{"kind":"Article","sha256":"bfb8ad5055728fbe0b27be0f815d484be7cecdbff03ac48f9483e2e842c4e285","slug":"bec-odt","location":"/bec/bec_odt.md","dependencies":[],"frontmatter":{"title":"Bose-Einstein condensation in an optical dipole trap","short_title":"BEC in ODT","subtitle":"Our nice source for non-classical states, detected with a (non burnt) MCP.","numbering":{"heading_1":{"enabled":true},"heading_2":{"enabled":true}},"content_includes_title":false,"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"}},"thumbnail":"/~gondret/phd_manuscript/build/dipoletrap_setup_pow-091b8143c65138ccc258d40d87118145.png","thumbnailOptimized":"/~gondret/phd_manuscript/build/dipoletrap_setup_pow-091b8143c65138ccc258d40d87118145.webp","exports":[{"format":"md","filename":"bec_odt.md","url":"/~gondret/phd_manuscript/build/bec_odt-c8309e793ead46b4071016efdc15b381.md"}]},"mdast":{"type":"root","children":[{"type":"block","children":[{"type":"heading","depth":2,"position":{"start":{"line":12,"column":1},"end":{"line":12,"column":1}},"children":[{"type":"text","value":"Optical dipole trap","position":{"start":{"line":12,"column":1},"end":{"line":12,"column":1}},"key":"RZkjQjKJ8p"}],"identifier":"dipole-trap","label":"dipole-trap","html_id":"dipole-trap","enumerator":"1","key":"JbPvUpTCQX"},{"type":"paragraph","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"children":[{"type":"text","value":"For the past few years, the dipole trap has not been very cooperative in our experiment. It started back in 2017 when the team chose to change the dipole trap laser to use more power and be able to load a hotter cloud for stability reasons. It was decided to buy a 30 W laser from Keopsys","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"key":"QbC1V3IDvI"},{"type":"footnoteReference","identifier":"keopsys_laser_ref","label":"keopsys_laser_ref","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"number":1,"enumerator":"1","key":"n9wwbqnt7m"},{"type":"text","value":". Sadly, after many delays, the new laser never delivered the expected power and was restrained to 20 W. During my thesis, it broke three times","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"key":"t1nb71cbn0"},{"type":"footnoteReference","identifier":"keopsys_reparation","label":"keopsys_reparation","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"number":2,"enumerator":"2","key":"OadrlRjKx4"},{"type":"text","value":", and we finally bought a new one from the ","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"key":"zdSMi7Kc9w"},{"type":"link","url":"https://www.ipgphotonics.com/products/lasers/industrial-cw-fiber-lasers/erbium-thulium-raman-fiber-lasers","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"children":[{"type":"text","value":"IPG","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"key":"hPpxSHROrr"}],"urlSource":"https://www.ipgphotonics.com/products/lasers/industrial-cw-fiber-lasers/erbium-thulium-raman-fiber-lasers","key":"XRFzvZ6hdE"},{"type":"text","value":" company","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"key":"By83c7mniE"},{"type":"footnoteReference","identifier":"ipg_laser","label":"ipg_laser","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"number":3,"enumerator":"3","key":"qgNuwtHL5J"},{"type":"text","value":".","position":{"start":{"line":14,"column":1},"end":{"line":14,"column":1}},"key":"dVyk4k7f3J"}],"key":"PyJnFksp9O"},{"type":"paragraph","position":{"start":{"line":16,"column":1},"end":{"line":16,"column":1}},"children":[{"type":"text","value":"However, when the dipole trap laser works, it works... on fire ! Indeed, the vertical beam arm hits (and heats) the micro-channel plate that burned... twice ! To overcome this issue, we placed a shield on the top of the ","key":"COQfeHyTuZ"},{"type":"abbreviation","title":"Micro-Channel Plate","children":[{"type":"text","value":"MCP","key":"qUyK7plgMZ"}],"key":"qlXgilOydp"},{"type":"text","value":" that reflects back the laser. This requires therefore to ","key":"fSBEoM2L3n"},{"type":"crossReference","position":{"start":{"line":16,"column":1},"end":{"line":16,"column":1}},"children":[{"type":"text","value":"deflect","position":{"start":{"line":16,"column":1},"end":{"line":16,"column":1}},"key":"cLfaA0XSS3"}],"identifier":"raman-transfer","label":"raman-transfer","kind":"heading","template":"Section %s","enumerator":"2","resolved":true,"html_id":"raman-transfer","key":"p2Vj8X8lVA"},{"type":"text","value":" the cloud when the trap is released so that the ","key":"fnySJfQlVO"},{"type":"abbreviation","title":"Micro-Channel Plate","children":[{"type":"text","value":"MCP","key":"hq9tSsvHez"}],"key":"nrBMaWMiIs"},{"type":"text","value":" detects the atoms. This is done during the Raman transfer. An entire section is dedicated to this shield installation on the ","key":"T2JOXmpdfl"},{"type":"crossReference","position":{"start":{"line":16,"column":1},"end":{"line":16,"column":1}},"children":[{"type":"text","value":"chapter","position":{"start":{"line":16,"column":1},"end":{"line":16,"column":1}},"key":"PlhcjPiCgk"}],"identifier":"shield_installation_section","label":"shield_installation_section","kind":"heading","template":"{name}","resolved":true,"html_id":"shield-installation-section","remote":true,"url":"/mcp-in-real-life","dataUrl":"/mcp-in-real-life.json","key":"YUUG3wc98U"},{"type":"text","value":" dedicated to the ","key":"redvAIikXL"},{"type":"abbreviation","title":"Micro-Channel Plate","children":[{"type":"text","value":"MCP","key":"lDwHY18YnX"}],"key":"EN8dvecfmC"},{"type":"text","value":".","key":"CKnvPlDFA4"}],"key":"lqd8ArFJeJ"},{"type":"container","kind":"figure","identifier":"dipole_trap_setup_power","label":"dipole_trap_setup_power","children":[{"type":"image","url":"/~gondret/phd_manuscript/build/dipoletrap_setup_pow-091b8143c65138ccc258d40d87118145.png","alt":"The dipole trap setup.","width":"80%","align":"center","key":"OZQTx33uGz","urlSource":"images/dipoletrap_setup_powerplot.png","urlOptimized":"/~gondret/phd_manuscript/build/dipoletrap_setup_pow-091b8143c65138ccc258d40d87118145.webp"},{"type":"caption","children":[{"type":"paragraph","position":{"start":{"line":31,"column":1},"end":{"line":31,"column":1}},"children":[{"type":"captionNumber","kind":"figure","label":"dipole_trap_setup_power","identifier":"dipole_trap_setup_power","html_id":"dipole-trap-setup-power","enumerator":"1","children":[{"type":"text","value":"Figure ","key":"MCDtsOulhu"},{"type":"text","value":"1","key":"h3mJ5lutV6"},{"type":"text","value":":","key":"duO9enHWHo"}],"template":"Figure %s:","key":"uXrAQjwVxl"},{"type":"text","value":"Left: Dipole trap setup: the vertical beam has a waist of 40.5(2) µm and the horizontal 109 µm. The vertical dipole trap hits the protective shield on the ","key":"DVu1ANIHqg"},{"type":"abbreviation","title":"Micro-Channel Plate","children":[{"type":"text","value":"MCP","key":"YZfJPh4U0y"}],"key":"uEk5DQgWTU"},{"type":"text","value":" not do damage it. The ","key":"RRVi0q1lS5"},{"type":"crossReference","position":{"start":{"line":31,"column":1},"end":{"line":31,"column":1}},"children":[{"type":"text","value":"Raman","position":{"start":{"line":31,"column":1},"end":{"line":31,"column":1}},"key":"QvMKHMy6M3"}],"identifier":"raman-transfer","label":"raman-transfer","kind":"heading","template":"Section %s","enumerator":"2","resolved":true,"html_id":"raman-transfer","key":"o0iUMOV357"},{"type":"text","value":" transfer kicks the atoms so that they do not hit the protective copper plate. Right: depth of the dipole trap as a function of the vertical position for 4W (top) and 0.7 W (bottom). The shaded vertical line represents the minimum of the trap, that shifts when the power changes.","position":{"start":{"line":31,"column":1},"end":{"line":31,"column":1}},"key":"j7EmDgWE2k"}],"key":"PwCD6NSpQE"}],"key":"q9zrubR3vb"}],"enumerator":"1","html_id":"dipole-trap-setup-power","key":"Els3ABMBTQ"},{"type":"paragraph","position":{"start":{"line":35,"column":1},"end":{"line":35,"column":1}},"children":[{"type":"text","value":"The dipole trap is formed of two arms: one vertical and one horizontal. The vertical trap has a waist of 40.5(2) µm and the horizontal waist is 108(2) µm","position":{"start":{"line":35,"column":1},"end":{"line":35,"column":1}},"key":"sxkRnN0pz6"},{"type":"footnoteReference","identifier":"note_waist","label":"note_waist","position":{"start":{"line":35,"column":1},"end":{"line":35,"column":1}},"number":4,"enumerator":"4","key":"lSvBgFLzaW"},{"type":"text","value":" ","position":{"start":{"line":35,"column":1},"end":{"line":35,"column":1}},"key":"q45XcwZ9nr"},{"type":"citeGroup","kind":"parenthetical","position":{"start":{"line":35,"column":1},"end":{"line":35,"column":1}},"children":[{"type":"cite","identifier":"partridge_bose_einstein_2010","label":"partridge_bose_einstein_2010","kind":"parenthetical","position":{"start":{"line":35,"column":169},"end":{"line":35,"column":198}},"children":[{"type":"text","value":"Partridge ","key":"vPNgNnZJPZ"},{"type":"emphasis","children":[{"type":"text","value":"et al.","key":"SOSF4A5hTl"}],"key":"TGo51MhXf1"},{"type":"text","value":", 2010","key":"SuAP47BNHg"}],"enumerator":"1","key":"TpupmsXs7Y"}],"key":"zYcmSML1LR"},{"type":"text","value":". The dipole trap is loaded from a 45 µK magnetic trap: only 10% of the atoms are trapped (","position":{"start":{"line":35,"column":1},"end":{"line":35,"column":1}},"key":"Xngya3i5on"},{"type":"inlineMath","value":"3\\times 10^6","position":{"start":{"line":35,"column":1},"end":{"line":35,"column":1}},"html":"3×1063\\times 10^63×106","key":"y7FTR7upVA"},{"type":"text","value":"). We use 4 W, which means the initial depth of the trap is 140 µK. Once loaded, the temperature of the trapped cloud is 20(2) µK, still above the condensation temperature of 3 µK. We therefore need to decrease the height of the trap. The latter is fixed on the vertical axis: the depth of the trap is a trade-off between the laser power and the gravity gradient.","position":{"start":{"line":35,"column":1},"end":{"line":35,"column":1}},"key":"aN0LW8In7m"}],"key":"tTcojQqz7T"},{"type":"paragraph","position":{"start":{"line":37,"column":1},"end":{"line":37,"column":1}},"children":[{"type":"text","value":"On the right of ","position":{"start":{"line":37,"column":1},"end":{"line":37,"column":1}},"key":"M5V2zkJ0gF"},{"type":"crossReference","position":{"start":{"line":37,"column":1},"end":{"line":37,"column":1}},"children":[{"type":"text","value":"Figure ","key":"XvLDeAybwZ"},{"type":"text","value":"1","key":"aqN1fIst7q"}],"identifier":"dipole_trap_setup_power","label":"dipole_trap_setup_power","kind":"figure","template":"Figure %s","enumerator":"1","resolved":true,"html_id":"dipole-trap-setup-power","key":"q7rvzy6WHo"},{"type":"text","value":" is shown the depth of the trap as a function of the vertical position for a 4 W laser (top) and a 0.7 W laser (bottom). When the power decreases, the depth of the trap decreases, but the center of the trap changes too: this is represented by the shaded vertical line on the figure. As we will see in subsection ","position":{"start":{"line":37,"column":1},"end":{"line":37,"column":1}},"key":"WCMQ0h5Zwu"},{"type":"crossReference","position":{"start":{"line":37,"column":1},"end":{"line":37,"column":1}},"children":[{"type":"text","value":"3","key":"ADzRojzk1r"}],"identifier":"evaporation_ramp_section","label":"evaporation_ramp_section","kind":"heading","template":"Section %s","enumerator":"3","resolved":true,"html_id":"evaporation-ramp-section","key":"eL3aS5yaxC"},{"type":"text","value":", the evaporation ramp must be smooth enough not to push the cloud.","position":{"start":{"line":37,"column":1},"end":{"line":37,"column":1}},"key":"CdqRgg7Bxp"}],"key":"FmJJ7JcXG5"},{"type":"comment","value":"The dipole trap vertical and horizontal arms are prepared on a dedicated bench for which more information are given in the [appendix](#dipole_trap_optics).","position":{"start":{"line":42,"column":1},"end":{"line":42,"column":1}},"key":"PrEl9EaAuQ"},{"type":"comment","value":"--> Dans le rapport de stage de Clothilde, il y a un typo dans un tableau. La façon dont est ajusté la taille du nuage ne va pas dans le cas du CBE. Il faut mettre un arctangeante. Le code qui calcul les résultat a-t-il ce typo ? Cela pourrait expliquer les résultats chelous.","position":{"start":{"line":44,"column":1},"end":{"line":44,"column":1}},"key":"bkpPybYtd3"},{"type":"comment","value":" \n### Adjusting the waist of the beams\n**The waist of the vertical beam** was measured by @bonneau_melange_2011 through parametric excitations. She reported a value of 43(1.5) µm. In the following two paragraphs, we give two protocols to measure the waist. We find a value of 42.5(3) and 41(1) in agreement with Bonneau's measurement.\n\n\n*Protocol*: we load a dipole trap and decrease the power up to a final value. Because of gravity, when the power of the beam decrease, the minimum of the total potential is shifted down. Here, we decrease the power of the laser beam, let the cloud expand for 1 ms and take a snapshot (emission imaging). We then adjust the density profile of the cloud with a Gaussian function to obtain its position.\\\n*Results:* On the left panel of [](#waist_verti_fig), the vertical position of the cloud is plotted as a function of the vertical beam power. The experimental points are fine-tuned by a waist of 42.5(3)µm which is in agreement with the expected waist.