Shell-shaped atomic gases. (English) Zbl 07880425
Summary: We review the quantum statistical properties of two-dimensional shell-shaped gases, produced by cooling and confining atomic ensembles in thin hollow shells. We consider both spherical and ellipsoidal shapes, discussing at zero and at finite temperature the phenomena of Bose-Einstein condensation and of superfluidity, the physics of vortices, and the crossover from the Bardeen-Cooper-Schrieffer regime to a Bose-Einstein condensate. The novel aspects associated to the curved geometry are elucidated in comparison with flat two-dimensional superfluids. We also describe the hydrodynamic excitations and their relation with the Berezinskii-Kosterlitz-Thouless transition for two-dimensional flat and curved superfluids. In the next years, shell-shaped atomic gases will be the leading experimental platform for investigations of quantum many-body physics in curved spatial domains.
Keywords:
quantum gases; ultracold atoms; shell traps; curved geometries; Bose-Einstein condensation; superfluidity; quantized vortices; collective modesReferences:
| [1] | Bose, S. N., Plancks gesetz und lichtquantenhypothese, Z. Phys., 26, 178, 1924 · JFM 51.0732.04 |
| [2] | Einstein, A., Quantentheorie des einatomigen idealen gases, Sitzber. Kgl. Preuss. Akad. Wiss., 261, 1924 |
| [3] | Einstein, A., Quantentheorie des einatomigen idealen gases. zweite abhandlung, Sitzungsber. Preuss. Akad. Wiss., 1, 3, 1925 |
| [4] | Pauli, W., Zur frage der theoretischen deutung der satelliten einiger spektrallinien und ihrer beeinflussung durch magnetische felder, Naturwissenschaften, 12, 741, 1924 |
| [5] | Kapitza, P., Viscosity of liquid helium below the \(\operatorname{\lambda} \)-point, Nature, 141, 74, 1938 |
| [6] | London, F., The \(\operatorname{\lambda} \)-phenomenon of liquid helium and the bose-Einstein degeneracy, Nature, 141, 643, 1938 |
| [7] | Balibar, S., The discovery of superfluidity, J. Low. Temp. Phys., 146, 441, 2007 |
| [8] | Landau, L. D., The theory of superfluidity of helium II, J. Phys. U.S.S.R., 5, 71, 1941 |
| [9] | Tisza, L., Transport phenomena in helium II, Nature, 141, 913, 1938 |
| [10] | Tisza, L., Sur la supraconductibilité thermique de l’hèlium II liquide et la statistique de bose-Einstein, C. R. Hebd. Seances Acad. Sci. Paris, 207, 1035, 1938 |
| [11] | Tisza, L., La viscosité de l’hèlium liquide et la statistique de bose-Einstein, C. R. Hebd. Seances Acad. Sci. Paris, 207, 1186, 1938 · Zbl 0019.42801 |
| [12] | Bogoliubov, N. N., On the theory of superfluidity, J. Phys. USSR, 11, 23, 1947 |
| [13] | Leggett, A. J., Superfluidity, Rev. Mod. Phys., 71, S318, 1999 |
| [14] | Anderson, M. H.; Ensher, J. R.; Matthews, M. R.; Wieman, C. E.; Cornell, E. A., Observation of bose-Einstein condensation in a dilute atomic vapor, Science, 269, 198, 1995 |
| [15] | Davis, K. B.; Mewes, M.-O.; Andrews, M. R.; van Druten, N. J.; Durfee, D. S.; Kurn, D. M.; Ketterle, W., Bose-Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett., 75, 3969, 1995 |
| [16] | Bradley, C. C.; Sackett, C. A.; Tollett, J. J.; Hulet, R. G., Evidence of bose-Einstein condensation in an atomic gas with attractive interactions, Phys. Rev. Lett., 75, 1687, 1995; Bradley, C. C.; Sackett, C. A.; Hulet, R. G., Bose-einstein condensation of lithium: observation of limited condensate number, Phys. Rev. Lett., 78, 985, 1997, Erratum: |
| [17] | Phillips, W. D.; Metcalf, H., Laser deceleration of an atomic beam, Phys. Rev. Lett., 48, 596, 1982 |
| [18] | Hänsch, T. W.; Schawlow, A. L., Cooling of gases by laser radiation, Opt. Commun., 13, 68, 1975 |
| [19] | Wineland, D. J.; Dehmelt, H., Proposed 1014 delta upsilon less than upsilon laser fluorescence spectroscopy on t1+ mono-ion oscillator iii, Bull. Am. Phys. Soc, 20, 637, 1975 |
| [20] | Chu, S.; Hollberg, L.; Bjorkholm, J. E.; Cable, A.; Ashkin, A., Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure, Phys. Rev. Lett., 55, 48, 1985 |
| [21] | Migdall, A. L.; Prodan, J. V.; Phillips, W. D.; Bergeman, T. H.; Metcalf, H. J., First observation of magnetically trapped neutral atoms, Phys. Rev. Lett., 54, 2596, 1985 |
