{"id":148901,"date":"2022-10-26T02:23:12","date_gmt":"2022-10-26T07:23:12","guid":{"rendered":"https:\/\/lifeboat.com\/blog\/2022\/10\/entanglement-enhanced-matter-wave-interferometry-in-a-high-finesse-cavity"},"modified":"2022-10-26T02:23:12","modified_gmt":"2022-10-26T07:23:12","slug":"entanglement-enhanced-matter-wave-interferometry-in-a-high-finesse-cavity","status":"publish","type":"post","link":"https:\/\/lifeboat.com\/blog\/2022\/10\/entanglement-enhanced-matter-wave-interferometry-in-a-high-finesse-cavity","title":{"rendered":"Entanglement-enhanced matter-wave interferometry in a high-finesse cavity"},"content":{"rendered":"<p><a class=\"aligncenter blog-photo\" href=\"https:\/\/lifeboat.com\/blog.images\/entanglement-enhanced-matter-wave-interferometry-in-a-high-finesse-cavity2.jpg\"><\/a><\/p>\n<p>Light-pulse matter-wave interferometers exploit the quantized momentum kick given to atoms during absorption and emission of light to split atomic wave packets so that they traverse distinct spatial paths at the same time. Additional momentum kicks then return the atoms to the same point in space to interfere the two matter-wave wave packets. The key to the precision of these devices is the encoding of information in the phase <i>\u03d5<\/i> that appears in the superposition of the two quantum trajectories within the interferometer. This phase must be estimated from quantum measurements to extract the desired information. For <i>N<\/i> atoms, the phase estimation is fundamentally limited by the independent quantum collapse of each atom to an r.m.s. angular uncertainty \\(\\Delta {\\theta }_{{\\rm{SQL}}}=1\/\\sqrt{N}\\) rad, known as the standard quantum limit (SQL)<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 2\" title=\"Itano, W. M. et al. Quantum projection noise: population fluctuations in two-level systems. Phys. Rev. A 47, 3554&ndash;3570 (1993).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR2\" id=\"ref-link-section-d68079938e656\">2<\/a><\/sup>.<\/p>\n<p>Here we demonstrate a matter-wave interferometer<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 31\" title=\"Kasevich, M. & Chu, S. Atomic interferometry using stimulated Raman transitions. Phys. Rev. Lett. 67181&ndash;184 (1991).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR31\" id=\"ref-link-section-d68079938e663\">31<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 32\" title=\"Cronin, A. D., Schmiedmayer, J. & Pritchard, D. E. Optics and interferometry with atoms and molecules. Rev. Mod. Phys. 81, 1051&ndash;1129 (2009).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR32\" id=\"ref-link-section-d68079938e666\">32<\/a><\/sup> with a directly observed interferometric phase noise below the SQL, a result that combines two of the most striking features of quantum mechanics: the concept that a particle can appear to be in two places at once and entanglement between distinct particles. This work is also a harbinger of future quantum many-body simulations with cavities<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Kroeze, R. M., Guo, Y. & Lev, B. L. Dynamical spin-orbit coupling of a quantum gas. Phys. Rev. Lett. 123, 160404 (2019).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR26\" id=\"ref-link-section-d68079938e670\">26<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Landini, M. et al. Formation of a spin texture in a quantum gas coupled to a cavity. Phys. Rev. Lett. 120, 223602 (2018).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR27\" id=\"ref-link-section-d68079938e670_1\">27<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Ke\u00dfler, H. et al. Observation of a dissipative time crystal. Phys. Rev. Lett. 127, 043602 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR28\" id=\"ref-link-section-d68079938e670_2\">28<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 29\" title=\"Schuster, S. C., Wolf, P., Ostermann, S., Slama, S. & Zimmermann, C. Supersolid properties of a Bose-Einstein condensate in a ring resonator. Phys. Rev. Lett. 124, 143602 (2020).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR29\" id=\"ref-link-section-d68079938e673\">29<\/a><\/sup> that will explore beyond mean-field physics by directly modifying and probing quantum fluctuations or in which the quantum measurement process induces a phase transition<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 30\" title=\"Skinner, B., Ruhman, J. & Nahum, A. Measurement-Induced phase transitions in the dynamics of entanglement. Phys. Rev. X 9, 031009 (2019).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR30\" id=\"ref-link-section-d68079938e677\">30<\/a><\/sup>.<\/p>\n<p>Quantum entanglement between the atoms allows the atoms to conspire together to reduce their total quantum noise relative to their total signal<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 1\" title=\"Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138&ndash;5143 (1993).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR1\" id=\"ref-link-section-d68079938e684\">1<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 3\" title=\"Wineland, D. J., Bollinger, J. J., Itano, W. M. & Heinzen, D. J. Squeezed atomic states and projection noise in spectroscopy. Phys. Rev. A 50, 67&ndash;88 (1994).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR3\" id=\"ref-link-section-d68079938e687\">3<\/a><\/sup>. Such entanglement has been generated between atoms using direct collisional<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Esteve, J., Gross, C., Weller, A., Giovanazzi, S. & Oberthaler, M. K. Squeezing and entanglement in a Bose-Einstein condensate. Nature 455, 1216&ndash;1219 (2008).