\n\n```{figure} images/waist_vertical.png\n:name: waist_verti_fig\n:alt: Measuring the waist of the vertical beam.\n:align: center\n:width: 100%\nMeasure of the waist by two different methods. Left: a snapshot of the cloud for various power gives access to the *in situ* position of the cloud. Data taken of February (21/02/2022). Right: excitation frequency of the breathing mode as a function of the laser power. Experimental points were extracted from various day, ranging from February 2022 to May 2024.\n```\n\n*Protocol:* The parametric excitation method consists of modulating the intensity of the dipole trap at a given frequency. When the frequency of excitation is equal to twice the transverse frequency, the breathing mode is excited [@chevy_transverse_2002]. When the excitation amplitude is quite high: typically a fraction of the final power, the system is excited in a quite a \"violent\" way, heating occurs and the width of the detected cloud is increased [@lopes_atomic_2014]. We expect also to detect fewer atoms. However, we sometime detect more atoms at resonance: this is due to the fact that the width of the BEC increased. The atomic flux is therefore lower, which increases the *detected* atom number due to the saturation of the MCP. Note however that this breathing mode frequency is 2$\\omega_\\perp$ only for a elongated trap: in the case of a spherical trap, its frequency is $\\sqrt{5}\\omega$ [@stringari_dynamics_1998]. \\\n*Results:* the excitation frequency is plotted as a function of the vertical power on the right panel of [](#waist_verti_fig). We adjust this curve with a theoretical waist of 41(1) µm which differs slightly from the expected waist. Note however that the experimental points that are reported here were extracted from different days (over a year and a half) and measured in different conditions (four different days). The power of the trap was not always really well calibrated due to a defective power-meter and a photodiode drift that was fixed recently.\n\n\n\n**The waist of the horizontal beam** was measured optically by two methods by @perrier_interferences_2020 who reported 107(3) µm and 110(4) µm. We can recover this value by measuring the trap frequency for several powers: we then adjust the theoretical curve with the waist as a free parameter. The trap frequency is measure by exciting the cloud in the first collective oscillation of the BEC [@stringari_collective_1996]. \\\n*Procedure:* we produce a BEC in the cross dipole trap (400 mW, 30 mW) respectively for the vertical and horizontal trap beams. At $t=0$, we quench the horizontal beam power to a different power. We then hold the cloud in the trap for different durations. For each hold time, we record the arrival time of the cloud measuring the atomic flux on the MCP with an oscilloscope. Indeed, the horizontal laser beam is responsible for the vertical confinement. We observe the arrival time to oscillate as a function of the hold time in the trap as shown on the left panel of [](#odth_waist_fig). We fit the signal to get the frequency of the oscillation, which corresponds to the frequency of the trap. The measurement is repeated for different laser powers: [](#odth_waist_fig) shows the trap frequency as a function of the power of the laser. \\\n*Result:* We adjust the waist of the trap to coincide the experimental data with the theoretical curve. This gives a value of 108(2) µm for the waist of the horizontal beam. This value is consistent with the value reported by @perrier_interferences_2020. \n\n\n```{figure} images/theoretical_waist_horizontal.png\n:name: odth_waist_fig\n:alt: Measuring the waist of the vertical beam.\n:align: center\n:width: 100%\nMeasure of the waist of the horizontal beam. Left: after a quench, the BEC oscillates in the trap. Its arrival time exhibits the same oscillation frequency. Each symbols corresponds to a different laser trap. The line is a sine fit of the experimental data from which we extract the frequency of the trap, which is the same than the frequency of the atoms. Right: the trap frequency as a function of the laser power. The solid line is adjusted to the experimental data that gives a waist of 108(2) µm. \n``` \n","key":"bCo8PCmkMw"},{"type":"heading","depth":2,"position":{"start":{"line":84,"column":1},"end":{"line":84,"column":1}},"children":[{"type":"text","value":"Raman