| [22] | Chu, S.; Bjorkholm, J. E.; Ashkin, A.; Cable, A., Experimental observation of optically trapped atoms, Phys. Rev. Lett., 57, 314, 1986 |
| [23] | Bagnato, V. S.; Lafyatis, G. P.; Martin, A. G.; Raab, E. L.; Ahmad-Bitar, R. N.; Pritchard, D. E., Continuous stopping and trapping of neutral atoms, Phys. Rev. Lett., 58, 2194, 1987 |
| [24] | Lett, P. D.; Watts, R. N.; Westbrook, C. I.; Phillips, W. D.; Gould, P. L.; Metcalf, H. J., Observation of atoms laser cooled below the Doppler limit, Phys. Rev. Lett., 61, 169, 1988 |
| [25] | Aspect, A.; Arimondo, E.; Kaiser, R.; Vansteenkiste, N.; Cohen-Tannoudji, C., Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping, Phys. Rev. Lett., 61, 826, 1988 |
| [26] | Raab, E. L.; Prentiss, M.; Cable, A.; Chu, S.; Pritchard, D. E., Trapping of neutral sodium atoms with radiation pressure, Phys. Rev. Lett., 59, 2631, 1987 |
| [27] | Masuhara, N.; Doyle, J. M.; Sandberg, J. C.; Kleppner, D.; Greytak, T. J.; Hess, H. F.; Kochanski, G. P., Evaporative cooling of spin-polarized atomic hydrogen, Phys. Rev. Lett., 61, 935, 1988 |
| [28] | Ketterle, W.; Van Druten, N. J., Evaporative cooling of trapped atoms, Adv. At. Mol. Opt. Phys., 37, 181, 1996 |
| [29] | Bloch, I.; Dalibard, J.; Zwerger, W., Many-body physics with ultracold gases, Rev. Mod. Phys., 80, 885, 2008 |
| [30] | Bloch, I.; Dalibard, J.; Nascimbène, S., Quantum simulations with ultracold quantum gases, Nat. Phys., 8, 267, 2012 |
| [31] | Lahaye, T.; Menotti, C.; Santos, L.; Lewenstein, M.; Pfau, T., The physics of dipolar bosonic quantum gases, Rep. Progr. Phys., 72, Article 126401 pp., 2009 |
| [32] | Feynman, R. P., Simulating physics with computers, Internat. J. Theoret. Phys., 21, 467, 1982 |
| [33] | Lloyd, S., Universal quantum simulators, Science, 273, 1073, 1996 · Zbl 1226.81059 |
| [34] | Georgescu, I. M.; Ashhab, S.; Nori, F., Quantum simulation, Rev. Mod. Phys., 86, 153, 2014 |
| [35] | Görlitz, A.; Vogels, J. M.; Leanhardt, A. E.; Raman, C.; Gustavson, T. L.; Abo-Shaeer, J. R.; Chikkatur, A. P.; Gupta, S.; Inouye, S.; Rosenband, T.; Ketterle, W., Realization of bose-Einstein condensates in lower dimensions, Phys. Rev. Lett., 87, Article 130402 pp., 2001 |
| [36] | Petrov, D. S.; Gangardt, D. M.; Shlyapnikov, G. V., Low-dimensional trapped gases, J. Phys. IV, 116, 5, 2004 |
| [37] | Petrov, D. S., Bose-Einstein Condensation in Low-Dimensional Trapped Gases, 2003, University of Amsterdam, (Ph.D. thesis) |
| [38] | Dalfovo, F.; Giorgini, S.; Pitaevskii, L. P.; Stringari, S., Theory of bose-Einstein condensation in trapped gases, Rev. Mod. Phys., 71, 463, 1999 |
| [39] | Zobay, O.; Garraway, B. M., Two-dimensional atom trapping in field-induced adiabatic potentials, Phys. Rev. Lett., 86, 1195, 2001 |
| [40] | Zobay, O.; Garraway, B. M., Properties of coherent matter-wave bubbles, Acta Phys. Slovaca, 2000, 3, 2000 |
| [41] | Zobay, O.; Garraway, B. M., Atom trapping and two-dimensional bose-Einstein condensates in field-induced adiabatic potentials, Phys. Rev. A, 69, Article 023605 pp., 2004 |
| [42] | Garraway, B. M.; Perrin, H., Recent developments in trapping and manipulation of atoms with adiabatic potentials, J. Phys. B: At. Mol. Opt. Phys., 49, Article 172001 pp., 2016 |
| [43] | Elliott, E. R.; Krutzik, M. C.; Williams, J. R.; Thompson, J. R.; Aveline, D. C., Nasa’s cold atom lab (CAL): system development and ground test status, npj Micrograv., 4, 16, 2018 |
| [44] | Aveline, D. C.; Williams, J. R.; Elliott, E. R.; Dutenhoffer, C.; Kellogg, J. R.; Kohel, J. M.; Lay, N. E.; Oudrhiri, K.; Shotwell, R. F.; Yu, N.; Thompson, R. J., Observation of bose-Einstein condensates in an earth-orbiting research lab, Nature, 582, 193, 2020 |
| [45] | van Zoest, T., Bose-Einstein condensation in microgravity, Science, 328, 1540, 2010 |
| [46] | Müntinga, H., Interferometry with bose-Einstein condensates in microgravity, Phys. Rev. Lett., 110, Article 093602 pp., 2013 |
| [47] | Vogt, C.; Woltmann, M.; Herrmann, S.; Lämmerzahl, C.; Albers, H.; Schlippert, D.; Rasel, E. M., Evaporative cooling from an optical dipole trap in microgravity, Phys. Rev. A, 101, Article 013634 pp., 2020 |
