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Towards Testing Bell's Inequality Using Atoms Correlated in Momentum

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Towards Testing Bell's Inequality Using Atoms Correlated in Momentum Towards testing Bell’s inequality using atoms correlated in momentum Almazbek Imanaliev To cite this version: Almazbek Imanaliev. Towards testing Bell’s inequality using atoms correlated in momentum. Optics [physics.optics]. Université Paris Saclay (COmUE), 2016. English. NNT : 2016SACLO003. tel- 01327148 HAL Id: tel-01327148 https://pastel.archives-ouvertes.fr/tel-01327148 Submitted on 6 Jun 2016 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. 1176$&/ 7+(6('('2&725$7 '(/¶81,9(56,7(3$5,66$&/$< SUpSDUpHj /¶,167,787'¶237,48(*5$'8$7(6&+22/ e&2/('2&725$/(1 2QGHVHW0DWLqUH ('20 6SpFLDOLWpGHGRFWRUDW3K\VLTXH 3DU $OPD]EHN,PDQDOLHY 7RZDUGVWHVWLQJ%HOO¶VLQHTXDOLW\XVLQJDWRPVFRUUHODWHGLQPRPHQWXP 7KqVHSUpVHQWpHHWVRXWHQXHj3DODLVHDXOHPDUV &RPSRVLWLRQGX-XU\ 07&RXGUHDX3UpVLGHQW8QLYHUVLWp3DULV9,, 0%/DEXUWKH7ROUD5DSSRUWHXU8QLYHUVLWpGH3DULV;,,, 0)3HUHLUD'RV6DQWRV5DSSRUWHXU6<57( 0PH/3UXYRVW([DPLQDWULFH8QLYHUVLWp3DULV6XG 0'%RLURQ'LUHFWHXUGHWKqVH,QVWLWXWG¶2SWLTXH 0$$VSHFW,QYLWp,QVWLWXWG¶2SWLTXH Declaration of Authorship I declare that this thesis is a presentation of my original research work unless oth- erwise stated with due reference to the literature and acknowledgement of collaborative research and discussions. i We must abandon the world view advocated by Einstein, sometimes referred to as 'local realism'. One might ask which of the ideas leading to the Bell inequalities should be abandoned: locality or realism? For our part, it seems difficult to understand these two notions as being independent. How could one conceive of independent physical realities for two spatially separated systems but which were nevertheless able to remain in contact via an instantaneous, superluminal interaction? It is our view that the nonlocality of quantum mechanics, often presented as the conclusion to be drawn from the violation of the Bell inequalities, represents a negation of the whole local realist view of the world. Grynberg, Aspect & Fabre 2010, p.432 [62] Acknowledgements Searching a short term project for a one month internship, I went to see Chris Westbrook hoping that he might have one in his group - atomic optics group of Charles Fabry laboratory. Chris kindly accepted me in his office and described the observation of the superradiance phenomenon with the "helium" experiment. I appreciated a lot the explanation of Chris with enthusiasm and I liked the subject which involved atoms, photons, quantum physics and more. Thanks to Chris, I could get the internship on the statistical analysis of the superradiance which was my first step in the cold atom experiments domain. I would like to thank Chris who made possible for me to do a PhD following the internship in his group. Although his administrative responsibilities, Chris could find time to see us to discuss physics and gave his point of view which contributed a lot to my understanding of physics. I feel very lucky for having met and having been supervised by Denis Boiron. He is a very good pedagogue and indeed had a great impact in my personal advancement of physics. Denis visits experiment in the morning and late in the afternoon each day. I was pleased to see my supervisor two times per day during which I enjoyed discussing confronting problems, new ideas and even experimenting till late hours. I have a good souvenir of having passed several hours on changing the mirror of one of the MOT beams although initially we thought that it should be done in few minutes. I appreciated Denis' personal traits and his nice humor. I would like to express my gratitude to Denis not only for supervising and teaching me but also supporting me through three years. I had a pleasure to work with Marc Cheneau who joined our group in 2012. He is a very talented scientist and I admired his analytical reasoning and his strong knowledge in physics. Indeed, I learned a lot from him both experiments and theory and I appreciated his invaluable advices. He backed us up not only in the laboratory but in the soccer tournament between different laboratories on the Saclay. I wish you all the best with your new experiment. I would like to thank our 'spiritual leader' Alain Aspect. I am very happy that I could work on the PhD thesis subject-Bell's inequality test, of our leader in his own group. During writing my thesis, I benefited a lot from his works which I admired for its simplicity and pedagogical approach. I was honored by his partipication in my thesis defense. Of course, experiments is the team work and each member