transfer","position":{"start":{"line":84,"column":1},"end":{"line":84,"column":1}},"key":"LZnDq4Pi8O"}],"identifier":"raman-transfer","label":"raman-transfer","html_id":"raman-transfer","enumerator":"2","key":"V1hvqTnI7A"},{"type":"paragraph","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"children":[{"type":"text","value":"As mentioned earlier, the atoms must be polarized to decrease the inelastic ","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"key":"YJOVDci0rs"},{"type":"crossReference","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"children":[{"type":"text","value":"collision","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"key":"cTJDlvKq9a"}],"identifier":"losses-section","label":"losses-section","kind":"heading","template":"{name}","resolved":true,"html_id":"losses-section","remote":true,"url":"/bec-mot","dataUrl":"/bec-mot.json","key":"u8La58Gjvf"},{"type":"text","value":" rate and obtain a Bose-Einstein condensate. Since these atoms are sensitive to magnetic fields, they are deflected by residual magnetic fields during their 308 ms time-of-flight towards the ","key":"TdeBdEZ6H6"},{"type":"abbreviation","title":"Micro-Channel Plate","children":[{"type":"text","value":"MCP","key":"dI7DCzZL47"}],"key":"YzHWyAYpE9"},{"type":"text","value":". Therefore, we need to transfer them to the ","key":"CaNjfVtFJW"},{"type":"inlineMath","value":"m_j=0","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"html":"mj=0m_j=0mj​=0","key":"nRns55q501"},{"type":"text","value":" state when the trap is switched off. This internal state transfer is achieved using two laser beams in a Raman configuration that induces a two-photon transition. The laser is blue-detuned (600 MHz) from the ","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"key":"LvYuEisTLx"},{"type":"inlineMath","value":"2^3S_1-2^3P_0","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"html":"23S1−23P02^3S_1-2^3P_023S1​−23P0​","key":"cEtCNwXsPr"},{"type":"text","value":" transition, with one beam being ","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"key":"Jtf1nI13VT"},{"type":"inlineMath","value":"\\sigma^-","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"html":"σ−\\sigma^-σ−","key":"hjpGdyEDTi"},{"type":"text","value":" polarized and the other being ","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"key":"qwELWBoai9"},{"type":"text","value":"π","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"key":"D48wjLQ4g3"},{"type":"text","value":" polarized","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"key":"GXzT9HhLsL"},{"type":"footnoteReference","identifier":"raman_details","label":"raman_details","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"number":5,"enumerator":"5","key":"hSECuEAKZ4"},{"type":"text","value":". Since the two lasers do not co-propagate, they impart a velocity kick to the atoms of ","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"key":"SMpeQbVD1i"},{"type":"inlineMath","value":"2h/\\lambda m \\sin \\theta=42.5","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"html":"2h/λmsin⁡θ=42.52h/\\lambda m \\sin \\theta=42.52h/λmsinθ=42.5","key":"Le7bCWPEGZ"},{"type":"text","value":" mm/s. This allows us to deflect the cloud during its free fall so that it does not hit the ","key":"hv1Ao59d5j"},{"type":"abbreviation","title":"Micro-Channel Plate","children":[{"type":"text","value":"MCP","key":"NrO4lCWROC"}],"key":"yojt3YuIfy"},{"type":"footnoteReference","identifier":"raman-note","label":"raman-note","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"number":6,"enumerator":"6","key":"xHn25v2kME"},{"type":"text","value":": after a 307 ms time of flight, the atoms are shifted by 11.5 mm, as shown in ","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"key":"lPDrCaYEGy"},{"type":"crossReference","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"children":[{"type":"text","value":"Figure ","key":"hQML53wDff"},{"type":"text","value":"2","key":"s4cwuwTpAy"}],"identifier":"raman_fig","label":"raman_fig","kind":"figure","template":"Figure %s","enumerator":"2","resolved":true,"html_id":"raman-fig","key":"xuPbhqPErP"},{"type":"text","value":". Note that ","position":{"start":{"line":85,"column":1},"end":{"line":85,"column":1}},"key":"jT73NGszTK"},{"type":"cite","identifier":"van_der_beek_bloch_2020","label":"van_der_beek_bloch_2020","kind":"narrative","position":{"start":{"line":85,"column":1012},"end":{"line":85,"column":1036}},"children":[{"type":"text","value":"Van Der Beek ","key":"ASEESMyw87"},{"type":"emphasis","children":[{"type":"text","value":"et