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Amapanea,b0000-0001-9449-2509, R. Arcidiaconoa,c0000-0001-5904-142X, S.
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Staianoa0000-0003-1803-624X, M. Tornagoa,b, D. Trocinoa0000-0002-2830-5872, A.
Vagnerinia,b INFN Sezione di Trieste a, Trieste, Italy, Università di Trieste
b, Trieste, Italy S. Belfortea0000-0001-8443-4460, V.
Candelisea,b0000-0002-3641-5983, M. Casarsaa0000-0002-1353-8964, F.
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Riccaa,b0000-0003-2831-6982, G. Sorrentinoa,b, F.
Vazzolera,b0000-0001-8111-9318 Kyungpook National University, Daegu, Korea S.
Dogra0000-0002-0812-0758, C. Huh0000-0002-8513-2824, B. Kim, D.H.
Kim0000-0002-9023-6847, G.N. Kim0000-0002-3482-9082, J. Kim, J. Lee, S.W.
Lee0000-0002-1028-3468, C.S. Moon0000-0001-8229-7829, Y.D.
Oh0000-0002-7219-9931, S.I. Pak, B.C. Radburn-Smith, S.
Sekmen0000-0003-1726-5681, Y.C. Yang Chonnam National University, Institute
for Universe and Elementary Particles, Kwangju, Korea H.
Kim0000-0001-8019-9387, D.H. Moon0000-0002-5628-9187 Hanyang University,
Seoul, Korea B. Francois0000-0002-2190-9059, T.J. Kim0000-0001-8336-2434, J.
Park0000-0002-4683-6669 Korea University, Seoul, Korea S. Cho, S.
Choi0000-0001-6225-9876, Y. Go, B. Hong0000-0002-2259-9929, K. Lee, K.S.
Lee0000-0002-3680-7039, J. Lim, J. Park, S.K. Park, J. Yoo Kyung Hee
University, Department of Physics, Seoul, Republic of Korea, Seoul, Korea J.
Goh0000-0002-1129-2083, A. Gurtu Sejong University, Seoul, Korea H.S.
Kim0000-0002-6543-9191, Y. Kim Seoul National University, Seoul, Korea J.
Almond, J.H. Bhyun, J. Choi, S. Jeon, J. Kim, J.S. Kim, S. Ko, H. Kwon, H.
Lee0000-0002-1138-3700, S. Lee, B.H. Oh, M. Oh0000-0003-2618-9203, S.B. Oh, H.
Seo0000-0002-3932-0605, U.K. Yang, I. Yoon0000-0002-3491-8026 University of
Seoul, Seoul, Korea W. Jang, D.Y. Kang, Y. Kang, S. Kim, B. Ko, J.S.H.
Lee0000-0002-2153-1519, Y. Lee, J.A. Merlin, I.C. Park, Y. Roh, M.S. Ryu, D.
Song, I.J. Watson0000-0003-2141-3413, S. Yang Yonsei University, Department of
Physics, Seoul, Korea S. Ha, H.D. Yoo Sungkyunkwan University, Suwon, Korea M.
Choi, H. Lee, Y. Lee, I. Yu0000-0003-1567-5548 College of Engineering and
Technology, American University of the Middle East (AUM), Egaila, Kuwait,
Dasman, Kuwait T. Beyrouthy, Y. Maghrbi Riga Technical University, Riga,
Latvia K. Dreimanis0000-0003-0972-5641, V. Veckalns480000-0003-3676-9711
Vilnius University, Vilnius, Lithuania M. Ambrozas, A. Carvalho Antunes De
Oliveira0000-0003-2340-836X, A. Juodagalvis0000-0002-1501-3328, A.
Rinkevicius0000-0002-7510-255X, G. Tamulaitis0000-0002-2913-9634 National
Centre for Particle Physics, Universiti Malaya, Kuala Lumpur, Malaysia N. Bin
Norjoharuddeen0000-0002-8818-7476, W.A.T. Wan Abdullah, M.N. Yusli, Z.
Zolkapli Universidad de Sonora (UNISON), Hermosillo, Mexico J.F.
Benitez0000-0002-2633-6712, A. Castaneda Hernandez0000-0003-4766-1546, M. León
Coello, J.A. Murillo Quijada0000-0003-4933-2092, A. Sehrawat, L. Valencia
Palomo0000-0002-8736-440X Centro de Investigacion y de Estudios Avanzados del
IPN, Mexico City, Mexico G. Ayala, H. Castilla-Valdez, E. De La Cruz-
Burelo0000-0002-7469-6974, I. Heredia-De La Cruz490000-0002-8133-6467, R.
Lopez-Fernandez, C.A. Mondragon Herrera, D.A. Perez Navarro, A. Sánchez
Hernández0000-0001-9548-0358 Universidad Iberoamericana, Mexico City, Mexico
S. Carrillo Moreno, C. Oropeza Barrera0000-0001-9724-0016, F. Vazquez Valencia
Benemerita Universidad Autonoma de Puebla, Puebla, Mexico I. Pedraza, H.A.
Salazar Ibarguen, C. Uribe Estrada University of Montenegro, Podgorica,
Montenegro J. Mijuskovic50, N. Raicevic University of Auckland, Auckland, New
Zealand D. Krofcheck0000-0001-5494-7302 University of Canterbury,
Christchurch, New Zealand P.H. Butler0000-0001-9878-2140 National Centre for
Physics, Quaid-I-Azam University, Islamabad, Pakistan A. Ahmad, M.I. Asghar,
A. Awais, M.I.M. Awan, H.R. Hoorani, W.A. Khan, M.A. Shah, M.
Shoaib0000-0001-6791-8252, M. Waqas0000-0002-3846-9483 AGH University of
Science and Technology Faculty of Computer Science, Electronics and
Telecommunications, Krakow, Poland V. Avati, L. Grzanka, M. Malawski National
Centre for Nuclear Research, Swierk, Poland H. Bialkowska, M.
Bluj0000-0003-1229-1442, B. Boimska0000-0002-4200-1541, M. Górski, M. Kazana,
M. Szleper0000-0002-1697-004X, P. Zalewski Institute of Experimental Physics,
Faculty of Physics, University of Warsaw, Warsaw, Poland K. Bunkowski, K.
Doroba, A. Kalinowski0000-0002-1280-5493, M. Konecki0000-0001-9482-4841, J.
Krolikowski0000-0002-3055-0236 Laboratório de Instrumentação e Física
Experimental de Partículas, Lisboa, Portugal M. Araujo, P.
Bargassa0000-0001-8612-3332, D. Bastos, A. Boletti0000-0003-3288-7737, P.
Faccioli0000-0003-1849-6692, M. Gallinaro0000-0003-1261-2277, J.
Hollar0000-0002-8664-0134, N. Leonardo0000-0002-9746-4594, T. Niknejad, M.
Pisano, J. Seixas0000-0002-7531-0842, O. Toldaiev0000-0002-8286-8780, J.
Varela0000-0003-2613-3146 Joint Institute for Nuclear Research, Dubna, Russia
S. Afanasiev, D. Budkouski, I. Golutvin, I. Gorbunov0000-0003-3777-6606, V.
Karjavine, V. Korenkov0000-0002-2342-7862, A. Lanev, A. Malakhov, V.
Matveev51,52, V. Palichik, V. Perelygin, M. Savina, D. Seitova, V. Shalaev, S.
Shmatov, S. Shulha, V. Smirnov, O. Teryaev, N. Voytishin, B.S. Yuldashev53, A.
Zarubin, I. Zhizhin Petersburg Nuclear Physics Institute, Gatchina (St.
Petersburg), Russia G. Gavrilov0000-0003-3968-0253, V. Golovtcov, Y. Ivanov,
V. Kim540000-0001-7161-2133, E. Kuznetsova55, V. Murzin, V. Oreshkin, I.
Smirnov, D. Sosnov0000-0002-7452-8380, V. Sulimov, L. Uvarov, S. Volkov, A.
Vorobyev Institute for Nuclear Research, Moscow, Russia Yu.
Andreev0000-0002-7397-9665, A. Dermenev, S. Gninenko0000-0001-6495-7619, N.
Golubev, A. Karneyeu0000-0001-9983-1004, D. Kirpichnikov0000-0002-7177-077X,
M. Kirsanov, N. Krasnikov, A. Pashenkov, G. Pivovarov0000-0001-6435-4463, A.
Toropin Institute for Theoretical and Experimental Physics named by A.I.
Alikhanov of NRC ‘Kurchatov Institute’, Moscow, Russia V. Epshteyn, V.
Gavrilov, N. Lychkovskaya, A. Nikitenko56, V. Popov, A. Stepennov, M. Toms, E.
Vlasov0000-0002-8628-2090, A. Zhokin Moscow Institute of Physics and
Technology, Moscow, Russia T. Aushev National Research Nuclear University
’Moscow Engineering Physics Institute’ (MEPhI), Moscow, Russia O. Bychkova, M.
Chadeeva570000-0003-1814-1218, A. Oskin, P. Parygin, E. Popova, V. Rusinov
P.N. Lebedev Physical Institute, Moscow, Russia V. Andreev, M. Azarkin, I.
Dremin0000-0001-7451-247X, M. Kirakosyan, A. Terkulov Skobeltsyn Institute of
Nuclear Physics, Lomonosov Moscow State University, Moscow, Russia A. Belyaev,
E. Boos0000-0002-0193-5073, V. Bunichev, M. Dubinin580000-0002-7766-7175, L.
Dudko0000-0002-4462-3192, A. Ershov, A. Gribushin, V.
Klyukhin0000-0002-8577-6531, O. Kodolova0000-0003-1342-4251, I.
Lokhtin0000-0002-4457-8678, S. Obraztsov, S. Petrushanko, V. Savrin
Novosibirsk State University (NSU), Novosibirsk, Russia V. Blinov59, T.
Dimova59, L. Kardapoltsev59, A. Kozyrev59, I. Ovtin59, O. Radchenko59, Y.
Skovpen590000-0002-3316-0604 Institute for High Energy Physics of National
Research Centre ‘Kurchatov Institute’, Protvino, Russia I.
Azhgirey0000-0003-0528-341X, I. Bayshev, D. Elumakhov, V. Kachanov, D.
Konstantinov0000-0001-6673-7273, P. Mandrik0000-0001-5197-046X, V. Petrov, R.
Ryutin, S. Slabospitskii0000-0001-8178-2494, A. Sobol, S.
Troshin0000-0001-5493-1773, N. Tyurin, A. Uzunian, A. Volkov National Research
Tomsk Polytechnic University, Tomsk, Russia A. Babaev, V. Okhotnikov Tomsk
State University, Tomsk, Russia V. Borshch, V. Ivanchenko0000-0002-1844-5433,
E. Tcherniaev0000-0002-3685-0635 University of Belgrade: Faculty of Physics
and VINCA Institute of Nuclear Sciences, Belgrade, Serbia P.
Adzic600000-0002-5862-7397, M. Dordevic0000-0002-8407-3236, P.
Milenovic0000-0001-7132-3550, J. Milosevic0000-0001-8486-4604 Centro de
Investigaciones Energéticas Medioambientales y Tecnológicas (CIEMAT), Madrid,
Spain M. Aguilar-Benitez, J. Alcaraz Maestre0000-0003-0914-7474, A. Álvarez
Fernández, I. Bachiller, M. Barrio Luna, Cristina F.
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Cruz, A. Delgado Peris0000-0002-8511-7958, J.P. Fernández
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Fouz0000-0003-2950-976X, O. Gonzalez Lopez0000-0002-4532-6464, S. Goy
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Navarro Tobar0000-0003-3606-1780, C. Perez Dengra, A. Pérez-Calero
Yzquierdo0000-0003-3036-7965, J. Puerta Pelayo0000-0001-7390-1457, I.
Redondo0000-0003-3737-4121, L. Romero, S. Sánchez Navas, L. Urda
Gómez0000-0002-7865-5010, C. Willmott Universidad Autónoma de Madrid, Madrid,
Spain J.F. de Trocóniz, R. Reyes-Almanza0000-0002-4600-7772 Universidad de
Oviedo, Instituto Universitario de Ciencias y Tecnologías Espaciales de
Asturias (ICTEA), Oviedo, Spain B. Alvarez Gonzalez0000-0001-7767-4810, J.
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Bouza0000-0002-7225-7310, A. Soto Rodríguez, A. Trapote, N.
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Cantabria (IFCA), CSIC-Universidad de Cantabria, Santander, Spain J.A.
Brochero Cifuentes0000-0003-2093-7856, I.J. Cabrillo, A.
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Jimeno0000-0002-3639-0368, L. Scodellaro0000-0002-4974-8330, I. Vila, J.M.
Vizan Garcia0000-0002-6823-8854 University of Colombo, Colombo, Sri Lanka M.K.
Jayananda, B. Kailasapathy61, D.U.J. Sonnadara, D.D.C. Wickramarathna
University of Ruhuna, Department of Physics, Matara, Sri Lanka W.G.D.
Dharmaratna0000-0002-6366-837X, K. Liyanage, N. Perera, N. Wickramage CERN,
European Organization for Nuclear Research, Geneva, Switzerland T.K.
Aarrestad0000-0002-7671-243X, D. Abbaneo, J. Alimena0000-0001-6030-3191, E.
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Tropea, A. Tsirou, G.P. Van Onsem0000-0002-1664-2337, J. Wanczyk64, K.A.
Wozniak, W.D. Zeuner Paul Scherrer Institut, Villigen, Switzerland L.
Caminada650000-0001-5677-6033, A. Ebrahimi0000-0003-4472-867X, W. Erdmann, R.
