
).34.
G. T.
Foster
, J. B.
Fixler
, J. M.
McGuirk
, and M. A.
Kasevich
, Opt. Lett.
27
, 951
(2002
).36.
P. A.
Altin
, M. T.
Johnsson
, G. R.
Dennis
, R. P.
Anderson
, J. E.
Debs
, S. S.
Szigeti
, K. S.
Hardman
, S.
Bennetts
, G. D.
McDonald
et al., New J. Phys.
15
, 023009
(2013
).37.
Z.-K.
Hu
, B.-L.
Sun
, X.-C.
Duan
, M.-K.
Zhou
, L.-L.
Chen
, S.
Zhan
, Q.-Z.
Zhang
, and J.
Luo
, Phys. Rev. A
88
, 043610
(2013
).38.
C.
Freier
, M.
Hauth
, V.
Schkolnik
, B.
Leykauf
, M.
Schilling
, H.
Wziontek
, H.-G.
Scherneck
, J.
Muller
, and A.
Peters
, J. Phys: Conf. Ser.
723
, 012050
(2016
).39.
C.
Overstreet
, P.
Asenbaum
, T.
Kovachy
, R.
Notermans
, J. M.
Hogan
, and M. A.
Kasevich
, Phys. Rev. Lett.
120
, 183604
(2018
).40.
G.
Rosi
, L.
Cacciapuoti
, F.
Sorrentino
, M.
Menchetti
, M.
Prevedelli
, and G. M.
Tino
, Phys. Rev. Lett.
114
, 013001
(2015
).41.
P.
Gillot
, B.
Cheng
, S.
Merlet
, and F.
Pereira Dos Santos
, Phys. Rev. A
93
, 013609
(2016
).42.
I.
Yavin
, M.
Weel
, A.
Andreyuk
, and A.
Kumarakrishnan
, Am. J. Phys.
70
, 149
(2002
).43.
Equation (21) assumes the clouds corresponding to states.
44.
. Our detector is an avalanche photodiode (APD) Hamamatsu C12703 with a diameter of 1.5 mm. This solution has been chosen because a fast photodiode is required for potassium. Indeed the detection of the two internal state is done sequentially due to the compactness of the experiment and the signal of F = 2 is weak because of the strong depumping rate due to potassium's compact level structure.
45.
D. A.
Steck
, “Rubidium 87 D Line Data,” available online at http://steck.us/alkalidata (revision 2.2.2, 9 July 2021
).46.
Q.-Q.
Hu
, C.
Freier
, B.
Leykauf
, V.
Schkolnik
, J.
Yang
, M.
Krutzik
, and A.
Peters
, Phys. Rev. A
96
, 033414
(2017
).47.
O.
Carraz
, R.
Charrière
, M.
Cadoret
, N.
Zahzam
, Y.
Bidel
, and A.
Bresson
, Phys. Rev. A
86
, 033605
(2012
).48.
S.
Templier
, J.
Hauden
, P.
Cheiney
, F.
Napolitano
, H.
Porte
, P.
Bouyer
, B.
Barrett
, and B.
Battelier
, Phys. Rev. Appl.
16
, 044018
(2021
).49.
A.
Bonnin
, N.
Zahzam
, Y.
Bidel
, and A.
Bresson
, Phys. Rev. A
88
, 043615
(2013
).50.
A.
Gauguet
, T. E.
Mehlstäubler
, T.
Lévèque
, J.
Le Gouët
, W.
Chaibi
, B.
Canuel
, A.
Clairon
, F.
Pereira Dos Santos
, and A.
Landragin
, Phys. Rev. A
78
, 043615
(2008
).51.
A.
Louchet-Chauvet
, T.
Farah
, Q.
Bodart
, A.
Clairon
, A.
Landragin
, S.
Merlet
, and F. P.
Dos Santos
, New J. Phys.
13
, 065025
(2011
).52.
A.
Trimeche
, M.
Langlois
, S.
Merlet
, and F.
Pereira Dos Santos
, Phys. Rev. Appl.
7
, 034016
(2017
).53.
R.
Karcher
, A.
Imanaliev
, S.
Merlet
, and F.
Pereira Dos Santos
, New J. Phys.
20
, 113041
(2018
).54.
P.
Wolf
and P.
Tourrenc
, Phys. Lett. A
251
, 241
(1999
).55.
P.
Storey
and C.
Cohen-Tannoudji
, J. Phys. II
4
, 1999
(1994
).56.
A.
Roura
, Phys. Rev. Lett.
118
, 160401
(2017
).57.
G.
D'Amico
, G.
Rosi
, S.
Zhan
, L.
Cacciapuoti
, M.
Fattori
, and G. M.
Tino
, Phys. Rev. Lett.
119
, 253201
(2017
).58.
D.
Aguilera
, H.
Ahlers
, B.
Battelier
, A.
Bawamia
, A.
Bertoldi
, R.
Bondarescu
, K.
Bongs
, P.
Bouyer
, C.
Braxmaier
et al., Classical Quantum Gravity
31
, 115010
(2014
).59.
B.
Canuel
, L.
Amand
, A.
Bertoldi
, W.
Chaibi
, R.
Geiger
, J.
Gillot
, A.
Landragin
, M.
Merzougui
, I.
Riou
et al., E3S Web Conf.
4
, 01004
(2014
).60.
P.
Cheiney
, L.
Fouché
, S.
Templier
, F.
Napolitano
, B.
Battelier
, P.
Bouyer
, and B.
Barrett
, Phys. Rev. Appl.
10
, 034030
(2018
).61.
R. E.
Kalman
, J. Basic Eng.
82
, 35
(1960
).62.
J.
VanderPlas
, in Proceedings of the 13th Python in Science Conference
, edited by S.
van der Walt
and J.
Bergstra
(SciPy, Austin, 2014
), pp. 85
–93
.© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