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR33\" id=\"ref-link-section-d68079938e691\">33<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Gross, C., Zibold, T., Nicklas, E., Est\u00e8ve, J. & Oberthaler, M. K. Nonlinear atom interferometer surpasses classical precision limit. Nature 464, 1165&ndash;1169 (2010).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR34\" id=\"ref-link-section-d68079938e691_1\">34<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"B\u00fccker, R. et al. Twin-atom beams. Nat. Phys. 7608&ndash;611 (2011).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR35\" id=\"ref-link-section-d68079938e691_2\">35<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Hamley, C. D., Gerving, C. S., Hoang, T. M., Bookjans, E. M. & Chapman, M. S. Spin-nematic squeezed vacuum in a quantum gas. Nat. Phys. 8305&ndash;308 (2012).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR36\" id=\"ref-link-section-d68079938e691_3\">36<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Luo, X.-Y. et al. Deterministic entanglement generation from driving through quantum phase transitions. Science 355620&ndash;623 (2017).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR37\" id=\"ref-link-section-d68079938e691_4\">37<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" title=\"Lange, K. et al. Entanglement between two spatially separated atomic modes. Science 360416&ndash;418 (2018).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR38\" id=\"ref-link-section-d68079938e691_5\">38<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 39\" title=\"Fadel, M., Zibold, T., D\u00e9camps, B. & Treutlein, P. Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in Bose-Einstein condensates. Science 360409&ndash;413 (2018).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR39\" id=\"ref-link-section-d68079938e694\">39<\/a><\/sup> or Coulomb<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 40\" title=\"Leibfried, D. et al. Creation of a six-atom \u2018Schr\u00f6dinger cat\u2019 state. Nature 438639&ndash;642 (2005).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR40\" id=\"ref-link-section-d68079938e698\">40<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 41\" title=\"Monz, T. et al. 14-Qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR41\" id=\"ref-link-section-d68079938e701\">41<\/a><\/sup> interactions, including relative atom number squeezing between matter waves in spatially separated traps<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 33\" title=\"Esteve, J., Gross, C., Weller, A., Giovanazzi, S. & Oberthaler, M. K. Squeezing and entanglement in a Bose-Einstein condensate. Nature 455, 1216&ndash;1219 (2008).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR33\" id=\"ref-link-section-d68079938e705\">33<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 35\" title=\"B\u00fccker, R. et al. Twin-atom beams. Nat. Phys. 7608&ndash;611 (2011).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR35\" id=\"ref-link-section-d68079938e708\">35<\/a>,<a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 39\" title=\"Fadel, M., Zibold, T., D\u00e9camps, B. & Treutlein, P. Spatial entanglement patterns and Einstein-Podolsky-Rosen steering in Bose-Einstein condensates. Science 360409&ndash;413 (2018).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR39\" id=\"ref-link-section-d68079938e711\">39<\/a><\/sup> and mapping of internal entanglement onto the relative atom number in different momentum states<sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 42\" title=\"Anders, F. et al. Momentum entanglement for atom interferometry. Phys. Rev. Lett. 127, 140402 (2021).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR42\" id=\"ref-link-section-d68079938e715\">42<\/a><\/sup>. A trapped matter-wave interferometer with relative number squeezing was realized in ref. <sup><a data-track=\"click\" data-track-action=\"reference anchor\" data-track-label=\"link\" data-test=\"citation-ref\" aria-label=\"Reference 35\" title=\"B\u00fccker, R. et al. Twin-atom beams. Nat. Phys. 7608&ndash;611 (2011).\" href=\"https:\/\/www.nature.com\/articles\/s41586-022-05197-9#ref-CR35\" id=\"ref-link-section-d68079938e720\">35<\/a><\/sup>, but the interferometer\u2019s phase was antisqueezed and thus the phase resolution was above the SQL.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Light-pulse matter-wave interferometers exploit the quantized momentum kick given to atoms during absorption and emission of light to split atomic wave packets so that they traverse distinct spatial paths at the same time. Additional momentum kicks then return the atoms to the same point in space to interfere the two matter-wave wave packets. The key [\u2026]<\/p>\n","protected":false},"author":427,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1965,48,1617],"tags":[],"class_list":["post-148901","post","type-post","status-publish","format-standard","hentry","category-mapping","category-particle-physics","category-quantum-physics"],"_links":{"self":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/148901","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/users\/427"}],"replies":[{"embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/comments?post=148901"}],"version-history":[{"count":0,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/posts\/148901\/revisions"}],"wp:attachment":[{"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/media?parent=148901"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/categories?post=148901"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lifeboat.com\/blog\/wp-json\/wp\/v2\/tags?post=148901"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}