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Universität Zürich, Zurich, Switzerland C. Amsler660000-0002-7695-501X, P.
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National Central University, Chung-Li, Taiwan C. Adloff67, C.M. Kuo, W. Lin,
A. Roy0000-0002-5622-4260, T. Sarkar370000-0003-0582-4167, S.S. Yu National
Taiwan University (NTU), Taipei, Taiwan L. Ceard, Y. Chao, K.F.
Chen0000-0003-1304-3782, P.H. Chen0000-0002-0468-8805, W.-S.
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Psallidas, A. Steen, H.y. Wu, E. Yazgan0000-0001-5732-7950, P.r. Yu
Chulalongkorn University, Faculty of Science, Department of Physics, Bangkok,
Thailand B. Asavapibhop0000-0003-1892-7130, C.
Asawatangtrakuldee0000-0003-2234-7219, N. Srimanobhas0000-0003-3563-2959
Çukurova University, Physics Department, Science and Art Faculty, Adana,
Turkey F. Boran0000-0002-3611-390X, S. Damarseckin68, Z.S.
Demiroglu0000-0001-7977-7127, F. Dolek0000-0001-7092-5517, I.
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Turkcapar, I.S. Zorbakir0000-0002-5962-2221 Middle East Technical University,
Physics Department, Ankara, Turkey B. Isildak73, G. Karapinar, K.
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Istanbul University, Istanbul, Turkey S. Cerci72, I. Hos81, B. Kaynak, S.
Ozkorucuklu, H. Sert0000-0003-0716-6727, D. Sunar Cerci720000-0002-5412-4688,
C. Zorbilmez Institute for Scintillation Materials of National Academy of
Science of Ukraine, Kharkov, Ukraine B. Grynyov National Scientific Center,
Kharkov Institute of Physics and Technology, Kharkov, Ukraine L.
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Jersey, Piscataway, New Jersey, USA B. Chiarito, J.P. Chou0000-0001-6315-905X,
A. Gandrakota0000-0003-4860-3233, Y. Gershtein0000-0002-4871-5449, E.
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Thomas, H. Wang0000-0002-3027-0752 University of Tennessee, Knoxville,
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Fiorendi0000-0003-3273-9419, S. Spanier0000-0002-8438-3197 Texas A&M
University, College Station, Texas, USA O. Bouhali950000-0001-7139-7322, M.
Dalchenko0000-0002-0137-136X, A. Delgado0000-0003-3453-7204, R. Eusebi, J.
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University, Lubbock, Texas, USA N. Akchurin, J. Damgov, V. Hegde, S. Kunori,
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Wang, A. Whitbeck Vanderbilt University, Nashville, Tennessee, USA E.
Appelt0000-0003-3389-4584, S. Greene, A. Gurrola0000-0002-2793-4052, W. Johns,
A. Melo, H. Ni, K. Padeken0000-0001-7251-9125, F. Romeo0000-0002-1297-6065, P.
Sheldon0000-0003-1550-5223, S. Tuo, J. Velkovska0000-0003-1423-5241 University
of Virginia, Charlottesville, Virginia, USA M.W. Arenton0000-0002-6188-1011,
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Hakala0000-0001-9586-3316, R. Hirosky0000-0003-0304-6330, M.
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Tannenwald0000-0002-5570-8095, S. White0000-0002-6181-4935, E.
Wolfe0000-0001-6553-4933 Wayne State University, Detroit, Michigan, USA N.
Poudyal0000-0003-4278-3464 University of Wisconsin - Madison, Madison, WI,
Wisconsin, USA K. Black0000-0001-7320-5080, T. Bose0000-0001-8026-5380, C.
Caillol, S. Dasu0000-0001-5993-9045, I. De Bruyn0000-0003-1704-4360, P.
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Mohammadi, D. Pinna, A. Savin, V. Shang, V. Sharma0000-0003-1287-1471, W.H.
Smith0000-0003-3195-0909, D. Teague, S. Trembath-Reichert, W.
Vetens0000-0003-1058-1163 †: Deceased
1: Also at TU Wien, Wien, Austria
2: Also at Institute of Basic and Applied Sciences, Faculty of Engineering,
Arab Academy for Science, Technology and Maritime Transport, Alexandria, Egypt
3: Also at Université Libre de Bruxelles, Bruxelles, Belgium
4: Also at Universidade Estadual de Campinas, Campinas, Brazil
5: Also at Federal University of Rio Grande do Sul, Porto Alegre, Brazil
6: Also at The University of the State of Amazonas, Manaus, Brazil
7: Also at University of Chinese Academy of Sciences, Beijing, China
8: Also at Department of Physics, Tsinghua University, Beijing, China
9: Also at UFMS, Nova Andradina, Brazil
10: Also at Nanjing Normal University Department of Physics, Nanjing, China
11: Now at The University of Iowa, Iowa City, Iowa, USA
12: Also at Institute for Theoretical and Experimental Physics named by A.I.
Alikhanov of NRC ‘Kurchatov Institute’, Moscow, Russia
13: Also at Joint Institute for Nuclear Research, Dubna, Russia
14: Now at British University in Egypt, Cairo, Egypt
15: Now at Ain Shams University, Cairo, Egypt
16: Also at Purdue University, West Lafayette, Indiana, USA
17: Also at Université de Haute Alsace, Mulhouse, France
18: Also at Ilia State University, Tbilisi, Georgia
19: Also at Erzincan Binali Yildirim University, Erzincan, Turkey
20: Also at CERN, European Organization for Nuclear Research, Geneva,
Switzerland
21: Also at RWTH Aachen University, III. Physikalisches Institut A, Aachen,
Germany
22: Also at University of Hamburg, Hamburg, Germany
23: Also at Isfahan University of Technology, Isfahan, Iran
24: Also at Brandenburg University of Technology, Cottbus, Germany
25: Also at Forschungszentrum Jülich, Juelich, Germany
26: Also at Physics Department, Faculty of Science, Assiut University, Assiut,
Egypt
27: Also at Karoly Robert Campus, MATE Institute of Technology, Gyongyos,
Hungary
28: Also at Institute of Physics, University of Debrecen, Debrecen, Hungary
29: Also at Institute of Nuclear Research ATOMKI, Debrecen, Hungary
30: Also at MTA-ELTE Lendület CMS Particle and Nuclear Physics Group, Eötvös
Loránd University, Budapest, Hungary
31: Also at Wigner Research Centre for Physics, Budapest, Hungary
32: Also at IIT Bhubaneswar, Bhubaneswar, India
33: Also at Institute of Physics, Bhubaneswar, India
34: Also at Punjab Agricultural University, Ludhiana, India
35: Also at Shoolini University, Solan, India
36: Also at University of Hyderabad, Hyderabad, India
37: Also at University of Visva-Bharati, Santiniketan, India
38: Also at Indian Institute of Technology (IIT), Mumbai, India
39: Also at Deutsches Elektronen-Synchrotron, Hamburg, Germany
40: Also at Sharif University of Technology, Tehran, Iran
41: Also at Department of Physics, University of Science and Technology of
Mazandaran, Behshahr, Iran
42: Now at INFN Sezione di Bari, Università di Bari, Politecnico di Bari,
Bari, Italy
43: Also at Italian National Agency for New Technologies, Energy and
Sustainable Economic Development, Bologna, Italy
44: Also at Centro Siciliano di Fisica Nucleare e di Struttura Della Materia,
Catania, Italy
45: Also at Scuola Superiore Meridionale, Università di Napoli Federico II,
Napoli, Italy
46: Also at Università di Napoli ’Federico II’, Napoli, Italy
47: Also at Consiglio Nazionale delle Ricerche - Istituto Officina dei
Materiali, Perugia, Italy
48: Also at Riga Technical University, Riga, Latvia
49: Also at Consejo Nacional de Ciencia y Tecnología, Mexico City, Mexico
50: Also at IRFU, CEA, Université Paris-Saclay, Gif-sur-Yvette, France
51: Also at Institute for Nuclear Research, Moscow, Russia
52: Now at National Research Nuclear University ’Moscow Engineering Physics
Institute’ (MEPhI), Moscow, Russia
53: Also at Institute of Nuclear Physics of the Uzbekistan Academy of
Sciences, Tashkent, Uzbekistan
54: Also at St. Petersburg Polytechnic University, St. Petersburg, Russia
55: Also at University of Florida, Gainesville, Florida, USA
56: Also at Imperial College, London, United Kingdom
57: Also at P.N. Lebedev Physical Institute, Moscow, Russia
58: Also at California Institute of Technology, Pasadena, California, USA
59: Also at Budker Institute of Nuclear Physics, Novosibirsk, Russia
60: Also at Faculty of Physics, University of Belgrade, Belgrade, Serbia
61: Also at Trincomalee Campus, Eastern University, Sri Lanka, Nilaveli, Sri
Lanka
62: Also at INFN Sezione di Pavia, Università di Pavia, Pavia, Italy
63: Also at National and Kapodistrian University of Athens, Athens, Greece
64: Also at Ecole Polytechnique Fédérale Lausanne, Lausanne, Switzerland
65: Also at Universität Zürich, Zurich, Switzerland
66: Also at Stefan Meyer Institute for Subatomic Physics, Vienna, Austria
67: Also at Laboratoire d’Annecy-le-Vieux de Physique des Particules,
IN2P3-CNRS, Annecy-le-Vieux, France
68: Also at Şırnak University, Sirnak, Turkey
69: Also at Near East University, Research Center of Experimental Health
Science, Nicosia, Turkey
70: Also at Konya Technical University, Konya, Turkey
71: Also at Piri Reis University, Istanbul, Turkey
72: Also at Adiyaman University, Adiyaman, Turkey
73: Also at Ozyegin University, Istanbul, Turkey
74: Also at Necmettin Erbakan University, Konya, Turkey
75: Also at Bozok Universitetesi Rektörlügü, Yozgat, Turkey
76: Also at Marmara University, Istanbul, Turkey
77: Also at Milli Savunma University, Istanbul, Turkey
78: Also at Kafkas University, Kars, Turkey
79: Also at Istanbul Bilgi University, Istanbul, Turkey
80: Also at Hacettepe University, Ankara, Turkey
81: Also at Istanbul University - Cerrahpasa, Faculty of Engineering,
Istanbul, Turkey
82: Also at Vrije Universiteit Brussel, Brussel, Belgium
83: Also at School of Physics and Astronomy, University of Southampton,
Southampton, United Kingdom
84: Also at Rutherford Appleton Laboratory, Didcot, United Kingdom
85: Also at IPPP Durham University, Durham, United Kingdom
86: Also at Monash University, Faculty of Science, Clayton, Australia
87: Also at Università di Torino, Torino, Italy
88: Also at Bethel University, St. Paul, Minneapolis, USA
89: Also at Karamanoğlu Mehmetbey University, Karaman, Turkey
90: Also at Bingol University, Bingol, Turkey
91: Also at Georgian Technical University, Tbilisi, Georgia
92: Also at Sinop University, Sinop, Turkey
93: Also at Erciyes University, Kayseri, Turkey
94: Also at Institute of Modern Physics and Key Laboratory of Nuclear Physics
and Ion-beam Application (MOE) - Fudan University, Shanghai, China
95: Also at Texas A&M University at Qatar, Doha, Qatar
96: Also at Kyungpook National University, Daegu, Korea