| [48] | Becker, D., Space-borne bose-Einstein condensation for precision interferometry, Nature, 562, 391, 2018 |
| [49] | Condon, G.; Rabault, M.; Barrett, B.; Chichet, L.; Arguel, R.; Eneriz-Imaz, H.; Naik, D.; Bertoldi, A.; Battelier, B.; Bouyer, P.; Landragin, A., All-optical bose-Einstein condensates in microgravity, Phys. Rev. Lett., 123, Article 240402 pp., 2019 |
| [50] | Lundblad, N.; Carollo, R. A.; Lannert, C.; Gold, M. J.; Jiang, X.; Paseltiner, D.; Sergay, N.; Aveline, D. C., Shell potentials for microgravity bose-Einstein condensates, npj Micrograv., 5, 30, 2019 |
| [51] | Carollo, R. A.; Aveline, D. C.; Rhyno, B.; Vishveshwara, S.; Lannert, C.; Murphree, J. D.; Elliott, E. R.; Williams, J. R.; Thompson, R. J.; Lundblad, N., Observation of ultracold atomic bubbles in orbital microgravity, Nature, 606, 281, 2022 |
| [52] | Frye, K., The bose-Einstein condensate and cold atom laboratory, EPJ Quantum Technol., 8, 1, 2021 |
| [53] | Jia, F.; Huang, Z.; Qiu, L.; Zhou, R.; Yan, Y.; Wang, D., Expansion dynamics of a shell-shaped bose-Einstein condensate, Phys. Rev. Lett., 129, Article 243402 pp., 2022 |
| [54] | Colombe, Y.; Knyazchyan, E.; Morizot, O.; Mercier, B.; Lorent, V.; Perrin, H., Ultracold atoms confined in rf-induced two-dimensional trapping potentials, Europhys. Lett., 67, 593, 2004 |
| [55] | White, M.; Gao, H.; Pasienski, M.; DeMarco, B., Bose-Einstein condensates in rf-dressed adiabatic potentials, Phys. Rev. A, 74, Article 023616 pp., 2006 |
| [56] | Merloti, K., A two-dimensional quantum gas in a magnetic trap, New J. Phys., 15, Article 033007 pp., 2013 |
| [57] | Harte, T. L., Ultracold atoms in multiple radio-frequency dressed adiabatic potentials, Phys. Rev. A, 97, Article 013616 pp., 2018 |
| [58] | Guo, Y.; Dubessy, R.; de Goër de Herve, M.; Kumar, A.; Badr, T.; Perrin, A.; Longchambon, L.; Perrin, H., Supersonic rotation of a superfluid: A long-lived dynamical ring, Phys. Rev. Lett., 124, Article 025301 pp., 2020 |
| [59] | Guo, Y.; Mercado Gutierrez, E.; Rey, D.; Badr, T.; Perrin, A.; Longchambon, L.; Bagnato, V. S.; Perrin, H.; Dubessy, R., Expansion of a quantum gas in a shell trap, New J. Phys., 24, Article 093040 pp., 2022 |
| [60] | Rey, D.; Thomas, S.; Sharma, R.; Badr, T.; Longchambon, L.; Dubessy, R.; Perrin, H., Loading a quantum gas from an hybrid dimple trap to a shell trap, J. Appl. Phys., 132, Article 214401 pp., 2022 |
| [61] | Tononi, A.; Salasnich, L., Bose-Einstein condensation on the surface of a sphere, Phys. Rev. Lett., 123, Article 160403 pp., 2019 |
| [62] | Tononi, A.; Cinti, F.; Salasnich, L., Quantum bubbles in microgravity, Phys. Rev. Lett., 125, Article 010402 pp., 2020 |
| [63] | Tononi, A.; Pelster, A.; Salasnich, L., Topological superfluid transition in bubble-trapped condensates, Phys. Rev. Res., 4, Article 013122 pp., 2022 |
| [64] | Tononi, A., Scattering theory and equation of state of a spherical two-dimensional bose gas, Phys. Rev. A, 105, Article 023324 pp., 2022 |
| [65] | Bereta, S. J.; Madeira, L.; Bagnato, V. S.; Caracanhas, M. A., Bose-Einstein condensation in spherically symmetric traps, Amer. J. Phys., 87, 924, 2019 |
| [66] | Rhyno, B.; Lundblad, N.; Aveline, D. C.; Lannert, C.; Vishveshwara, S., Thermodynamics in expanding shell-shaped bose-Einstein condensates, Phys. Rev. A, 104, Article 063310 pp., 2021 |
| [67] | He, Y.; Guo, H.; Chien, C.-C., BCS-bec crossover of atomic Fermi superfluid in a spherical bubble trap, Phys. Rev. A, 105, Article 033323 pp., 2022 |
| [68] | Kotsubo, V.; Williams, G. A., Kosterlitz-thouless superfluid transition for helium in packed powders, Phys. Rev. Lett., 53, 691, 1984 |
| [69] | Kotsubo, V.; Williams, G. A., Superfluid transition of \({}^4\) he films adsorbed in porous materials, Phys. Rev. B, 33, 6106, 1986 |
| [70] | t. Wang, C.; Yu, L., Vortex dynamics of superfluid helium films on spherical surfaces, Phys. Rev. B, 33, 599, 1986 |
| [71] | Ovrut, B. A.; Thomas, S., Theory of vortices and monopoles on a sphere, Phys. Rev. D, 43, 1314, 1991 |