of team progresses based on the accomplished works by the earlier colleagues. I would like to thank Marie Bonneau and Josselin Ruaudel for their contribution whom I met at the beginning of my PhD. I worked two years with Raphael Lopes and I thank him for having me introduced to the experimental physics and coming to my thesis despite the long journey from London. You are hardworking student and I wish you success in your scientific career. I enjoyed iii a lot to work with Pierre Dussarrat, a cheerful and intelligent guy. He helped me a lot in realizing many tests on the Bragg pulse and taught me french phrases which I find useful in my daily life in France. I am sure that with Maxime Perrier, new PhD student in our team, the experiment is in good hands, and the test of the non-locality will be demonstrated successfully. Besides the science, I had a great three years with my colleagues in the Charles Fabry laboratory: Guilhem, Amaudric, Qeuntin, Hugo, Lorenzo, Cecile, Vincent, Ais- ling, Bess, Laurianne, Lynn, Samuel, Ralf, Kilian, Jeremie, Rockson, Valentin, Henning. Whether it is summer school of les Houches or YAO, soccer tournament, partys or just our daily life in the laboratories, I have good memories with you. Moreover I would like to thank permanent members of the atom optics group and quantum optics: Isabelle Bouchoule, Thomas Bourdel, David Clement, Vincent Josse, Laurent Sanchez-Palencia, Antoine Browaeys, Yvan Sortais, Thierry Lahaye for the discussions and loans of material. My gratitudes are to Andre Villing, Fred Moron, Andre Guilbaud, and Patrick Roth, Florence Nogrette for their technical assistance. I would like to thank also reporters who accepted reading my thesis. Last but not the least, I would like to thank people who supported me, my family, my friends. Physical Constants Speed of light in vacuum c = 2:997 924 58 108 m s−1 × −27 Atomic mass constant mu = 1:660 539 040 10 kg × −23 −1 Boltzmann constant kB = 1:380 648 52 10 JK × −12 −1 Electric constant "0 = 8:854 187 817::: 10 F m × −31 Electron mass me = 9:109 383 56 10 kg × Elementary charge e = 1:602 176 6208 10−19 C × −7 −2 Magnetic constant µ0 = 12:566 370 614::: 10 NA × Planck constant h = 6:626 070 040 10−34 J s × −34 Planck constant over 2π ~ = 1:054 571 800 10 J s × −10 Bohr radius a0 = 0:529 177 210 67 10 m × −26 −1 Bohr magneton µB = 927:400 9994 10 JT × Fine-structure constant α = 7:297 352 5664 10−3 × −27 Proton mass mp = 1:672 621 898 10 kg × −27 −1 Nuclear magneton µN = 5:050 783 699 10 JT × v Contents Declaration of Authorship i Acknowledgements iii Introduction 4 1 Second-order coherence of superradiance from Bose-Einstein conden- sate 5 1.1 Correlations and coherence .......................... 6 1.1.1 Definition of correlation function ................... 6 1.1.2 First order correlation function: phase coherence .......... 6 1.1.3 Second order correlation function: intensity coherence . 11 1.2 Superradiance from the Bose-Einsten condensate . 16 1.2.1 Superradiance from a sub-wavelength sample . 17 1.2.2 Raman superradiance from the Bose-Einstein condensate . 20 1.2.2.1 Experimental configuration . 20 1.2.3 Theory of Raman superradiance ................... 22 1.2.4 Experimental observation of superradiance . 25 1.3 Measurement of the second order correlation of superradiant peaks . 26 1.4 Conclusion ................................... 28 2 Bell's inequality test with massive particles: theory 34 2.1 Bell's theorem .................................. 34 2.1.1 Joint measurements of polarization correlated photon pairs . 34 2.1.2 Polarization correlation of EPR pairs . 36 2.1.3 The idea of local hidden variable theories . 38 2.1.4 Bell's inequalities ............................ 39 2.1.5 The experimental violation of Bell's inequality . 42 2.1.6 Loopholes in the experimental Bell's inequality tests . 43 2.2 The Bell's inequality test with helium atoms correlated in momentum space 45 2.2.1 The equivalence between schemes using external and internal de- grees of freedom for the Bell's inequality test . 45 2.2.2 The proposed scheme of the Bell's inequality test with the helium atoms .................................. 48 2.2.3 The atomic pair creation ....................... 49 2.2.3.1 The dynamical instability . 49 2.2.3.2 The dynamical instability as a four wave mixing process . 52 vi Contents vii 2.2.3.3 The four wave mixing in the non-depleted classical pump regime ............................. 55 2.2.3.4 The resulting state and its properties . 56 2.2.4 The bragg pulse ............................ 60 2.2.4.1 Statement of problem .................... 61 2.2.4.2 The equations of motion . 62 2.2.4.3 Solution of the equations .
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