††thanks: These authors contributed equally to this work.††thanks: These
authors contributed equally to this work.††thanks: Corresponding author:
<EMAIL_ADDRESS>Corresponding author<EMAIL_ADDRESS>
# Quantum Non-Demolition Measurement on the Spin Precession of Laser-Trapped
171Yb Atoms

Y. A. Yang  CAS Center for Excellence in Quantum Information and Quantum
Physics, School of Physical Sciences, University of Science and Technology of
China, Hefei 230026, China  T. A. Zheng  CAS Center for Excellence in Quantum
Information and Quantum Physics, School of Physical Sciences, University of
Science and Technology of China, Hefei 230026, China  S.-Z. Wang  CAS Center
for Excellence in Quantum Information and Quantum Physics, School of Physical
Sciences, University of Science and Technology of China, Hefei 230026, China
W.-K. Hu  CAS Center for Excellence in Quantum Information and Quantum
Physics, School of Physical Sciences, University of Science and Technology of
China, Hefei 230026, China  Chang-Ling Zou  CAS Center for Excellence in
Quantum Information and Quantum Physics, School of Physical Sciences,
University of Science and Technology of China, Hefei 230026, China  Hefei
National Laboratory, University of Science and Technology of China, Hefei
230088, China  CAS Key Laboratory of Quantum Information,
University of Science and Technology of China, Hefei 230026, China.  T. Xia
CAS Center for Excellence in Quantum Information and Quantum Physics, School
of Physical Sciences, University of Science and Technology of China, Hefei
230026, China  Z.-T. Lu  CAS Center for Excellence in Quantum Information and
Quantum Physics, School of Physical Sciences, University of Science and
Technology of China, Hefei 230026, China  Hefei National Laboratory,
University of Science and Technology of China, Hefei 230088, China

