Abstract
Quantum atomic and molecular gases are flexible systems for studies of fundamental many-body physics. They have traditionally been produced in harmonic electromagnetic traps and thus had inhomogeneous densities, but recent advances in light shaping for optical trapping of neutral particles have led to the development of flat-bottomed optical box traps, allowing the creation of homogeneous samples. Box trapping simplifies the interpretation of experimental results, provides more direct connections with theory and, in some cases, allows qualitatively new, hitherto impossible experiments. It has now been achieved for both Bose and Fermi atomic gases in various dimensionalities, and also for gases of heteronuclear molecules. Here we review these developments and the consequent breakthroughs in the study of both equilibrium and non-equilibrium phenomena such as superfluidity, turbulence and the dynamics of phase transitions.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
$29.99 / 30 days
cancel any time
Subscribe to this journal
Receive 12 print issues and online access
$259.00 per year
only $21.58 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Dalfovo, F., Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of Bose–Einstein condensation in trapped gases. Rev. Mod. Phys. 71, 463–512 (1999).
Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of ultracold atomic Fermi gases. Rev. Mod. Phys. 80, 1215–1274 (2008).
Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).
Görlitz, A. et al. Realization of Bose–Einstein condensates in lower dimensions. Phys. Rev. Lett. 87, 130402 (2001).
Andrews, M. R. et al. Observation of interference between two Bose condensates. Science 275, 637–641 (1997).
Anderson, B. P. & Kasevich, M. A. Macroscopic quantum interference from atomic tunnel arrays. Science 282, 1686 (1998).
Greiner, M., Bloch, I., Mandel, O., Hänsch, T. W. & Esslinger, T. Exploring phase coherence in a 2D lattice of Bose–Einstein condensates. Phys. Rev. Lett. 87, 160405 (2001).
Bloch, I. Ultracold quantum gases in optical lattices. Nat. Phys. 1, 23–30 (2005).
Jin, D. S., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Collective excitations of a Bose–Einstein condensate in a dilute gas. Phys. Rev. Lett. 77, 420–423 (1996).
Mewes, M.-O. et al. Collective excitations of a Bose–Einstein condensate in a magnetic trap. Phys. Rev. Lett. 77, 988–991 (1996).
Andrews, M. R. et al. Propagation of sound in a Bose–Einstein condensate. Phys. Rev. Lett. 79, 553–556 (1997).
Stamper-Kurn, D. M. et al. Reversible formation of a Bose–Einstein condensate. Phys. Rev. Lett. 81, 2194–2197 (1998).
Greiner, M., Mandel, M. O., Esslinger, T., Hänsch, T. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002).
Gaunt, A. L., Schmidutz, T. F., Gotlibovych, I., Smith, R. P. & Hadzibabic, Z. Bose–Einstein condensation of atoms in a uniform potential. Phys. Rev. Lett. 110, 200406 (2013).
Chomaz, L. et al. Emergence of coherence via transverse condensation in a uniform quasi-two-dimensional Bose gas. Nat. Commun. 6, 6162 (2015).
Tajik, M. et al. Designing arbitrary one-dimensional potentials on an atom chip. Optics Express 27, 33474 (2019).
Mukherjee, B. et al. Homogeneous atomic Fermi gases. Phys. Rev. Lett. 118, 123401 (2017).
Hueck, K. et al. Two-dimensional homogeneous Fermi gases. Phys. Rev. Lett. 120, 060402 (2018).
Bause, R. et al. Collisions of ultracold molecules in bright and dark optical dipole traps. Phys. Rev. Res. 3, 033013 (2021).
Navon, N., Gaunt, A. L., Smith, R. P. & Hadzibabic, Z. Emergence of a turbulent cascade in a quantum gas. Nature 539, 72–75 (2016).
Ville, J. L. et al. Sound propagation in a uniform superfluid two-dimensional Bose gas. Phys. Rev. Lett. 121, 145301 (2018).
Patel, P. B. et al. Universal sound diffusion in a strongly interacting Fermi gas. Science 370, 1222–1226 (2020).
Baird, L., Wang, X., Roof, S. & Thomas, J. E. Measuring the hydrodynamic linear response of a unitary Fermi gas. Phys. Rev. Lett. 123, 160402 (2019).
Garratt, S. J. et al. From single-particle excitations to sound waves in a box-trapped atomic Bose–Einstein condensate. Phys. Rev. A 99, 021601 (2019).
Christodoulou, P. et al. Observation of first and second sound in a BKT superfluid. Nature 594, 191–194 (2021).
