1. MOE Key Laboratory of Fundamental Physical Quantities Measurements, Hubei Key Laboratory of Gravitation and Quantum Physics, PGMF and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China 2. Wuhan Institute of Quantum Technology, Wuhan 430206, China
We report an experimental study of magnetic-field-sensitive multi-wave interference, realized in a three-wave RF-atom system. In the F = 1 hyperfine level of the ground state, Ramsey fringes were observed via the spin-selective Raman detection. A decrease in the fringe contrast was observed with increasing free evolution time. The maximum evolution time for observable fringe contrasts was investigated at different atom temperatures, under free-falling and trapped conditions. As the main interest of the Ramsey method, the improvement in magnetic field resolution is observed with an increase of evolution time T up to 3 ms and with the measurement resolution reaching 0.85 nT. This study paves the way for precision magnetic field measurements based on cold atoms.
P. Heavner T. , A. Donley E. , Levi F. , Costanzo G. , E. Parker T. , H. Shirley J. , Ashby N. , Barlow S. , R. Jefferts S. . First accuracy evaluation of NIST-F2. Metrologia, 2014, 51(3): 174 https://doi.org/10.1088/0026-1394/51/3/174
3
Guena J. , Abgrall M. , Rovera D. , Laurent P. , Chupin B. , Lours M. , Santarelli G. , Rosenbusch P. , E. Tobar M. , Li Ruoxin , Gibble K. , Clairon A. , Bize S. . Progress in atomic fountains at LNE-SYRTE. IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 2012, 59(3): 391 https://doi.org/10.1109/TUFFC.2012.2208
4
Gerginov V. , Nemitz N. , Weyers S. , Schröder R. , Griebsch D. , Wynands R. . Uncertainty evaluation of the caesium fountain clock PTB-CSF2. Metrologia, 2010, 47(1): 65 https://doi.org/10.1088/0026-1394/47/1/008
5
Sadgrove M. , Eto Y. , Sekine S. , Suzuki H. , Hirano T. . Ramsey interferometry using the Zeeman sublevels in a spin-2 Bose gas. J. Phys. Soc. Jpn., 2013, 82(9): 094002 https://doi.org/10.7566/JPSJ.82.094002
6
Chen L. , Zhang K. , Xu Y. , Luo Q. , Xu W. , Zhou M. , Hu Z. . Multi-wave atom interferometer based on Doppler-insensitive Raman transition. Opt. Express, 2020, 28(6): 8463 https://doi.org/10.1364/OE.387086
7
I. Herrera, P. Lombardi, F. Schäfer , F. S. Cataliotti. Petrovic . A multi-state interferometer on an atom chip. New J. Phys., 2013, 15(4): 043002 https://doi.org/10.1088/1367-2630/15/4/043002
8
Robert-de-Saint-Vincent M. , P. Brantut J. , J. Bordé C. , Aspect A. , Bourdel T. , Bouyer P. . A quantum trampoline for ultra-cold atoms. Europhys. Lett., 2010, 89(1): 10002 https://doi.org/10.1209/0295-5075/89/10002
9
Gustavsson M. , Haller E. , J. Mark M. , G. Danzl J. , Hart R. , J. Daley A. , C. Nägerl H. . Interference of interacting matter waves. New J. Phys., 2010, 12(6): 065029 https://doi.org/10.1088/1367-2630/12/6/065029
10
K. Zhou M. , Zhang K. , C. Duan X. , Ke Y. , G. Shao C. , K. Hu Z. . Atomic multiwave interferometer for Aharonov−Casher-phase measurements. Phys. Rev. A, 2016, 93(2): 023641 https://doi.org/10.1103/PhysRevA.93.023641
11
Di Domenico G. , Saudan H. , Bison G. , Knowles P. , Weis A. . Sensitivity of double-resonance alignment magnetometers. Phys. Rev. A, 2007, 76(2): 023407 https://doi.org/10.1103/PhysRevA.76.023407
12
Knappe S. , D. D. Schwindt P. , Gerginov V. , Shah V. , Liew L. , Moreland J. , G. Robinson H. , Hollberg L. , Kitching J. . Microfabricated atomic clocks and magnetometers. J. Opt. A, 2006, 8(7): S318 https://doi.org/10.1088/1464-4258/8/7/S04