| [72] | Mitra, K.; Williams, C. J.; Sa de Melo, C. A.R., Superfluid and mott-insulating shells of bosons in harmonically confined optical lattices, Phys. Rev. A, 77, Article 033607 pp., 2008 |
| [73] | Turner, A. M.; Vitelli, V.; Nelson, D. R., Vortices on curved surfaces, Rev. Mod. Phys., 82, 1301, 2010 |
| [74] | Padavić, K.; Sun, K.; Lannert, C.; Vishveshwara, S., Vortex-antivortex physics in shell-shaped bose-Einstein condensates, Phys. Rev. A, 102, Article 043305 pp., 2020 |
| [75] | Bereta, S. J.; Caracanhas, M. A.; Fetter, A. L., Superfluid vortex dynamics on a spherical film, Phys. Rev. A, 103, Article 053306 pp., 2021 |
| [76] | Song, C.-H.; Gao, Q.-C.; Hou, X.-Y.; Wang, X.; Zhou, Z.; He, Y.; Guo, H., Machine learning of XY model on a spherical fibonacci lattice, Phys. Rev. Res., 4, Article 023005 pp., 2022 |
| [77] | Kanai, T.; Guo, W., True mechanism of spontaneous order from turbulence in two-dimensional superfluid manifolds, Phys. Rev. Lett., 127, Article 095301 pp., 2021 |
| [78] | G. Tomishiyo, L. Madeira, M.A. Caracanhas, Superfluid excitations in a rotating two-dimensional bubble trap, arXiv:2212.11027. |
| [79] | Ruban, V. P., Systems of vortices in a binary core-shell bose-Einstein condensate, JETP Lett., 116, 329-334, 2022 |
| [80] | Xiong, Y.; Yu, X., Hydrodynamics of quantum vortices on a closed surface, Phys. Rev. Res., 6, Article 013133 pp., 2024 |
| [81] | White, A. C., Triangular vortex-lattices and giant vortices in rotating bubble bose-Einstein condensates, Phys. Rev. A, 108, Article 053303 pp., 2023 |
| [82] | He, Y.; Chien, C.-C., Vortex structure and spectrum of atomic Fermi superfluid in a spherical bubble trap, Phys. Rev. A, 108, Article 053303 pp., 2023 |
| [83] | Caracanhas, M. A.; Massignan, P.; Fetter, A. L., Superfluid vortex dynamics on an ellipsoid and other surfaces of revolution, Phys. Rev. A, 105, Article 023307 pp., 2022 |
| [84] | Bogomolov, V. A., Dynamics of vorticity at a sphere, Fluid Dyn., 12, 863, 1977 · Zbl 0442.76020 |
| [85] | Kimura, Y.; Okamoto, H., Vortex motion on a sphere, J. Phys. Soc. Japan, 56, 4203, 1987 |
| [86] | Kimura, Y., Vortex motion on surfaces with constant curvature, Proc. R. Soc. Lond. A., 455, 245, 1999 · Zbl 0966.53046 |
| [87] | Newton, P. K., The N -Vortex Problem, 2001, Springer: Springer New York · Zbl 0981.76002 |
| [88] | Kim, S.-C., Latitudinal point vortex rings on the spheroid, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 466, 1749, 2010 · Zbl 1273.76068 |
| [89] | Lannert, C.; Wei, T.-C.; Vishveshwara, S., Dynamics of condensate shells: Collective modes and expansion, Phys. Rev. A, 75, Article 013611 pp., 2007 |
| [90] | Sun, K.; Padavić, K.; Yang, F.; Vishveshwara, S.; Lannert, C., Static and dynamic properties of shell-shaped condensates, Phys. Rev. A, 98, Article 013609 pp., 2018 |
| [91] | Padavić, K.; Sun, K.; Lannert, C.; Vishveshwara, S., Physics of hollow bose-Einstein condensates, Europhys. Lett., 120, 20004, 2018 |
| [92] | Saito, H.; Hayashi, M., Rossby-haurwitz wave in a rotating bubble-shaped bose-Einstein condensate, J. Phys. Soc. Japan, 92, Article 044003 pp., 2023 |
| [93] | Li, G.; Efimkin, D. K., Equatorial waves in rotating bubble-trapped superfluids, Phys. Rev. A, 107, Article 023319 pp., 2023 |
| [94] | Boegel, P.; Wolf, A.; Meister, M.; Efremov, M. A., Controlled expansion of shell-shaped bose-Einstein condensates, Quant. Sci. Technol., 8, Article 034001 pp., 2023 |
| [95] | Zhang, J.; Ho, T.-L., Potential scattering on a spherical surface, J. Phys. B, 51, Article 115301 pp., 2018 |
| [96] | Shi, Z.-Y.; Zhai, H., Emergent gauge field for a chiral bound state on curved surface, J. Phys. B: At. Mol. Opt. Phys., 50, Article 184006 pp., 2017 |
| [97] | Ouvry, S.; Polychronakos, A. P., Anyons on the sphere: Analytic states and spectrum, Nucl. Phys. B, 949, Article 114797 pp., 2019 · Zbl 1435.81262 |
| [98] | Prestipino, S.; Giaquinta, P. V., Ground state of weakly repulsive soft-core bosons on a sphere, Phys. Rev. A, 99, Article 063619 pp., 2019 |