al.","key":"JV0MmF1wn3"}],"key":"VqKeim5YBO"},{"type":"text","value":" (2020)","key":"vyAnZzXJc4"}],"enumerator":"2","key":"Tk3q9dIMJR"},{"type":"text","value":" used a similar trick to install a vertical lattice on their setup: they displaced their ","key":"qOdNlfyQy8"},{"type":"abbreviation","title":"Micro-Channel Plate","children":[{"type":"text","value":"MCP","key":"OP5x1XImUF"}],"key":"sJf0gAmNg9"},{"type":"text","value":" from the center and kicked the cloud during its free fall with a magnetic field pusher rather than a laser pulse.","key":"HME0uMsAvK"}],"key":"h5wOC0m9ek"},{"type":"paragraph","position":{"start":{"line":88,"column":1},"end":{"line":88,"column":1}},"children":[{"type":"text","value":"The Raman transition consists of a short and intense laser pulse","position":{"start":{"line":88,"column":1},"end":{"line":88,"column":1}},"key":"KkFlkqqU91"},{"type":"footnoteReference","identifier":"note_raman","label":"note_raman","position":{"start":{"line":88,"column":1},"end":{"line":88,"column":1}},"number":7,"enumerator":"7","key":"MS4I3Apf7w"},{"type":"text","value":" of 13 µs that transfers 97(2)% of the cloud. 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On the graph, the higher number of points around the first minimum allows for precisely determining the duration that transfers the most atoms. ©Left scheme from ","key":"vrgRE1IZM0"},{"type":"cite","identifier":"leprince_phase_2024","label":"leprince_phase_2024","kind":"narrative","position":{"start":{"line":102,"column":1118},"end":{"line":102,"column":1138}},"children":[{"type":"text","value":"Leprince (2024)","key":"KfoImeyXXm"}],"enumerator":"3","key":"ORjfk1aLcF"},{"type":"text","value":".","position":{"start":{"line":102,"column":1},"end":{"line":102,"column":1}},"key":"AMr3WMRrY4"}],"key":"EHqmNuXze1"}],"key":"Ixg6LKB8RO"}],"enumerator":"2","html_id":"raman-fig","key":"htOtNoi3za"},{"type":"heading","depth":2,"position":{"start":{"line":107,"column":1},"end":{"line":107,"column":1}},"children":[{"type":"text","value":"Dipole trap evaporation ramp","position":{"start":{"line":107,"column":1},"end":{"line":107,"column":1}},"key":"qAz1pLD4Tv"}],"identifier":"evaporation_ramp_section","label":"evaporation_ramp_section","html_id":"evaporation-ramp-section","enumerator":"3","key":"aw2KBfKMI7"},{"type":"paragraph","position":{"start":{"line":108,"column":1},"end":{"line":109,"column":1}},"children":[{"type":"text","value":"Once the dipole trap is loaded, the power of the laser is decreased to perform the last evaporation ramp. In order to obtain a ","key":"E8KlZVZcYC"},{"type":"abbreviation","title":"Bose-Einstein Condensate","children":[{"type":"text","value":"BEC","key":"cFhMJrhU17"}],"key":"JtCMpRxKfQ"},{"type":"text","value":", one must decrease the trap potential in order to keep the elastic collision rate high (so that the evaporation ramp is efficient) while having a low inelastic collision rate. In practice, the ramp duration is 1.3 seconds and the ramp parameters have an impact on the atom number of the final ","key":"uMeWJLaxgl"},{"type":"abbreviation","title":"Bose-Einstein Condensate","children":[{"type":"text","value":"BEC","key":"qJSgLMUX7Z"}],"key":"EiKWifkOyU"},{"type":"text","value":".","key":"QdX6WiVoL7"},{"type":"break","position":{"start":{"line":108,"column":1},"end":{"line":108,"column":1}},"key":"SIstbK62qV"},{"type":"text","value":"The trapping laser is vertical; hence, when the power of the trap decreases, the position of the minimum shifts due to gravity. Depending on the dynamics of the ramp, the position of this minimum exhibits different trajectories. 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The evaporation ramp of the laser power is shown on the left panel of ","position":{"start":{"line":115,"column":1},"end":{"line":115,"column":1}},"key":"puSUxosigp"},{"type":"crossReference","position":{"start":{"line":115,"column":1},"end":{"line":115,"column":1}},"children":[{"type":"text","value":"Figure ","key":"bs0aCGHWfb"},{"type":"text","value":"3","key":"P6ggeLEicY"}],"identifier":"evaporation_figure","label":"evaporation_figure","kind":"figure","template":"Figure %s","enumerator":"3","resolved":true,"html_id":"evaporation-figure","key":"MLQQ1ZgTZj"},{"type":"text","value":". When ","position":{"start":{"line":115,"column":1},"end":{"line":115,"column":1}},"key":"pDUDirqVRk"},{"type":"inlineMath","value":"\\alpha=1","position":{"start":{"line":115,"column":1},"end":{"line":115,"column":1}},"html":"α=1\\alpha=1α=1","key":"VAB75U7Ixl"},{"type":"text","value":", the