###### Abstract

Quantum non-demolition (QND) measurement enhances the detection efficiency and
measurement fidelity, and is highly desired for its applications in precision
measurements and quantum information processing. We propose and demonstrate a
QND measurement scheme for the spin states of laser-trapped atoms. On 171Yb
atoms held in an optical dipole trap, a transition that is simultaneously
cycling, spin-state selective, and spin-state preserving is created by
introducing a circularly polarized beam of control laser to optically dress
the spin states in the excited level, while leaving the spin states in the
ground level unperturbed. We measure the phase of spin precession of $5\times
10^{4}$ atoms in a bias magnetic field of 20 mG. This QND approach reduces the
optical absorption detection noise by $\sim$19 dB, to a level of 2.3 dB below
the atomic quantum projection noise. In addition to providing a general
approach for efficient spin-state readout, this all-optical technique allows
quick switching and real-time programming for quantum sensing and quantum
information processing.

††preprint: APS/123-QED

##  I Introduction

The nuclear and electronic spin states of atoms, with the advantage of having
long coherence times, are of great importance in precision measurement and
quantum information experiments. Measurements on atomic spin states are
performed to realize magnetometers [1, 2, 3], optical clocks [4, 5, 6, 7], and
in experiments that search for permanent electric dipole moment [8, 9, 10, 11,
12, 13, 14, 15]. As an information carrier, the spin state is also widely used
in quantum information processing [16, 17, 18, 19, 20, 21, 22, 23] and quantum
simulation [24, 25]. For these applications, it is often crucial to measure
the population in each spin state with a high efficiency in order to reduce
the statistical errors in precision measurements and to enhance the readout
fidelities in quantum information experiments.

The populations in spin states can be determined either dispersively by
measuring the state-dependent phase shift of an off-resonant laser beam, or
dissipatively by measuring the absorption of or the fluorescence induced by
near-resonant light. In the recent quantum computing experiments, it is
challenging to achieve high fidelity of spin selectivity in the qubit-state
readout [21, 20, 23]. The detection efficiency is often limited by
measurement-induced spin flipping, upon which the quantum state is demolished
prematurely. For example, probing the states of a spin-1/2 system on non-
cycling transitions, as shown in Figs. 1(a) and 1(b), induces a spin flip with
just a few excitation–emission cycles [10, 16]. Alternatively, in a quantum
non-demolition (QND) measurement [26, 27, 28], the state is preserved under
repeated excitation–emission cycles, thus the signal-to-noise ratio of state
detection can be greatly enhanced. For this reason, QND measurements have
attracted increasing interests and have been successfully demonstrated on
various systems achieving improved measurement fidelity in quantum information
processing [29, 30, 31] and higher precision in quantum measurements [32, 33,
34].

Several QND strategies for spin-state detection have been demonstrated. For
example, a magnetic field can be applied to lift the degeneracy among
transitions of different magnetic sublevels [35], under the condition that the
induced Zeeman splittings are much larger than the transition linewidth. While
this method works efficiently, the required magnetic field and its on-and-off
switching can disturb the spin states, resulting in decoherence and loss of
sensitivity. Another strategy, more suitable for solid-state systems, is to
modify the density of states and induce a state-dependent spontaneous
relaxation rate via the Purcell effect [36]. Recently, such a scheme is
implemented for single rare-earth ions embedded in a nano-photonic cavity,
boosting the transition cyclicity by several orders of magnitude [37].