13
D. D. Schwindt P. , Knappe S. , Shah V. , Hollberg L. , Kitching J. , A. Liew L. , Moreland J. . Chip-scale atomic magnetometer. Appl. Phys. Lett., 2004, 85(26): 6409 https://doi.org/10.1063/1.1839274
14
Li J. , Quan W. , Zhou B. , Wang Z. , Lu J. , Hu Z. , Liu G. , Fang J. . SERF atomic magnetometer – recent advances and applications: A review. IEEE Sens. J., 2018, 18(20): 8198 https://doi.org/10.1109/JSEN.2018.2863707
W. Mitchell M. , P. Alvarez S. . Quantum limits to the energy resolution of magnetic field sensors. Rev. Mod. Phys., 2020, 92(2): 021001 https://doi.org/10.1103/RevModPhys.92.021001
17
Zhao W. , Qian W. , Lv D. , Wei R. . Improvement of average magnetic field measurement based on magnetic-field-sensitive Ramsey fringes. Opt. Lett., 2022, 47(8): 2073 https://doi.org/10.1364/OL.455269
18
Wang W. , Dong R. , Wei R. , Lin J. , Zou F. , Chen T. , Wang Y. . Measuring magnetic field vector by stimulated Raman transitions. Appl. Phys. Lett., 2016, 108(12): 122401 https://doi.org/10.1063/1.4944700
19
Shi C. , Wei R. , Zhou Z. , Lv D. , Li T. , Wang Y. . Magnetic field measurement on 87Rb atomic fountain clock. Chin. Opt. Lett., 2010, 8: 549 https://doi.org/10.3788/COL20100806.0549
20
Peters A. , Y. Chung K. , Chu S. . High-precision gravity measurements using atom interferometry. Metrologia, 2001, 38(1): 25 https://doi.org/10.1088/0026-1394/38/1/4
21
K. Hu Z. , L. Sun B. , C. Duan X. , K. Zhou M. , L. Chen L. , Zhan S. , Z. Zhang Q. , Luo J. . Demonstration of an ultrahigh-sensitivity atom-interferometry absolute gravimeter. Phys. Rev. A, 2013, 88(4): 043610 https://doi.org/10.1103/PhysRevA.88.043610
22
Y. Wang Z. , Chen T. , L. Wang X. , Zhang Z. , F. Xu Y. , Lin Q. . A precision analysis and determination of the technical requirements of an atom interferometer for gravity measurement. Front. Phys. China, 2009, 4(2): 174 https://doi.org/10.1007/s11467-009-0017-7
23
Wang J. , Zhou L. , B. Li R. , Liu M. , S. Zhan M. . Cold atom interferometers and their applications in precision measurements. Front. Phys. China, 2009, 4(2): 179 https://doi.org/10.1007/s11467-009-0045-3
24
Gautier R. , Guessoum M. , A. Sidorenkov L. , Bouton Q. , Landragin A. , Geiger R. . Accurate measurement of the Sagnac effect for matter waves. Sci. Adv., 2022, 8(23): eabn8009 https://doi.org/10.1126/sciadv.abn8009
25
J. Xu W. , Cheng L. , Liu J. , Zhang C. , Zhang K. , Cheng Y. , Gao Z. , S. Cao L. , C. Duan X. , K. Zhou M. , K. Hu Z. . Effects of wave-front tilt and air density fluctuations in a sensitive atom interferometry gyroscope. Opt. Express, 2020, 28(8): 12189 https://doi.org/10.1364/OE.391780
26
W. Yao Z. , B. Lu S. , B. Li R. , Luo J. , Wang J. , S. Zhan M. . Calibration of atomic trajectories in a large-area dual-atom-interferometer gyroscope. Phys. Rev. A, 2018, 97(1): 013620 https://doi.org/10.1103/PhysRevA.97.013620
27
Alauze X. , Bonnin A. , Solaro C. , P. D. Santos F. . A trapped ultracold atom force sensor with a μm-scale spatial resolution. New J. Phys., 2018, 20(8): 083014 https://doi.org/10.1088/1367-2630/aad716
28
Bennett R. , H. J. O’Dell D. . Revealing short-range non-Newtonian gravity through Casimir–Polder shielding. New J. Phys., 2019, 21(3): 033032 https://doi.org/10.1088/1367-2630/ab0ca6
29
Wolf P. , Lemonde P. , Lambrecht A. , Bize S. , Landragin A. , Clairon A. . From optical lattice clocks to the measurement of forces in the Casimir regime. Phys. Rev. A, 2007, 75(6): 063608 https://doi.org/10.1103/PhysRevA.75.063608