| [99] | Prestipino, S., Ultracold bosons on a regular spherical mesh, Entropy, 22, 1289, 2020 |
| [100] | Ciardi, M.; Cinti, F.; Pellicane, G.; Prestipino, S., Supersolid phases of bosonic particles in a bubble trap, Phys. Rev. Lett., 132, Article 026001 pp., 2024 |
| [101] | Diniz, P. C.; Oliveira, E. A.B.; Lima, A. R.P.; Henn, E. A.L., Ground state and collective excitations of a dipolar bose-Einstein condensate in a bubble trap, Sci. Rep., 10, 4831, 2020 |
| [102] | Arazo, M.; Mayol, R.; Guilleumas, M., Shell-shaped condensates with gravitational sag: contact and dipolar interactions, New J. Phys., 23, Article 113040 pp., 2021 |
| [103] | Móller, N. S.; dos Santos, F. E.A.; Bagnato, V. S.; Pelster, A., Bose-Einstein condensation on curved manifolds, New J. Phys., 22, Article 063059 pp., 2020 |
| [104] | Biral, E. J.P.; Móller, N. S.; Pelster, A.; dos Santos, F. E.A., Bose-Einstein condensates and the thin-shell limit in anisotropic bubble traps, New J. Phys., 26, Article 013035 pp., 2024 |
| [105] | Andriati, A.; Brito, L.; Tomio, L.; Gammal, A., Stability of a bose condensed mixture on a bubble trap, Phys. Rev. A, 104, Article 033318 pp., 2021 |
| [106] | He, Y.; Chien, C.-C., Winding real and order-parameter spaces via lump solitons of spinor BEC on sphere, J. Phys. B: At. Mol. Opt. Phys., 56, Article 215303 pp., 2023 |
| [107] | Tononi, A.; Salasnich, L., Low-dimensional quantum gases in curved geometries, Nat. Rev. Phys., 5, 398, 2023 |
| [108] | Lundblad, N., Perspective on quantum bubbles in microgravity, Quantum Sci. Technol., 8, Article 024003 pp., 2023 |
| [109] | Berezinskii, V. L., Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group. II. Quantum systems, Sov. Phys.—JETP, 34, 610, 1972 |
| [110] | Kosterlitz, J. M.; Thouless, D., Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C, 5, L124, 1972 |
| [111] | Kosterlitz, J. M.; Thouless, D. J., Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C, 6, 1181, 1973 |
| [112] | Kosterlitz, J. M., The critical properties of the two-dimensional xy model, J. Phys. C: Solid State Phys., 7, 1046, 1974 |
| [113] | Desbuquois, R.; Yefsah, T.; Chomaz, L.; Weitenberg, C.; Corman, L.; Nascimbène, S.; Dalibard, J., Determination of scale-invariant equations of state without fitting parameters: Application to the two-dimensional bose gas across the berezinskii-kosterlitz-thouless transition, Phys. Rev. Lett., 113, Article 020404 pp., 2014 |
| [114] | Nelson, D. R.; Kosterlitz, J. M., Universal jump in the superfluid density of two-dimensional superfluids, Phys. Rev. Lett., 39, 1201, 1977 |
| [115] | Bishop, D. J.; Reppy, J. D., Study of the superfluid transition in two-dimensional \({}^4\) he films, Phys. Rev. Lett., 40, 1727, 1978 |
| [116] | Hadzibabic, Z.; Krüger, P.; Cheneau, M.; Battelier, B.; Dalibard, J., Berezinski-kosterlitz-thouless crossover in a trapped atomic gas, Nature, 441, 1118, 2006 |
| [117] | Christodoulou, P.; Gałka, M.; Dogra, N.; Lopes, R.; Schmitt, J.; Hadzibabic, Z., Observation of first and second sound in a BKT superfluid, Nature, 594, 191, 2021 |
| [118] | Bohlen, M.; Sobirey, L.; Luick, N.; Biss, H.; Enss, T.; Lompe, T.; Moritz, H., Sound propagation and quantum-limited damping in a two-dimensional Fermi gas, Phys. Rev. Lett., 124, Article 240403 pp., 2020 |
| [119] | (Zwerger, W., BCS-BEC Crossover and the Unitary Fermi Gas. BCS-BEC Crossover and the Unitary Fermi Gas, Lecture Notes in Physics, 2012, Springer) |
| [120] | Calvanese Strinati, G.; Pieri, P.; Röpke, G.; Schuck, P.; Urban, M., The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems, Phys. Rep., 738, 1, 2018 · Zbl 1392.82064 |
| [121] | Huang, K., Statistical Mechanics, 1987, Wiley · Zbl 1041.82500 |
| [122] | Mermin, N. D.; Wagner, H., Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic heisenberg models, Phys. Rev. Lett., 17, 1133, 1966 |
| [123] | Hohenberg, P. C., Existence of long-range order in one and two dimensions, Phys. Rev., 158, 383, 1967 |
| [124] | Salasnich, L., Quantum Physics of Light and Matter, 2017, Springer · Zbl 1397.81002 |