In this work, we present a theoretical analysis and an experimental
demonstration of a QND approach to probe spin states and measure the phase of
spin precession via optical excitation. By applying an ancillary control laser
to shift the excited states via the ac-Stark effect, while leaving the spin
states in the ground level unperturbed, the chosen optical transition can
simultaneously become cycling, spin-selective, and spin-preserving. AC Stark
shift has been successfully employed in many applications, including state-
selective manipulation of atomic internal states [38, 39, 40], site-selective
addressing in atom array [41, 42, 43, 44, 45], and narrow-line Sisyphus
cooling [46, 47, 48, 49]. Our approach is demonstrated on 171Yb atoms in an
optical dipole trap (ODT) whose wavelength satisfies the magic condition for
the probe transition [50]. QND measurements are performed on spin precession,
demonstrating a reduction in optical noise by $\sim$19 dB. This all-optical
approach of QND measurement avoids the need to switch and shield any control
magnetic fields. Its principle can be applied to many different atomic systems
and is compatible with general cold-atom experiments in precision measurements
and quantum information science. This novel method was introduced in Ref.[51],
where it was used in a measurement of the electric dipole moment of 171Yb.

##  II Principle

Figure 1: (a) The $F=1/2\leftrightarrow F=1/2$ case for detection of nuclear
spin states in a non-QND method. An atom in the dark state
$|g;1/2,+1/2\rangle$ does not scatter photons; an atom in $|g;1/2,-1/2\rangle$
scatters on average 3 photons before a spin flip occurs. (b) The
$F=1/2\leftrightarrow F=3/2$ case for detection of nuclear spin states in a
non-QND method. An atom in $|g;1/2,+1/2\rangle$ can be probed on a cycling
transition; an atom in $|g;1/2,-1/2\rangle$ scatters on average 1.5 photons
before a spin flip occurs. (c) The proposed QND approach for detection of
nuclear spin states. The optical dressing of the $|e\rangle$ state is by the
control beam. In this condition, the $|g;1/2,-1/2\rangle$ $\leftrightarrow$
$|e;3/2,+1/2\rangle$ transition is optically shifted and suppressed, while
$|g;1/2,+1/2\rangle$ $\leftrightarrow$ $|e;3/2,+3/2\rangle$ remains
unaffected. The spin state can be probed without risking spin flips. (d)
Layout of the setup. The atoms are trapped by an optical dipole trap (ODT) in
a vacuum chamber and $\mu$-metal shields (dashed rectangle). A $\cos\theta$
coil is used to generate a uniform bias magnetic field of 20 mG in the $x$
direction. The ODT, polarization beam, probe beam, and control beam are all
combined and directed in the $z$ direction. ODT is linearly polarized in the
$y$ direction; the polarization, probe, and control beams have the same
$\sigma^{+}$ circular polarization. (e) Energy levels and transitions of Yb.
In the QND approach, the probe is on the intercombination transition at 556
nm; the control transition is at 423 nm. The fast singlet-to-singlet
transition at 399 nm is used for optical pumping to produce spin polarization,
and for detecting spin states in the non-QND method.

The principle of optical pumping and spin-state detection is often explained
with the simple case of $F=1/2\leftrightarrow F=1/2$ [Fig. 1(a)]. Throughout
this paper, the quantization direction is chosen to be along the common
$\hat{k}$ vector of the polarization beam, probe beam and control beam. A
laser beam of resonant frequency and $\sigma^{+}$ polarization excites the
$m_{F}=-1/2$ state in the ground level, but not the $m_{F}=+1/2$ “dark state”.
In this case, an atom in $|g;1/2,-1/2\rangle$ absorbs and emits on average
only three photons before dropping into $|g;1/2,+1/2\rangle$, thus limiting
the fidelity of state detection. For the case of a different transition,
$F=1/2\leftrightarrow F=3/2$ [Fig. 1(b)], even though an atom in
$|g;1/2,+1/2\rangle$ can be probed repeatedly on the $|g;1/2,+1/2\rangle$
$\leftrightarrow$ $|e;3/2,+3/2\rangle$ cycling transition, an atom in
$|g;1/2,-1/2\rangle$ absorbs and emits on average only 1.5 photons before a
spin flip occurs. For a QND measurement, we need a transition that is
simultaneously cycling, spin selective and spin preserving.

We propose a QND measurement scheme based on the optical dressing effect.
Consider a ladder-type atomic system with three levels: the ground level
$|g\rangle$, the excited level $|e\rangle$, and the excited level $|c\rangle$
[Fig. 1(c)] ($|c\rangle$ can be either higher or lower than $|e\rangle$ in
energy). Their angular momenta are 1/2, 3/2, and 3/2, and spontaneous decay
rates are 0, $\Gamma_{e}$, and $\Gamma_{c}$, respectively. The control beam,
on resonance with the $|e\rangle\leftrightarrow|c\rangle$ transition, dresses
the $|e\rangle$ state with Rabi frequency $\Omega_{c}$. The optical dressing
is on all Zeeman states $|e;3/2,m_{F}\rangle$, except for the stretched state
$|e;3/2,+3/2\rangle$. The dressed Zeeman states are shifted by
$\pm\Omega_{c}/2$ to form Aulter-Towns doublets [52] and the stretched state
is protected by the angular momentum selection rules. Such a difference among
the Zeeman states is essential for spin-selective detection of the spin state.

To probe the nuclear spin state, the probe beam resonantly drives the
$|g\rangle\leftrightarrow|e\rangle$ transition with Rabi frequency
$\Omega_{p}$. In the condition where $\Omega_{p}\ll\Omega_{c},\Gamma_{e}$, the
optical transition strength to the dressed Zeeman states is reduced by a
factor of $\sim\Omega_{c}^{2}/(\Gamma_{e}\Gamma_{c})$. The
$|g;1/2,-1/2\rangle$ state then becomes a “dark state” and the rate of spin
flip is reduced by the same factor. With modest intensity of the control beam,
the reduction factor can be on the order of $10^{3}$. The atoms in
$|g;1/2,+1/2\rangle$ can be excited to the unaffected stretched state
repeatedly, and optical detection of the nuclear spin state with cycling
transition is realized. It is important to note that the control beam can be
switched on and off at a rate much faster than the spin precession rate, and
does not affect the spin states in the ground level.

##  III Experimental setup

We have implemented the QND measurement on the spin states of 171Yb (I = 1/2)
atoms in the ground level. The three levels $6s^{2}\,{}^{1}S_{0}\ (F=1/2)$,
$6s6p\,{}^{3}P_{1}\ (F=3/2)$ and $6s8s\,{}^{3}S_{1}\ (F=3/2)$ form a ladder
system as shown in Fig. 1(e). The QND measurement employs the following laser
beams and transitions: The probe beam at 556 nm, tuned to the resonance of
$6s^{2}\,{}^{1}S_{0}\leftrightarrow 6s6p\,{}^{3}P_{1}$ ($\Gamma_{e}/2\pi=182$
kHz), is supplied by a frequency-doubled diode laser; the control beam at 423
nm, tuned to the resonance of $6s6p\,{}^{3}P_{1}\leftrightarrow
6s8s\,{}^{3}S_{1}$($\Gamma_{c}=2\pi\times 1.7$ MHz), is supplied by a
frequency-doubled Ti:Sapphire laser; the polarization beam at 399 nm, tuned to
the resonance of $6s^{2}\,{}^{1}S_{0}\leftrightarrow
6s6p\,{}^{1}P_{1}$($\Gamma_{399}/2\pi=28$ MHz), is supplied by a frequency-
doubled diode laser. The probe beam, the control beam, and the polarization
beam all have the same circular polarization (e.g., $\sigma^{+}$), and all co-
propagate with the stationary ODT beam along the $z$ direction [Fig. 1(d)].
The absorption of the probe beam by the trapped atoms is imaged onto a CMOS
camera.