30
Dimopoulos S. , A. Geraci A. . Probing submicron forces by interferometry of Bose−Einstein condensed atoms. Phys. Rev. D, 2003, 68(12): 124021 https://doi.org/10.1103/PhysRevD.68.124021
31
B. Deng X. , Y. Xu Y. , C. Duan X. , K. Hu Z. . Precisely mapping the absolute magnetic field in vacuum by an optical ramsey atom interferometer. Phys. Rev. Appl., 2021, 15(5): 054062 https://doi.org/10.1103/PhysRevApplied.15.054062
32
Zhang H. , Ren X. , Yan W. , Cheng Y. , Zhou H. , Gao Z. , Luo Q. , Zhou M. , Hu Z. . Effects related to the temperature of atoms in an atom interferometry gravimeter based on ultra-cold atoms. Opt. Express, 2021, 29(19): 30007 https://doi.org/10.1364/OE.433968
33
Yan W. , Ren X. , Zhou M. , Hu Z. . Precision magnetic field sensing with dual multi-wave atom interferometer. Sensors (Basel), 2022, 23(1): 173 https://doi.org/10.3390/s23010173
34
Reinhard F., Design and construction of an atomic clock on an atom chip, Thesis, Université Pierre et Marie Curie-Paris VI, 2009
35
Eto Y. , Sadgrove M. , Hasegawa S. , Saito H. , Hirano T. . Control of spin current in a Bose gas by periodic application of π pulses. Phys. Rev. A, 2014, 90(1): 013626 https://doi.org/10.1103/PhysRevA.90.013626
36
Fattori M. , D’Errico C. , Roati G. , Zaccanti M. , Jona-Lasinio M. , Modugno M. , Inguscio M. , Modugno G. . Atom interferometry with a weakly interacting Bose−Einstein condensate. Phys. Rev. Lett., 2008, 100(8): 080405 https://doi.org/10.1103/PhysRevLett.100.080405
37
Fattori M. , Koch T. , Goetz S. , Griesmaier A. , Hensler S. , Stuhler J. , Pfau T. . Demagnetization cooling of a gas. Nat. Phys., 2006, 2(11): 765 https://doi.org/10.1038/nphys443
38
Hensler S. , Greiner A. , Stuhler J. , Pfau T. . Depolarisation cooling of an atomic cloud. Europhys. Lett., 2005, 71(6): 918 https://doi.org/10.1209/epl/i2005-10181-4
39
Widera A. , Gerbier F. , Fölling S. , Gericke T. , Mandel O. , Bloch I. . Precision measurement of spin-dependent interaction strengths for spin-1 and spin-2 87Rb atoms. New J. Phys., 2006, 8(8): 152 https://doi.org/10.1088/1367-2630/8/8/152
40
Schmaljohann H. , Erhard M. , Kronjäger J. , Kottke M. , van Staa S. , Cacciapuoti L. , J. Arlt J. , Bongs K. , Sengstock K. . Dynamics of F = 2 Spinor Bose−Einstein condensates. Phys. Rev. Lett., 2004, 92(4): 040402 https://doi.org/10.1103/PhysRevLett.92.040402
41
Kuwamoto T. , Araki K. , Eno T. , Hirano T. . Magnetic field dependence of the dynamics of 87Rb spin-2 Bose−Einstein condensates. Phys. Rev. A, 2004, 69(6): 063604 https://doi.org/10.1103/PhysRevA.69.063604
42
T. Xu X. , Y. Wang Z. , H. Jiao R. , R. Yi C. , Sun W. , Chen S. . Ultra-low noise magnetic field for quantum gases. Rev. Sci. Instrum., 2019, 90(5): 054708 https://doi.org/10.1063/1.5087957
43
Merkel B. , Thirumalai K. , E. Tarlton J. , M. Schäfer V. , J. Ballance C. , P. Harty T. , M. Lucas D. . Magnetic field stabilization system for atomic physics experiments. Rev. Sci. Instrum., 2019, 90(4): 044702 https://doi.org/10.1063/1.5080093
44
Riehle F., Frequency Standards: Basics and Applications, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2004
45
C. J. Gan H. , Maslennikov G. , W. Tseng K. , R. Tan T. , Kaewuam R. , J. Arnold K. , Matsukevich D. , D. Barrett M. . Oscillating-magnetic-field effects in high-precision metrology. Phys. Rev. A, 2018, 98(3): 032514 https://doi.org/10.1103/PhysRevA.98.032514