| [125] | Feynman, R. P., Space-time approach to non-relativistic quantum mechanics, Rev. Mod. Phys., 20, 367, 1948 · Zbl 1371.81126 |
| [126] | Negele, J. W.; Orland, H., Quantum Many-Particle Systems, 2018, CRC Press |
| [127] | Tononi, A., Bose-Einstein Condensation and Superfluidity in 3D and 2D Bosons, 2018, Università degli Studi di Padova, (M.Sc. thesis) |
| [128] | Chin, C.; Grimm, R.; Julienne, P.; Tiesinga, E., Feshbach resonances in ultracold gases, Rev. Mod. Phys., 82, 1225, 2010 |
| [129] | Nagaosa, N., Quantum Field Theory in Condensed Matter Physics, 1999, Springer: Springer Berlin · Zbl 0998.81533 |
| [130] | Cooper, L. N., Bound electron pairs in a degenerate Fermi gas, Phys. Rev., 104, 1189, 1956 · Zbl 0074.23705 |
| [131] | Tempere, J.; Devreese, J. P.A., Path-integral description of cooper pairing, (Gabovich, A., Superconductors-Materials, Properties and Applications, 2012, IntechOpen Ltd.: IntechOpen Ltd. London, UK) |
| [132] | Diener, R. B.; Sensarma, R.; Randeria, M., Quantum fluctuations in the superfluid state of the BCS-bec crossover, Phys. Rev. A, 77, Article 023626 pp., 2008 |
| [133] | Ketterle, W.; Durfee, D. S.; Stamper-Kurn, D. M., Making, probing and understanding bose-Einstein condensates, (Inguscio, M.; Stringari, S.; Wieman, C., Proceedings of the International School of Physics Enrico Fermi, 1999), arXiv:cond-mat/9904034v2 |
| [134] | Majorana, E., Atomi orientati in campo magnetico variabile, Il Nuovo Cimento (1924-1942), 9, 43, 1932 · JFM 58.1373.01 |
| [135] | Schumm, T.; Hofferberth, S.; Andersson, L. M.; Wildermuth, S.; Groth, S.; Bar-Joseph, I.; Schmiedmayer, J.; Krüger, P., Matter-wave interferometry in a double well on an atom chip, Nat. Phys., 1, 57, 2005 |
| [136] | Sherlock, B. E.; Gildemeister, M.; Owen, E.; Nugent, E.; Foot, C. J., Time-averaged adiabatic ring potential for ultracold atoms, Phys. Rev. A, 83, Article 043408 pp., 2011 |
| [137] | de Goër de Herve, M.; Guo, Y.; de Rossi, C.; Kumar, A.; Badr, T.; Dubessy, R.; Longchambon, L.; Perrin, H., A versatile ring trap for quantum gases, J. Phys. B: At. Mol. Opt. Phys., 54, Article 125302 pp., 2021 |
| [138] | Popov, V. N., On the theory of the superfluidity of two- and one-dimensional bose systems, Theoret. Math. Phys., 11, 354, 1972 |
| [139] | A. Altl, B. Simons, |
| [140] | Salasnich, L.; Toigo, F., Zero-point energy of ultracold atoms, Phys. Rep., 640, 1, 2016 · Zbl 1359.82024 |
| [141] | Kleinert, H.; Schmidt, S.; Pelster, A., Reentrant phenomenon in the quantum phase transitions of a gas of bosons trapped in an optical lattice, Phys. Rev. Lett., 93, Article 160402 pp., 2004 |
| [142] | Kleinert, H.; Schmidt, S.; Pelster, A., Quantum phase diagram for homogeneous bose-Einstein condensate, Ann. Phys., 14, 214, 2005 · Zbl 1059.82005 |
| [143] | Griffin, A., Conserving and gapless approximations for an inhomogeneous bose gas at finite temperatures, Phys. Rev. B, 53, 9341, 1996 |
| [144] | Giorgini, S.; Pitaevskii, L. P.; Stringari, S., Thermodynamics of a trapped bose-condensed gas, J. Low Temp. Phys., 109, 309, 1997 |
| [145] | Schick, M., Two-dimensional system of hard-core bosons, Phys. Rev. A, 3, 1067, 1971 |
| [146] | Yukalov, V. I.; Yukalova, E. P., Bose-Einstein condensation temperature of weakly interacting atoms, Laser Phys. Lett., 14, Article 073001 pp., 2017 |
| [147] | Baym, G.; Blaizot, J.-P.; Zinn-Justin, J., The transition temperature of the dilute interacting bose gas for n internal states, Europhys. Lett., 49, 150, 2000 |
| [148] | Holzmann, M.; Baym, G.; Blaizot, J.-P.; Laloë, F., Nonanalytic dependence of the transition temperature of the homogeneous dilute bose gas on scattering length, Phys. Rev. Lett., 87, Article 120403 pp., 2001 |
| [149] | Holzmann, M.; Krauth, W., Transition temperature of the homogeneous, weakly interacting bose gas, Phys. Rev. Lett., 83, 2687, 1999 |
| [150] | Kashurnikov, V. A.; Prokof’ev, N. V.; Svistunov, B. V., Critical temperature shift in weakly interacting bose gas, Phys. Rev. Lett., 87, Article 120402 pp., 2001 |
| [151] | Prokof’ev, N.; Svistunov, B., Two-dimensional weakly interacting bose gas in the fluctuation region, Phys. Rev. A, 66, Article 043608 pp., 2002 |