To prepare the atomic ensemble, 171Yb atoms are loaded into a two-stage
magneto-optical trap (MOT): The first-stage MOT is operated on the strong
transition (same as the polarization transition) to efficiently capture the
atoms from a Zeeman slower; the second-stage MOT on the narrow-linewidth
intercombination transition (same as the probe transition) cools the atoms to
20 $\mu$K. The cold atoms are then handed over to a movable ODT. More details
of the apparatus are given in Ref [50]. The atoms are carried into a
neighboring science chamber by translating the focal point of the movable ODT
along the $y$ direction [Fig. 1(d)] and, finally, handed over to a stationary
ODT pointed in the $z$ direction. The two ODTs are provided by two separate
fiber lasers. We prepare $10^{3}-10^{4}$ 171Yb atoms in the ODT for
measurements. A $\cos\theta$ coil [53] inside magnetic shields generates a
uniform B field ($\sim$ 20 mG) in the $x$ direction to drive spin precession.

The stationary ODT in the science chamber has a waist of $50\ \mathrm{\mu m}$
and a Rayleigh length of $\sim$ 4 mm, is linearly polarized in the $y$
direction, and has a power of 35 W and a wavelength of 1035.84 nm. This
wavelength meets the magic condition for the probe transition so that the
probe remains effective despite of the deep trapping potential of 200 $\mu$K
[50]. The probe linewidth is measured to be $\sim$ 400 kHz, reflecting Doppler
broadening at 100 $\mu$K. The vector light shift of the spin states introduced
by the linearly polarized ODT beam is negligible (< 1 mHz). The control beam
is focused on the atoms with a beam waist of about 300 $\mu$m. The parameters
for the control beam is determined by measuring the induced light shifts of
the probe transition (Appendix B). At the control beam power of 40 mW
($\Omega_{c}\sim 2\pi\times 40$ MHz), the spin-flip rate in the ground level
is reduced by a factor of $\Omega_{c}^{2}/(\Gamma_{e}\Gamma_{c})\sim 10^{3}$.
Since the control beam is far detuned from any transitions that connect to the
ground level, its effects on spin precession are negligible: the scalar light
shift of $|g\rangle$ induced by the control beam is at $\sim$ kHz, much less
than $\Gamma_{e}$; the vector light shift is at $\sim$ mHz, much less than the
precession frequency of 15 Hz.

##  IV Phase measurement of spin precession

Figure 2: (a) Timing sequence of the QND measurement. Atoms are initially
polarized by a 399 nm pulse (“Pol. 1”,
$\color[rgb]{0.015,0.2,1}\blacksquare$). After a given precession time, two
556 nm probe pulses (“Probe 1”, $\color[rgb]{0.498,1,0}\blacksquare$),
separated by $T_{p}/2$, measure the populations on $m_{F}=\pm 1/2$ states
successively. Each probe pulse is overlapped with a 423 nm control pulse
($\color[rgb]{0,0.753,1}\blacksquare$). The probe pulses can be repeated
multiple times. (b) The evolution of the atomic spin Bloch vector under a QND
measurement. (c) Timing sequence of a non-QND optical pumping measurement. A
normalization pulse (“Norm.”, $\color[rgb]{0.015,0.2,1}\blacksquare$) is
needed to measure the total population. The spin state population can only be
measured once with only a few excitation-emission cycles. (d) Spin precession
in the QND measurement. The initial spin polarization is about 90%. The
precession time is chosen to be 1s. (e) Spin precession measured with the non-
QND method, with other parameters identical to those of (d). (f) $S_{z,1}$ is
highly correlated with $S_{z,2}$. The reduced $\chi^{2}=1.03$ for the
proportional fit (solid line).

We demonstrate the advantage of the QND approach with phase measurements of
the spin precession of 171Yb atoms. The timing sequence for the QND
measurement is shown in Fig. 2(a). Initial spin polarization is produced by a
2 ms pulse of the polarization beam (“Pol. 1”, $I/I_{s}=3\times 10^{-4}$). The
spin polarized atoms precess about the bias magnetic field ($\sim$ 20 mG) at a
Larmor frequency of $\sim$ 15 Hz. After a given precession time, chosen to be
1 s in this study, an overlapping pulse of both the probe beam (0.4 ms,
$I/I_{s}=0.25$) and control beam, named “Probe 1+”, is applied for a spin
projection measurement. The population in $|g;1/2,+1/2\rangle$ ($\rho_{+}$) is
measured, while the population in $|g;1/2,-1/2\rangle$ ($\rho_{-}$) remains
unchanged because its excitation is suppressed by the presence of the control
beam. Half of a period ($T_{p}/2$) later, the precession swaps the populations
of $|g;1/2,+1/2\rangle$ and $|g;1/2,-1/2\rangle$ states, and “Probe 1-” is
fired to measure the original $\rho_{-}$ prior to swapping. The probe pulses
are repeated, each with a $T_{p}/2$ delay from the previous pulse [Fig. 2(a)].
The Bloch vector $S_{z}$ can be calculated as

$S_{z}=\rho_{+}-\rho_{-}=\frac{N_{+}-N_{-}}{N_{+}+N_{-}},$ (1)

where $\rho_{+}+\rho_{-}=1$, $N_{+}$ and $N_{-}$ are the number of atoms in
$|g;\,1/2,\,+1/2\rangle$ and $|g;\,1/2,\,-1/2\rangle$ derived from absorption
images of the probe pulses. For each pulse, “Probe 1+” or “Probe 1-”, an
absorption image taken by the CMOS camera is compared to a background image
taken without atoms to derive an optical depth value at each pixel. Both
$\rho_{+}$ and $\rho_{-}$ are measured under the same set of probe conditions,
with only $T_{p}/2$ apart in timing. In this way of calculating $S_{z}$, many
common-mode imperfections in the laser and detector parameters are suppressed.

For comparison, we have also conducted phase measurements based on the non-QND
optical pumping method. Here, the normalization, polarization and probe all
use the same laser tuned to the resonance of $6s^{2}\,{}^{1}S_{0}\
(F=1/2)\leftrightarrow 6s6p\,{}^{1}P_{1}\ (F=1/2)$ at 399 nm, and no control
beam is needed. A different timing sequence is used [Fig. 2(c)]. A 0.2 ms
normalization pulse [“Norm.” in Fig. 2(c)], fired at $T_{p}/2$ after the
initial polarization pulse (“Pol. 1”), measures the total population
$N_{+}+N_{-}$. Afterwards the atoms need to be repolarized with “Pol. 2”.
Following the free precession time, a 0.2 ms “Probe” pulse ($I/I_{sat}=3\times
10^{-4}$) is applied to measures $\rho_{-}$. In this non-QND approach, the
probe causes spin flips and can only be applied briefly before the spin
information is lost.