ramp is a straight line (solid pink curve) and when ","position":{"start":{"line":115,"column":1},"end":{"line":115,"column":1}},"key":"olJ3L0mJ9D"},{"type":"text","value":"α","position":{"start":{"line":115,"column":1},"end":{"line":115,"column":1}},"key":"UAtB10lv1v"},{"type":"text","value":" is higher, the power is more exponentially damped (dashed dotted green).","position":{"start":{"line":115,"column":1},"end":{"line":115,"column":1}},"key":"krEtNdRl9l"},{"type":"break","position":{"start":{"line":115,"column":1},"end":{"line":115,"column":1}},"key":"R1WMZaeZEj"},{"type":"text","value":"On the right panel of ","position":{"start":{"line":115,"column":1},"end":{"line":115,"column":1}},"key":"DAJCs1mSsV"},{"type":"crossReference","position":{"start":{"line":115,"column":1},"end":{"line":115,"column":1}},"children":[{"type":"text","value":"Figure ","key":"TaEPtw17IT"},{"type":"text","value":"3","key":"zYH2rQ4utR"}],"identifier":"evaporation_figure","label":"evaporation_figure","kind":"figure","template":"Figure %s","enumerator":"3","resolved":true,"html_id":"evaporation-figure","key":"nwt6DIBV7V"},{"type":"text","value":" is shown the position of the minimum of the trap of the center of the cloud as a function of time. The ","position":{"start":{"line":115,"column":1},"end":{"line":115,"column":1}},"key":"vqZbpGoj8l"},{"type":"inlineMath","value":"\\alpha=1","position":{"start":{"line":115,"column":1},"end":{"line":115,"column":1}},"html":"α=1\\alpha=1α=1","key":"dpkoOCMeNN"},{"type":"text","value":" solid pink curve exhibits a sharp angle at the end of the evaporation ramp. This means that the velocity of the minimum of the trap is not continuous, which might induce an oscillation of the cloud. 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Left: exponential decrease of the laser power as a function of time according to equation ","position":{"start":{"line":124,"column":1},"end":{"line":124,"column":1}},"key":"uUfECOcq75"},{"type":"crossReference","position":{"start":{"line":124,"column":1},"end":{"line":124,"column":1}},"children":[{"type":"text","value":"(","key":"sl7LIixqIH"},{"type":"text","value":"1","key":"SxLqYMRmDr"},{"type":"text","value":")","key":"F5xDSlSMaZ"}],"identifier":"evaporation_ramp","label":"evaporation_ramp","kind":"equation","template":"(%s)","enumerator":"1","resolved":true,"html_id":"evaporation-ramp","key":"Cx9EYf6rTb"},{"type":"text","value":". 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For ","key":"RjcY2u0rXP"},{"type":"inlineMath","value":"\\alpha=1","position":{"start":{"line":124,"column":1},"end":{"line":124,"column":1}},"html":"α=1\\alpha=1α=1","key":"f1olE6RRKb"},{"type":"text","value":", the cloud oscillates at the trap frequency while this oscillation seems suppressed for ","position":{"start":{"line":124,"column":1},"end":{"line":124,"column":1}},"key":"BPj4ashg9t"},{"type":"inlineMath","value":"\\alpha =8","position":{"start":{"line":124,"column":1},"end":{"line":124,"column":1}},"html":"α=8\\alpha =8α=8","key":"Q4e2ldSd2O"},{"type":"text","value":".","position":{"start":{"line":124,"column":1},"end":{"line":124,"column":1}},"key":"bKo5POmVtb"}],"key":"tfULHn8C95"}],"key":"zrjK6Nlh05"}],"enumerator":"3","html_id":"evaporation-figure","key":"UUWHYWR7jb"},{"type":"paragraph","position":{"start":{"line":128,"column":1},"end":{"line":128,"column":1}},"children":[{"type":"text","value":"In order to ensure that the evaporation ramp does not induce any oscillation of the cloud, we perform the following experiment. 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We then scan the hold time in the trap after the evaporation ramp, from 500 to 600 ms. The arrival time of the cloud on the detector is proportional to the in-trap velocity of the cloud at the moment the cloud is released. If the evaporation ramp induces an oscillation of the cloud, the arrival time of the cloud should exhibit an oscillation too. The arrival time of the ","key":"sIQGOfZFHV"},{"type":"abbreviation","title":"Bose-Einstein Condensate","children":[{"type":"text","value":"BEC","key":"G1V6S7o7iK"}],"key":"cy6v5HYmJq"},{"type":"text","value":" as a function of the hold time in the trap is shown in the inset of the left panel of ","key":"ZUV2KySk9r"},{"type":"crossReference","position":{"start":{"line":128,"column":1},"end":{"line":128,"column":1}},"children":[{"type":"text","value":"Figure ","key":"rwf670P8X6"},{"type":"text","value":"3","key":"HHFplfOxME"}],"identifier":"evaporation_figure","label":"evaporation_figure","kind":"figure","template":"Figure %s","enumerator":"3","resolved":true,"html_id":"evaporation-figure","key":"p8p5lEr8lh"},{"type":"text","value":", as pink circles for ","position":{"start":{"line":128,"column":1},"end":{"line":128,"column":1}},"key":"daIF1uV38p"},{"type":"inlineMath","value":"\\alpha = 1","position":{"start":{"line":128,"column":1},"end":{"line":128,"column":1}},"html":"α=1\\alpha = 1α=1","key":"sKAX6RrXEo"},{"type":"text","value":" and green squares for ","position":{"start":{"line":128,"column":1},"end":{"line":128,"column":1}},"key":"B6gNTEj264"},{"type":"inlineMath","value":"\\alpha = 8","position":{"start":{"line":128,"column":1},"end":{"line":128,"column":1}},"html":"α=8\\alpha = 8α=8","key":"mxYxuO3pjh"},{"type":"text","value":". We observe a strong oscillation of the cloud when ","position":{"start":{"line":128,"column":1},"end":{"line":128,"column":1}},"key":"YOtr6nx8p8"},{"type":"inlineMath","value":"\\alpha = 1","position":{"start":{"line":128,"column":1},"end":{"line":128,"column":1}},"html":"α=1\\alpha = 1α=1","key":"KafFCJ8LtD"},{"type":"text","value":", while for the ","position":{"start":{"line":128,"column":1},"end":{"line":128,"column":1}},"key":"FOz2Dm93jR"},{"type":"inlineMath","value":"\\alpha = 8","position":{"start":{"line":128,"column":1},"end":{"line":128,"column":1}},"html":"α=8\\alpha = 8α=8","key":"wKcnN2PZmg"},{"type":"text","value":" case, if the oscillation still exists, it is indiscernible from the shot-to-shot variations.","position":{"start":{"line":128,"column":1},"end":{"line":128,"column":1}},"key":"HSQWSkoCQj"}],"key":"xnP1isrT5V"},{"type":"heading","depth":2,"position":{"start":{"line":131,"column":1},"end":{"line":131,"column":1}},"children":[{"type":"text","value":"Stability of the ","key":"oVMVLwiyY6"},{"type":"abbreviation","title":"Bose-Einstein Condensate","children":[{"type":"text","value":"BEC","key":"Jiwbjj2wbG"}],"key":"xeh3tHi8Rg"}],"identifier":"stab_bec","label":"stab_bec","html_id":"stab-bec","enumerator":"4","key":"ksLRgTLJ6M"},{"type":"paragraph","position":{"start":{"line":132,"column":1},"end":{"line":132,"column":1}},"children":[{"type":"text","value":"The estimation of the stability of the dipole trap is the following. 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Here we report a stability of 10(5) µs","position":{"start":{"line":132,"column":1},"end":{"line":132,"column":1}},"key":"U9YIsC34H2"},{"type":"footnoteReference","identifier":"stability_bec_2024","label":"stability_bec_2024","position":{"start":{"line":132,"column":1},"end":{"line":132,"column":1}},"number":9,"enumerator":"9","key":"UvdDyYftrm"},{"type":"text","value":", which corresponds to 0.10(5) mm/s in speed. Such improvement is due to the adiabatic extinction of the magnetic trap when we transfer it to the dipole trap, a good optical alignment between all lasers and the shape of the ","position":{"start":{"line":132,"column":1},"end":{"line":132,"column":1}},"key":"vuTh51E9ad"},{"type":"crossReference","position":{"start":{"line":132,"column":1},"end":{"line":132,"column":1}},"children":[{"type":"text","value":"evaporation ramp","position":{"start":{"line":132,"column":1},"end":{"line":132,"column":1}},"key":"o3QtM8c5Ix"}],"identifier":"evaporation_ramp_section","label":"evaporation_ramp_section","kind":"heading","template":"Section %s","enumerator":"3","resolved":true,"html_id":"evaporation-ramp-section","key":"tbTxbSExzz"},{"type":"text","value":". The stability in the single dipole trap was highly improved: from 100 µs, it reached 10(5) µs hence the same stability as the crossed dipole trap. The fact that the laser power available is higher than in 2012 might also help as we load a much hotter trap: we are less sensitive to the fluctuations of the magnetic trap position.","position":{"start":{"line":132,"column":1},"end":{"line":132,"column":1}},"key":"ayjsODL0aX"}],"key":"hg0rL2Xzs5"},{"type":"comment","value":"Note however that The explanation for this improvement is not entirely clear for me. The dipole trap evaporation ramp that was used after the installation of the dipole trap was already exponential [@jaskula_creation_2010]. The only reason I see for this stability improvement is the transfer from the magnetic trap to the vertical. With the 2010's laser, the dipole trap was loaded from a 15 µK magnetic trap while we are now able to load a 45 µK trap. 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