| [152] | Lippmann, B. A.; Schwinger, J., Variational principles for scattering processes. I, Phys. Rev., 79, 469, 1950 · Zbl 0039.42406 |
| [153] | Stoof, H. K.; Gubbels, K. B.; Dickerscheid, D. B.M., Ultracold Quantum Fields, 2009, Springer: Springer Dordrecht · Zbl 1177.81005 |
| [154] | Mora, C.; Castin, Y., Extension of bogoliubov theory to quasicondensates, Phys. Rev. A, 67, Article 053615 pp., 2003 |
| [155] | Mora, C.; Castin, Y., Ground state energy of the two-dimensional weakly interacting bose gas: First correction beyond bogoliubov theory, Phys. Rev. Lett., 102, Article 180404 pp., 2009 |
| [156] | Landau, L. D.; Lifshitz, E. M., Quantum Mechanics Non-Relativistic Theory, 1981, Pergamon Press: Pergamon Press New York |
| [157] | Petrov, D. S.; Shlyapnikov, G. V., Interatomic collisions in a tightly confined bose gas, Phys. Rev. A, 64, Article 012706 pp., 2001 |
| [158] | Tononi, A.; Cappellaro, A.; Salasnich, L., Condensation and superfluidity of dilute bose gases with finite-range interaction, New J. Phys., 20, Article 125007 pp., 2018 |
| [159] | Stringari, S., Collective excitations of a trapped bose-condensed gas, Phys. Rev. Lett., 77, 2360, 1996 |
| [160] | Onsager, L., Statistical hydrodynamics, Nuovo Cim., 6, 279, 1949 |
| [161] | Feynman, R. P., Chapter II application of quantum mechanics to liquid helium, Progr. Low Temp. Phys., 1, 17, 1955 |
| [162] | Babaev, E.; Kleinert, H., Nonperturbative XY-model approach to strong coupling superconductivity in two and three dimensions, Phys. Rev. B, 59, 12083, 1999 |
| [163] | Young, A. P., On the theory of the phase transition in the two-dimensional planar spin model, J. Phys. C, 11, L453, 1978 |
| [164] | Kosterlitz, J. M., Kosterlitz-thouless physics: a review of key issues, Rep. Progr. Phys., 79, Article 026001 pp., 2016 |
| [165] | Maccari, I.; Defenu, N.; Benfatto, L.; Castellani, C.; Enss, T., Interplay of spin waves and vortices in the two-dimensional XY model at small vortex-core energy, Phys. Rev. B, 102, Article 104505 pp., 2020 |
| [166] | Szeto, K. Y.; Dresselhaus, G., Zero-field susceptibility of finite-size kosterlitz-thouless systems, Phys. Rev. B, 32, 3142, 1985 |
| [167] | Bramwell, S. T.; Holdsworth, P. C.W., Magnetization: A characteristic of the kosterlitz-thouless-berezinskii transition, Phys. Rev. B, 49, 8811, 1994 |
| [168] | Komura, Y.; Okabe, Y., Large-scale Monte Carlo simulation of two-dimensional classical XY model using multiple GPUs, J. Phys. Soc. Japan, 81, Article 113001 pp., 2012 |
| [169] | Foster, C. J.; Blakie, P. B.; Davis, M. J., Vortex pairing in two-dimensional bose gases, Phys. Rev. A, 81, Article 023623 pp., 2010 |
| [170] | Salasnich, L., Self-consistent derivation of the modified gross-pitaevskii equation with lee-huang-yang correction, Appl. Sci., 8, 1998, 2018 |
| [171] | Gross, E. P., Structure of a quantized vortex in boson systems, Nuovo Cim., 20, 454, 1961 · Zbl 0100.42403 |
| [172] | Pitaevskii, L. P., Vortex lines in an imperfect bose gas, Sov. Phys.—JETP, 13, 451, 1961 |
| [173] | Bighin, G.; Salasnich, L., Finite-temperature quantum fluctuations in two-dimensional Fermi superfluids, Phys. Rev. B, 93, Article 014519 pp., 2016 |
| [174] | Ota, M.; Larcher, F.; Dalfovo, F.; Pitaevskii, L.; Proukakis, N. P.; Stringari, S., Collisionless sound in a uniform two-dimensional bose gas, Phys. Rev. Lett., 121, Article 145302 pp., 2018 |
| [175] | Cappellaro, A.; Toigo, F.; Salasnich, L., Collisionless dynamics in two-dimensional bosonic gases, Phys. Rev. A, 98, Article 043605 pp., 2018 |
| [176] | Landau, L. D.; Lifshits, E. M., Statistical Physics, Part 1, 1980, Pergamon: Pergamon Oxford |
| [177] | Klimin, S. N.; Devreese, J. T.; Tempere, J., Pseudogap and preformed pairs in the imbalanced Fermi gas in two dimensions, New J. Phys., 14, Article 103044 pp., 2012 |
| [178] | Bighin, G., Mean Field and Fluctuations for Fermionic Systems: From Ultracold Fermi Gases To Cuprates, 2016, Università degli Studi di Padova, (Ph.D. thesis) |