The Bloch vector evolves as $S_{z}=P_{z}\cos(2\pi ft+\phi_{0})$, where $P_{z}$
is the degree of spin polarization, $f$ is the Larmor precession frequency and
$\phi_{0}$ is the initial phase. The sinusoidal precession signal, shown in
Fig. 2(d) and 2(e) are obtained by measuring $S_{z}$ at different precession
times around 1 s. The measurement uncertainties in the QND approach are
significantly reduced in comparison with those in non-QND approach. A key
requirement of the QND approach is that the Bloch vector can be repeatedly
measured. As shown in Fig. 2(f), $S_{z,1}$, measured by “Probe 1”, is highly
correlated with $S_{z,2}$, measured by “Probe 2”.

##  V Measurement Uncertainty

The Larmor precession phase is determined in the $S_{z}$ measurements, with
the highest sensitivity occurring at the points of $\rho_{+}=\rho_{-}$. In the
QND approach, the variance of $S_{z}$ can be expressed as (see Appendix A.2),

$\sigma^{2}_{S_{z}}=\sigma^{2}_{\textbf{op}}+\frac{1}{N_{a}}\simeq\frac{4\overline{p}}{(N_{a}\bar{n})^{2}\epsilon}+\frac{1}{N_{a}},$
(2)

where the first term, denoted $\sigma^{2}_{\textbf{op}}$, describes the
optical noise arising from the fluctuations of both the incoming and the
absorbed photons. The second term is the atomic quantum projection noise. All
variables in Eq. (2) are defined in Table 1. Results of Eq. (2) are
approximation for weak absorption cases when $N_{a}\bar{n}/\overline{p}\ll 1$.
The numerical factor “4” is the total number of images used in the measurement
sequence combining “Probe 1+” and “Probe 1-”, with each containing both the
absorption and background images. The atomic quantum projection noise is
induced by the detection pulse “Probe 1+”, after which all other detection
pulses do not contribute any more quantum projection noise. Detailed
derivation for both QND and non-QND cases are given in Appendix A.

In principle, the excitation cycle in the QND measurement can be repeated
indefinitely until the optical noise becomes negligible compared to $1/N_{a}$.
In actual experiments, however, the number of excitation cycles is limited by
atom losses due to either heating or imperfection in the near-cycling
transition. Consider a pulse of $\bar{p}$ photons shot on the atomic clouds
through a region of interest of area $A_{\mathrm{ROI}}$, it induces an average
number of excitation cycles ($\bar{n}$). The two quantities are related as

$\exp(-b_{l}\overline{p}\frac{A_{\mathrm{abs}}}{A_{\mathrm{ROI}}})+\bar{n}b_{l}=1,$
(3)

where the first term characterizes the probability for the atom to survive in
the bright state, and the second term for the atom to either escape the trap
or decay into a dark state. The variables in the equation above are defined in
Table 1. The average number of excitation cycles ($\bar{n}$) is affected by
the loss branching ratio ($b_{l}$) that takes into account both loss
mechanisms. In the QND measurement of this study, the atoms are lost from the
trap after an average of 80 excitation cycles due to heating ($b_{l}=1/80$).
For comparison, in the non-QND measurement, the spin state is demolished after
an average of 3 excitation cycles due to optical pumping ($b_{l}=1/3$). This
large difference is indeed the essence of the QND advantage.

Table 1:  Term | Description |  Value in the QND approach |  Value in the non-QND approach
---|---|---|---
$A_{\mathrm{abs}}$ | Absorption cross section of an atom |  111The natural absorption cross section of the 556-nm probe transition on resonance is $0.147\ {\rm\mu m}^{2}$. However, the residual Doppler broadening results in a reduced cross section. $0.074\ {\rm\mu m}^{2}$ | $0.076\ {\rm\mu m}^{2}$
$A_{\mathrm{ROI}}$ | Area of region of interest(ROI) | $8900\ {\rm\mu m}^{2}$ | $8900\ {\rm\mu m}^{2}$
$\overline{p}$ |  Average number of probe photons inside ROI | $3.4\times 10^{6}$ | $0.57\times 10^{6}$
$\overline{n}$ |  Average number of excitation cycles | 23 | 2.5
$b_{l}$ |  Loss branching ratio | 1/80 | 1/3
$N_{a}$ | Number of atoms | $5\times 10^{4}$ | $5\times 10^{4}$
$\epsilon$ | Quantum efficiency of the camera | 0.8 (at 556 nm) | 0.4 (at 399 nm)
Figure 3: (a) Number of excitation cycles $\bar{n}$ vs. photon number
$\overline{p}$ in the probe pulse. In the non-QND case, $\bar{n}$ is limited
by spin flipping; In QND, $\bar{n}$ is limited by atom loss from the trap due
to heating. (b)Optical noise $\sigma^{2}_{\textbf{op}}$ vs. $\overline{p}$.
Number of atoms probed is $N_{a}=5\times 10^{4}$. The optimum conditions for
QND and non-QND cases occur at different $\overline{p}$ values.  Figure 4: The
variance $\sigma^{2}_{S_{z}}$ vs. the number of trapped atoms $N_{a}$. Blue
data points are for non-QND cases, and the green data points for QND cases.
The red dashed line indicates the $1/N_{a}$ atomic quantum projection noise.
For QND cases, the green dashed line models the optical noise, and the green
solid line is combined variance of both the optical noise and the atomic
quantum projection noise. The blue dashed line and blue solid line are
overlapped.

Fig. 3 shows the average number of excitation cycles $\bar{n}$ and the optical
noise $\sigma^{2}_{\textbf{op}}$ as a function of the photon number
($\overline{p}$) in the probe pulse. When $\overline{p}$ is small, $\bar{n}$
is proportional to $\overline{p}$, while $\sigma^{2}_{\textbf{op}}$ is
inversely proportional to $\overline{p}$. As $\overline{p}$ increases, loss
mechanisms come into effect, $\bar{n}$ becomes saturated and
$\sigma^{2}_{S_{z}}$ increases due to the photon shot noise. The optimum
choice for $\overline{p}$ occurs at the point when $\bar{n}$ starts to
saturate, and $\bar{n}$ is different between QND and non-QND cases.

Fig. 4 shows the variances of $S_{z}$ for both the QND and non-QND cases with
the number of trapped atoms varying in the range of $10^{3}-10^{4}$. The
measured results agree well with calculated ones. From non-QND to QND cases,
the optical noise is reduced by 19 dB, independent of the number of atoms. The
QND optical noise goes below the atomic quantum projection noise when
$N_{a}>3\times 10^{4}$, and is 2.3 dB below at $N_{a}=5\times 10^{4}$.

##  VI Discussion and Outlook

In this work, we have demonstrated a QND phase measurement of the spin
precession of atoms in an optical dipole trap. The 19 dB gain in the optical
noise can be further improved by reducing heating loss of the atoms due to
optical probing and scattering loss due to impure laser polarization of the
control beam. In the current setup, the atoms are transferred into the ODT of
200 $\mu$K depth at a temperature of 100 $\mu$K, and are heated out of the ODT
after an average of 80 excitation cycles. By applying laser cooling in the ODT
prior to the measurement sequence, the atom temperature could be lowered down
toward the Doppler-cooling limit of $4.4\ \mathrm{\mu K}$, thus increasing the
number of excitation cycles $\bar{n}$. Laser cooling would also reduce the
Doppler-broadened width of 400 kHz, towards the natural linewidth of 182 kHz,
and thus increase the photon absorption cross-section. Furthermore, replacing
the traveling wave ODT with an optical lattice would increase the trap depth
and reduce heating losses due to the probe beam. The impure laser polarization
of control beam causes excitation to the $|c\rangle$ state, followed by decay
into the lower-lying P levels. This leakage in the cycling transition can be
reduced with better polarization control. All these steps would combine to
reduce the loss branching ratio $b_{l}$, increase $\bar{n}$ and further
suppress the optical noise.

