{"kind":"Article","sha256":"73e3039dc80bb25789a1f80844e3f9c1c5f10c35666c975722a246ce9db05862","slug":"cosqua","location":"/experiment_controlling/cosqua.md","dependencies":[],"frontmatter":{"title":"Controlling the quasi-particle creation","short_title":"Controlling the phonons","authors":[{"nameParsed":{"literal":"Victor Gondret","given":"Victor","family":"Gondret"},"name":"Victor Gondret","orcid":"0009-0005-8468-161X","email":"victor.gondret@normalesup.org","affiliations":["Université Paris-Saclay, CNRS"],"url":"http://www.normalesup.org/~gondret/","id":"contributors-myst-generated-uid-0","corresponding":true}],"license":{"content":{"id":"CC-BY-NC-SA-4.0","name":"Creative Commons Attribution Non Commercial Share Alike 4.0 International","CC":true,"url":"https://creativecommons.org/licenses/by-nc-sa/4.0/"}},"github":"https://github.com/QuantumVictor","keywords":[],"affiliations":[{"id":"Université Paris-Saclay, CNRS","name":"Université Paris-Saclay, CNRS"}],"abbreviations":{"MOT":"Magneto-Optical Trap","BEC":"Bose-Einstein Condensate","MCP":"Micro-Channel Plate","DCE":"Dynamical Casimir Effect","HBT":"Hanbury-Brown and Twiss","CFD":"Constant Fraction Discriminator","TDC":"Time-to-Digital Converter","FPGA":"Field Programmable Gate Array","AOM":"Acousto-Optics Modulator","RF":"Radio-frequency","ODT":"Optical Dipole Trap","IGBT":"Insulated-Gap Bipolar Transistor","MPQ":"Max Planck Institute of Quantum Optics","PPT":"Positive Partial Transpose","SSR":"SuperSelection Rule","LN":"Logarithmic Negativity","UV":"UltraViolet","TOF":"Time-Of-Flight","TF":"Thomas-Fermi","CMB":"Cosmic Background Radiation"},"settings":{"myst_to_tex":{"codeStyle":"minted"}},"exports":[{"format":"md","filename":"cosqua.md","url":"/~gondret/phd_manuscript/build/cosqua-074b64474a8104988ea4a69d94c65c93.md"}]},"mdast":{"type":"root","children":[{"type":"block","position":{"start":{"line":8,"column":1},"end":{"line":8,"column":1}},"children":[{"type":"paragraph","position":{"start":{"line":10,"column":1},"end":{"line":13,"column":1}},"children":[{"type":"text","value":"This chapter focuses on the pair creation process and its dynamics. In the first section, we observe the breathing mode of the ","key":"FfRpZTHoNS"},{"type":"abbreviation","title":"Bose-Einstein Condensate","children":[{"type":"text","value":"BEC","key":"WaTzY19fFa"}],"key":"vLuJ1Kbpgk"},{"type":"text","value":" (","key":"qEivsuJGHc"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"1","key":"KFg4dpUduw"}],"identifier":"breathing_mode_section","label":"breathing_mode_section","kind":"heading","template":"Section %s","enumerator":"1","resolved":true,"html_id":"breathing-mode-section","remote":true,"url":"/cosqua-1spectrum","dataUrl":"/cosqua-1spectrum.json","key":"MRdHEwVC3l"},{"type":"text","value":"), then implement the protocol proposed in ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"kHwOculEK9"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"section","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"P6p3m10M22"}],"identifier":"forcing_oscillations","label":"forcing_oscillations","kind":"heading","template":"Section %s","enumerator":"3","resolved":true,"html_id":"forcing-oscillations","remote":true,"url":"/dce-bec-time","dataUrl":"/dce-bec-time.json","key":"RhF8RIkf5w"},{"type":"text","value":" ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"lHbgChRF6V"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"3","key":"UpelKmtgrp"}],"identifier":"forcing_oscillations","label":"forcing_oscillations","kind":"heading","template":"Section %s","enumerator":"3","resolved":true,"html_id":"forcing-oscillations","remote":true,"url":"/dce-bec-time","dataUrl":"/dce-bec-time.json","key":"TUmZ3RUi0h"},{"type":"text","value":" of ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"fQlXbKFWwd"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"Chapter 1","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"VZV8afwo4S"}],"identifier":"forcing_oscillations","label":"forcing_oscillations","kind":"heading","template":"Section %s","enumerator":"3","resolved":true,"html_id":"forcing-oscillations","remote":true,"url":"/dce-bec-time","dataUrl":"/dce-bec-time.json","key":"mKd42P5Q2h"},{"type":"text","value":" to drive oscillations at an arbitrary frequency ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"NerDaDUIGr"},{"type":"inlineMath","value":"\\omega_d","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"html":"<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><msub><mi>ω</mi><mi>d</mi></msub></mrow><annotation encoding=\"application/x-tex\">\\omega_d</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.5806em;vertical-align:-0.15em;\"></span><span class=\"mord\"><span class=\"mord mathnormal\" style=\"margin-right:0.03588em;\">ω</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.3361em;\"><span style=\"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">d</span></span></span></span><span class=\"vlist-s\">​</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.15em;\"><span></span></span></span></span></span></span></span></span></span>","key":"jK2tRmjpgl"},{"type":"text","value":".