| [179] | Salasnich, L., Low-temperature thermodynamics of the unitary Fermi gas: Superfluid fraction, first sound, and second sound, Phys. Rev. A, 82, Article 063619 pp., 2010 |
| [180] | Verney, L.; Pitaevskii, L.; Stringari, S., Hybridization of first and second sound in a weakly interacting bose gas, Europhys. Lett., 111, 40005, 2015 |
| [181] | Tononi, A.; Cappellaro, A.; Bighin, G.; Salasnich, L., Propagation of first and second sound in a two-dimensional Fermi superfluid, Phys. Rev. A, 103, Article L061303 pp., 2021 |
| [182] | Bighin, G.; Salasnich, L., Vortices and antivortices in two-dimensional ultracold Fermi gases, Sci. Rep., 7, 45702, 2017 |
| [183] | Mondal, M.; Kumar, S.; Chand, M.; Kamlapure, A.; Saraswat, G.; Seibold, G.; Benfatto, L.; Raychaudhuri, P., Role of the vortex-core energy on the berezinskii-kosterlitz-thouless transition in thin films of NbN, Phys. Rev. Lett., 107, Article 217003 pp., 2011 |
| [184] | Minnhagen, P.; Nylén, M., Charge density of a vortex in the Coulomb-gas analogy of superconducting films, Phys. Rev. B, 31, 5768, 1985 |
| [185] | Al Khawaja, U.; Andersen, J. O.; Proukakis, N. P.; Stoof, H. T.C., Low dimensional bose gases, Phys. Rev. A, 66, Article 013615 pp., 2002 |
| [186] | Zhang, W.; Lin, G.-D.; Duan, L.-M., Berezinskii-kosterlitz-thouless transition in a trapped quasi-two-dimensional Fermi gas near a Feshbach resonance, Phys. Rev. A, 78, Article 043617 pp., 2008 |
| [187] | Luick, N.; Sobirey, L.; Bohlen, M.; Pal Singh, V.; Mathey, L.; Lompe, T.; Moritz, H., An ideal josephson junction in an ultracold two-dimensional Fermi gas, Science, 369, 89, 2020 |
| [188] | Arahata, E.; Nikuni, T., Propagation of second sound in a superfluid Fermi gas in the unitary limit, Phys. Rev. A, 80, Article 043613 pp., 2009 |
| [189] | Noziéres, P.; Pines, D., The Theory of Quantum Liquids II: Superfluid Bose Liquids, 1999, Westview Press: Westview Press Boulder |
| [190] | Ozawa, T.; Stringari, S., Discontinuities in the first and second sound velocities at the berezinskii-kosterlitz-thouless transition, Phys. Rev. Lett., 112, Article 025302 pp., 2014 |
| [191] | Sidorenkov, L. A.; Tey, M.; Grimm, R.; Hou, Y.-H.; Pitaevskii, L.; Stringari, S., Second sound and the superfluid fraction in a Fermi gas with resonant interactions, Nature, 498, 78, 2013 |
| [192] | Furutani, K.; Tononi, A.; Salasnich, L., Sound modes in collisional superfluid bose gases, New J. Phys., 23, Article 043043 pp., 2021 |
| [193] | Stringari, S., Second sound seen, Nat. Phys., 17, 770, 2021 |
| [194] | Dalibard, J., Fluides quantiques de basse dimension et transition de Kosterlitz-Thouless, 2016, Collège de France Lecture Notes |
| [195] | Machta, J.; Guyer, R., Superfluid films on a cylindrical surface, J. Low Temp. Phys., 74, 231, 1989 |
| [196] | Chomaz, L.; Ferrier-Barbut, I.; Ferlaino, F.; Laburthe-Tolra, B.; Lev, B. L.; Pfau, T., Dipolar physics: a review of experiments with magnetic quantum gases, Rep. Progr. Phys., 86, Article 026401 pp., 2023 |
| [197] | Dalibard, J.; Gerbier, F.; Juzeliūnas, G.; Öhberg, P., Colloquium: Artificial gauge potentials for neutral atoms, Rev. Mod. Phys., 83, 1523, 2011 |
| [198] | Eckel, S.; Kumar, A.; Jacobson, T.; Spielman, I. B.; Campbell, G. K., A rapidly expanding bose-Einstein condensate: An expanding universe in the lab, Phys. Rev. X, 8, Article 021021 pp., 2018 |
| [199] | Salasnich, L., Bose-Einstein condensate in an elliptical waveguide, SciPost Phys. Core, 5, 015, 2022 |
| [200] | Del Pace, G.; Xhani, K.; Muzi Falconi, A.; Fedrizzi, M.; Grani, N.; Hernandez Rajkov, D.; Inguscio, M.; Scazza, F.; Kwon, W.-J.; Roati, G., Imprinting persistent currents in tunable Fermionic rings, Phys. Rev. X, 12, Article 041037 pp., 2022 |
| [201] | Amico, L.; Anderson, D.; Boshier, M.; Brantut, J.-P.; Kwek, L.-C.; Minguzzi, A.; von Klitzing, W., Colloquium: Atomtronic circuits: From many-body physics to quantum technologies, Rev. Mod. Phys., 94, Article 041001 pp., 2022 |
| [202] | Gradshteyn, I. S.; Ryzhik, I. M., Table of Integrals, Series, and Products, 1996, Academic Press · Zbl 0918.65001 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