The use of the QND method introduced in this work can be expanded to a wide
range of applications. For example, QND measurements can help improve the
search sensitivity of a permanent electric dipole moment (EDM) of atoms [10,
54, 51]. The recently demonstrated tweezer array of Yb atoms, with their spin
states acting as qubits, is an emerging platform for quantum computation [16,
17, 20, 21, 23], on which the QND approach would help improve readout
fidelity. Suppression of spin-flip shown in this work can also be used to
decrease spin noise and increase interrogation time in spin squeezing
experiments [32]. Moreover, the QND approach can be employed to implement
quantum error correction that requires non-destructive detection of error
syndromes [55], as well as real-time feedback control on atomic spin states
[56, 57]. We emphasize that the all-optical control allows quick switching and
real-time programming [58].

While we have focused on the $(F,F+1,F+1)$ ladder-type system, the approach
can be generalized to other configurations, such as a $\Lambda$-type systems
or $(F,F+1,F)$ systems. Moreover, instead of the dissipative readout
demonstrated in this work, the optical dressing effect can also be applied to
dispersive atom-photon interaction [35], leading to applications such as
measurement-based spin squeezing, or generation of entanglement between
distant atomic ensembles for distributed quantum sensing [59].

###### Acknowledgements.

We would like to thank D. Sheng, Z.-S. Yuan, Y.-G. Zheng, and Y.-N. Lv for
helpful discussions. This work has been supported by the National Natural
Science Foundation of China through Grants No. 91636215, No. 12174371, No.
11704368, the Strategic Priority Research Program of the Chinese Academy of
Sciences through Grant No. XDB21010200, and Anhui Initiative in Quantum
Information Technologies through Grant No. AHY110000. C.-L.Z. was supported by
NSFC through Grant No. 11922411.

##  Appendix A Measurement uncertainty

###  A.1 Optical noise in absorption imaging

Population is detected by measuring the optical depth ($OD$) of the atomic
ensemble. $OD$ is derived from the number of detected photons in the reference
image without atoms ($p_{1}$) and that in the absorption image of the atomic
ensemble ($p_{2}$),

$OD=\ln({p_{1}}/{p_{2}}).$

For the number of incident probe photons of $p$, and take into account the
quantum efficiency of the camera $\epsilon$, the reference image has

$p_{1}=\sum_{i=1}^{p}d_{i},$

where $d_{i}$ is a binary variable indexing whether the $i$-th photon is
detected: $d_{i}\sim B(1,\epsilon)$. The number of photons in the absorption
image is

$p_{2}=\sum_{i=1}^{p-\sum_{j=1}^{N_{\pm}}n_{j}}d_{i},$

where $N_{\pm}$ is the number of atoms in the probed state and $n_{j}$ is the
number of photons scattered (absorbed) by the $j$-th atom.

The expectation values and variances for $p_{1}$ and $p_{2}$ can be expressed
as

$\displaystyle\mathrm{E}(p_{1})$ $\displaystyle=$
$\displaystyle\sigma_{p_{1}}^{2}=\overline{p}\epsilon,$
$\displaystyle\mathrm{E}(p_{2})$ $\displaystyle=$
$\displaystyle\overline{p}\epsilon-\frac{N_{a}}{2}\bar{n}\epsilon,$
$\displaystyle\sigma_{p_{2}}^{2}$ $\displaystyle=$
$\displaystyle\mathrm{E}(p-\sum_{j=1}^{N_{\pm}}n_{j})\mathrm{Var}(d_{i})+\mathrm{Var}(p-\sum_{j=1}^{N_{\pm}}n_{j})[\mathrm{E}(d_{i})]^{2}$
$\displaystyle=$
$\displaystyle\overline{p}\epsilon+N_{a}\overline{n}(2\epsilon^{2}-\epsilon)/2+N_{a}\overline{n}^{2}\epsilon^{2}/4.$

When calculating $\sigma_{p_{2}}^{2}$, it is assumed that $n_{j}$ follows the
Poisson distribution.

In our case, $\overline{p}\gg N_{a}\bar{n}\gg 1$. The expectation value and
variance for $OD$ are

$\displaystyle\mathrm{E}(OD)$ $\displaystyle\simeq$
$\displaystyle\frac{N_{a}\bar{n}}{2\overline{p}},$
$\displaystyle\sigma_{OD}^{2}$ $\displaystyle\simeq$
$\displaystyle\frac{2}{\overline{p}\epsilon}+\frac{N_{a}\overline{n}^{2}}{4\overline{p}^{2}}.$

These results follow the more detailed derivations found in Ref. [60, 61]. It
is worth noting that the optical noise in absorption imaging originates from
not only the intrinsic photon shot noise discussed above, but also technical
noise. In order to reach the fundamental photon-shot-noise level, a total of
30 images without atoms are taken after the detection pulses for a fringe-
removal algorithm [62].

###  A.2 Variance of measured $S_{z}$

As the populations of $|g;\frac{1}{2},-\frac{1}{2}\rangle$ and
$|g;\frac{1}{2},+\frac{1}{2}\rangle$ states are equal, the expectation value
and variance for $\rho_{+}$ are

$\displaystyle\mathrm{E}(\rho_{+})$ $\displaystyle=$
$\displaystyle\frac{1}{2},$ $\displaystyle\sigma_{\rho_{+}}^{2}$
$\displaystyle\simeq$
$\displaystyle\frac{5\overline{p}}{2(N_{a}\bar{n})^{2}\epsilon}+\frac{1}{4N_{a}}.$

For non-QND measurements, the variance of measured $S_{z}$ is

$\displaystyle\sigma_{S_{z}}^{2}$ $\displaystyle=$
$\displaystyle\mathrm{Var}(2\rho_{+}-1)$ $\displaystyle\simeq$
$\displaystyle\frac{10\overline{p}}{(N_{a}\bar{n})^{2}\epsilon}+\frac{1}{N_{a}}.$

For QND measurements, the variance of measured $S_{z}$ is

$\displaystyle\sigma_{S_{z}}^{2}$ $\displaystyle=$
$\displaystyle\mathrm{Var}(\rho_{+}-\rho_{-})$ $\displaystyle\simeq$
$\displaystyle\frac{4\overline{p}}{(N_{a}\bar{n})^{2}\epsilon}+\frac{1}{N_{a}}.$

The reduction in variances from non-QND to QND is largely due to the
difference in the $\bar{n}$ values, and is independent of $N_{a}$.

Figure 5: The measured light shift $\delta_{p}$ of the probe transition
against the control laser detuning. At a control laser beam of 4 mW and 300
$\mu$m radius, the Rabi frequency $\Omega_{c}/(2\pi)=12.5(1)\,\mathrm{MHz}$ is
determined.

##  Appendix B Parameters for the control laser

The 423 nm control beam drives the $6s6p\,{}^{3}P_{1}\leftrightarrow
6s8s\,{}^{3}S_{1}$ transition. The natural linewidth of this transition is
estimated to be $2\pi\times 1.7$ MHz, based on the known lifetime of the
$6s8s\,{}^{3}S_{1}$ level[63] and the estimated branching ratios. The detuning
$\Delta_{c}$ and the Rabi frequency $\Omega_{c}$ are experimentally determined
by measuring the light shift $\delta_{p}$ of the 556 nm probe transition (Fig.
5),

$\delta_{p}=\frac{\Delta_{c}}{2}\ln(1+\frac{2\Omega_{c}^{2}}{\Gamma_{c}^{2}+4\Delta_{c}^{2}}).$

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