\nIn ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"GJaJ5V9PEb"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"subsection","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"SnCzJx83QG"}],"identifier":"bogo_dispersion_section","label":"bogo_dispersion_section","kind":"heading","template":"Section %s","enumerator":"3","resolved":true,"html_id":"bogo-dispersion-section","remote":true,"url":"/cosqua-1spectrum","dataUrl":"/cosqua-1spectrum.json","key":"C2nyATvjjN"},{"type":"text","value":" ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"AC83ke7X8F"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"3","key":"LsApRNWhlL"}],"identifier":"bogo_dispersion_section","label":"bogo_dispersion_section","kind":"heading","template":"Section %s","enumerator":"3","resolved":true,"html_id":"bogo-dispersion-section","remote":true,"url":"/cosqua-1spectrum","dataUrl":"/cosqua-1spectrum.json","key":"SKLRtx7YQh"},{"type":"text","value":", we measure the wave-vector of the detected quasi-particles as a function of frequency which allow us to recover the Bogoliubov dispersion relation.\nThe next section focuses on the exponential pair creation process. We observe a strong oscillation of the atom number that we explain in ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"tlToiBFpfz"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"subsection","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"Fj99z5mkUs"}],"identifier":"oscillation_atom_vs_phonon_basis","label":"oscillation_atom_vs_phonon_basis","kind":"heading","template":"Section %s","enumerator":"3","resolved":true,"html_id":"oscillation-atom-vs-phonon-basis","remote":true,"url":"/cosqua-2exponential-creation","dataUrl":"/cosqua-2exponential-creation.json","key":"NBvrUkNaGJ"},{"type":"text","value":" ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"V42Jq2egTk"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"3","key":"NOBD9tcwFE"}],"identifier":"oscillation_atom_vs_phonon_basis","label":"oscillation_atom_vs_phonon_basis","kind":"heading","template":"Section %s","enumerator":"3","resolved":true,"html_id":"oscillation-atom-vs-phonon-basis","remote":true,"url":"/cosqua-2exponential-creation","dataUrl":"/cosqua-2exponential-creation.json","key":"IDXsfv0ySU"},{"type":"text","value":".\nSuch oscillation is due to the non-adiabaticity of the mapping from the phonon basis to the atom basis that was introduced in the ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"FmZll0eCMF"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"chapter 1, section","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"NnOkw63Nmj"}],"identifier":"controlling_creation_phonons","label":"controlling_creation_phonons","kind":"heading","template":"Section %s","enumerator":"3","resolved":true,"html_id":"controlling-creation-phonons","remote":true,"url":"/dce-bogoliubov","dataUrl":"/dce-bogoliubov.json","key":"djahhwqBSC"},{"type":"text","value":" ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"SFzhbJzt9o"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"3","key":"klYjbk2l6g"}],"identifier":"controlling_creation_phonons","label":"controlling_creation_phonons","kind":"heading","template":"Section %s","enumerator":"3","resolved":true,"html_id":"controlling-creation-phonons","remote":true,"url":"/dce-bogoliubov","dataUrl":"/dce-bogoliubov.json","key":"rNxonhfh5l"},{"type":"text","value":". ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"dbplG5wGGi"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"Subsection","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"OchEEnbCOk"}],"identifier":"measuring_growth_rate","label":"measuring_growth_rate","kind":"heading","template":"Section %s","enumerator":"4","resolved":true,"html_id":"measuring-growth-rate","remote":true,"url":"/cosqua-2exponential-creation","dataUrl":"/cosqua-2exponential-creation.json","key":"hd6XWjopYl"},{"type":"text","value":" ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"OXUswkp3ge"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"4","key":"TCWpEKiPJY"}],"identifier":"measuring_growth_rate","label":"measuring_growth_rate","kind":"heading","template":"Section %s","enumerator":"4","resolved":true,"html_id":"measuring-growth-rate","remote":true,"url":"/cosqua-2exponential-creation","dataUrl":"/cosqua-2exponential-creation.json","key":"Kqx9XWX3mm"},{"type":"text","value":" focuses on the measurement of the growth rate. We observe a deviation from the theoretical growth rate, which we interpret as the decay rate. Although these measurements are preliminary, they align with the decay rate recently derived by ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"zRqoq1Xrxy"},{"type":"cite","identifier":"micheli_phonon_2022","label":"micheli_phonon_2022","kind":"narrative","position":{"start":{"line":10,"column":1338},"end":{"line":10,"column":1358}},"children":[{"type":"text","value":"Micheli & Robertson (2022)","key":"tz1PFUC9nT"}],"enumerator":"1","key":"vawdOLtq8f"},{"type":"text","value":" for a quasi-","key":"jdaKqrUG4J"},{"type":"abbreviation","title":"Bose-Einstein Condensate","children":[{"type":"text","value":"BEC","key":"hIGgG5Wxql"}],"key":"V2XYWFc19s"},{"type":"text","value":". Finally, in ","key":"UTbYsFGD9S"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"subsection","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"FssaLQXa1v"}],"identifier":"saturation_growth_section","label":"saturation_growth_section","kind":"heading","template":"Section %s","enumerator":"5","resolved":true,"html_id":"saturation-growth-section","remote":true,"url":"/cosqua-2exponential-creation","dataUrl":"/cosqua-2exponential-creation.json","key":"wFSqowF8JE"},{"type":"text","value":" ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"b6S02Gad78"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"5","key":"zmkcdH777h"}],"identifier":"saturation_growth_section","label":"saturation_growth_section","kind":"heading","template":"Section %s","enumerator":"5","resolved":true,"html_id":"saturation-growth-section","remote":true,"url":"/cosqua-2exponential-creation","dataUrl":"/cosqua-2exponential-creation.json","key":"wDQlHJwx8a"},{"type":"text","value":", we present the saturation of the growth process, and in ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"ajiZ7QK3Ty"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"subsection","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"ESZcImpOMG"}],"identifier":"shift_section","label":"shift_section","kind":"heading","template":"Section %s","enumerator":"6","resolved":true,"html_id":"shift-section","remote":true,"url":"/cosqua-2exponential-creation","dataUrl":"/cosqua-2exponential-creation.json","key":"PUMXFp0zBr"},{"type":"text","value":" ","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"Cq3tpXRIF1"},{"type":"crossReference","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"children":[{"type":"text","value":"6","key":"hM6BfgplGD"}],"identifier":"shift_section","label":"shift_section","kind":"heading","template":"Section %s","enumerator":"6","resolved":true,"html_id":"shift-section","remote":true,"url":"/cosqua-2exponential-creation","dataUrl":"/cosqua-2exponential-creation.json","key":"DBKKPfjmrU"},{"type":"text","value":", we report on an unexpected shift in the phonon wavevector.","position":{"start":{"line":10,"column":1},"end":{"line":10,"column":1}},"key":"WhozQCAihq"}],"key":"rPYhk8rT8z"},{"type":"comment","value":" \n\n\n[Subsection](#measuring_growth_rate) [%s](#measuring_growth_rate) focuses on the measurement of the growth rate. We measure a deviation from the theoretical growth rate that we interpret as the decay rate. Even though these measurements are preliminary, they are compatible with the decay rate recently derived by @micheli_phonon_2022 for a quasi-BEC. Finally, we show in [subsection](#saturation_growth_section) [%s](#saturation_growth_section) the saturation of the growth process and we report in [subsection](#shift_section) [%s](#shift_section) about an unknown shift of the phonon wave-vector.  ","key":"RM40GZ97SC"},{"type":"comment","value":" \n```{figure} images/apparatus.png\n:name: expe_setup_apparatus\n:alt: Image of the experimental setup\n:align: center\n:width: 65%\n\nExperimental setup: the vertically elongated BEC is trapped in a cross dipole trap. The trapping laser is modulated at twice the trap frequency with a small amplitude for a few periods (6 periods in the red curve inset). The BEC enters breathing mode, its width oscillates at twice the trap frequency and the amplitude of its oscillation increases with both the amplitude and the excitation duration. The BEC expected width is shown in the inset, with the green curve. When the laser stops modulating, the BEC keeps oscillating, hence keeps exciting one Bogoliubov mode. Once the trap is switched off, the collective excitation is mapped to witness atoms that are detected just before and after the BEC. \n``` \n","key":"Vgvu3VUy9T"},{"type":"comment","value":" \nThis chapter goes through the description of the experimental results. The protocol to excite pairs always follows the same recipe: the BEC is excited about a few oscillations near the breathing mode by modulating the trap frequency, see the red inset of [](#expe_setup_apparatus). The BEC enters a breathing mode at twice the frequency of the trap and keeps oscillating even after the trap modulation stopped, see green inset. \n\n```{figure} images/apparatus.png\n:name: expe_setup_apparatus\n:alt: Image of the experimental setup\n:align: center\n:width: 65%\n\nExperimental setup: the vertically elongated BEC is trapped in a cross dipole trap. The trapping laser is modulated at twice the trap frequency with a small amplitude for a few periods (6 periods in the red curve inset). The BEC enters breathing mode, its width oscillates at twice the trap frequency and the amplitude of its oscillation increases with both the amplitude and the excitation duration. The BEC expected width is shown in the inset, with the green curve. When the laser stops modulating, the BEC keeps oscillating, hence keeps exciting one Bogoliubov mode. Once the trap is switched off, the collective excitation is mapped to witness atoms that are detected just before and after the BEC. \n```\n\nThe breathing of the BEC excites a single Bogoliubov mode, whose energy corresponds to half the breathing frequency. As a result, a well-defined Bogoliubov mode $k$ is excited. When the trap is released, the collective excitation is mapped to witness atoms that are detected with the MCP. Phonon being produced in pairs, with opposite momenta along the vertical direction, one pair arrive before the BEC and one after. The last blue plot of [](#expe_setup_apparatus) represents the histogram of the detected atoms. The BEC is detected after a 307.3 time-fo-flight: it is the central peak. The two phonon peaks are detected before and after the BEC, around 306.3 and 308.3 ms.\n\nThe first part of this chapter focuses on the creation  ","key":"Te0n5vqkR8"}],"data":{"part":"abstract"},"key":"RHVfUwbIne"},{"type":"block","position":{"start":{"line":49,"column":1},"end":{"line":49,"column":1}},"children":[{"type":"admonition","kind":"tip","children":[{"type":"admonitionTitle","children":[{"type":"text","value":"What we knew, what is new ?","position":{"start":{"line":56,"column":1},"end":{"line":56,"column":1}},"key":"qlElY3JeDS"}],"key":"KjvI8Dm8EC"},{"type":"paragraph","position":{"start":{"line":57,"column":1},"end":{"line":57,"column":1}},"children":[{"type":"text","value":"The experiments reported in this chapter were conducted as part of this PhD work and represent original research.","position":{"start":{"line":57,"column":1},"end":{"line":57,"column":1}},"key":"rV8ziEdI5o"}],"key":"fC92sjy58J"}],"key":"b5gmATEohw"}],"key":"fbbwlaBms2"}],"key":"aI0tnqZI3q"},"references":{"cite":{"order":["micheli_phonon_2022"],"data":{"micheli_phonon_2022":{"label":"micheli_phonon_2022","enumerator":"1","doi":"10.1103/PhysRevB.106.214528","html":"Micheli, A., & Robertson, S. (2022). Phonon decay in 1D atomic Bose quasicondensates via Beliaev-Landau damping. <i>Physical Review B</i>, <i>106</i>(21), 214528. <a target=\"_blank\" rel=\"noreferrer\" href=\"https://doi.org/10.1103/PhysRevB.106.214528\">10.1103/PhysRevB.106.214528</a>","url":"https://doi.org/10.1103/PhysRevB.106.214528"}}}},"footer":{"navigation":{"prev":{"title":"Physical description and limits of the detector","short_title":"Physics of the detector","url":"/mcp-physics","group":"On the entanglement of quasi-particles in a Bose-Einstein condensate"},"next":{"title":"Measuring the Bogoliubov dispersion relation","url":"/cosqua-1spectrum","group":"On the entanglement of quasi-particles in a Bose-Einstein condensate"}}},"domain":"http://localhost:3011"}