Bohlen, M. et al. Sound propagation and quantum-limited damping in a two-dimensional Fermi gas. Phys. Rev. Lett. 124, 240403 (2020).
Zhang, J. et al. Many-body decay of the gapped lowest excitation of a Bose–Einstein condensate. Phys. Rev. Lett. 126, 060402 (2021).
Lopes, R. et al. Quantum depletion of a homogeneous Bose–Einstein condensate. Phys. Rev. Lett. 119, 190404 (2017).
Biss, H. et al. Excitation spectrum and superfluid gap of an ultracold Fermi gas. Preprint at https://arxiv.org/abs/2105.09820 (2021).
Sobirey, L. et al. Comparing fermionic superfluids in two and three dimensions. Preprint at https://arxiv.org/abs/2106.11893 (2021).
Rauer, B. et al. Recurrences in an isolated quantum many-body system. Science 360, 307–310 (2018).
Schmidutz, T. F. et al. Quantum Joule–Thomson effect in a saturated homogeneous Bose gas. Phys. Rev. Lett. 112, 040403 (2014).
Saint-Jalm, R. et al. Dynamical symmetry and breathers in a two-dimensional Bose gas. Phys. Rev. X 9, 021035 (2019).
Amico, L. et al. Roadmap on Atomtronics: State of the art and perspective. AVS Quantum Sci. 3, 039201 (2021).
Kaufman, A. & Ni, K.-K. & Quantum science with optical tweezer arrays of ultracold atoms and molecules. Nat. Phys. https://doi.org/10.1038/s41567-021-01357-2 (2021).
Corman, L. et al. Quench-induced supercurrents in an annular Bose gas. Phys. Rev. Lett. 113, 135302 (2014).
Navon, N., Gaunt, A. L., Smith, R. P. & Hadzibabic, Z. Critical dynamics of spontaneous symmetry breaking in a homogeneous Bose gas. Science 347, 167–170 (2015).
Keesling, A. et al. Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg simulator. Nature 568, 207 (2019).
Shibata, K., Ikeda, H., Suzuki, R. & Hirano, T. Compensation of gravity on cold atoms by a linear optical potential. Phys. Rev. Res. 2, 013068 (2020).
Gauthier, G. et al. Direct imaging of a digital-micromirror device for configurable microscopic optical potentials. Optica 3, 1136–1143 (2016).
Gauthier, G. et al. in Advances In Atomic, Molecular, and Optical Physics Vol. 70, 1–101 (Academic, 2021).
Gaunt, A. L., Degenerate Bose Gases: Tuning Interactions & Geometry PhD thesis, Univ. Cambridge (2014).
Manek, I., Ovchinnikov, Y. B. & Grimm, R. Generation of a hollow laser beam for atom trapping using an axicon. Opt. Comm. 147, 67–70 (1998).
Henderson, K., Ryu, C., MacCormick, C. & Boshier, M. G. Experimental demonstration of painting arbitrary and dynamic potentials for Bose–Einstein condensates. N. J. Phys. 11, 043030 (2009).
Davidson, N., Lee, H. J., Adams, C. S., Kasevich, M. & Chu, S. Long atomic coherence times in an optical dipole trap. Phys. Rev. Lett. 74, 1311 (1995).
Ozeri, R., Khaykovich, L. & Davidson, N. Long spin relaxation times in a single-beam blue-detuned optical trap. Phys. Rev. A 59, R1750 (1999).
Friedman, N., Khaykovich, L., Ozeri, R. & Davidson, N. Compression of cold atoms to very high densities in a rotating-beam blue-detuned optical trap. Phys. Rev. A 61, 031403 (2000).
Rychtarik, D., Engeser, B., Nägerl, H.-C. & Grimm, R. Two-dimensional Bose–Einstein condensate in an optical surface trap. Phys. Rev. Lett. 92, 173003 (2004).
Meyrath, T. P., Schreck, F., Hanssen, J. L., Chuu, C.-S. & Raizen, M. G. Bose–Einstein condensate in a box. Phys. Rev. A 71, 041604 (2005).
Van Es, J. et al. Box traps on an atom chip for one-dimensional quantum gases. J. Phys. B 43, 155002 (2010).
Ville, J. L. et al. Loading and compression of a single two-dimensional Bose gas in an optical accordion. Phys. Rev. A 95, 013632 (2017).
Anderson, B. P. & Kasevich, M. A. Spatial observation of Bose–Einstein condensation of 87Rb in a confining potential. Phys. Rev. A 59, R938–R941 (1999).
Truscott, A., Strecker, K., McAlexander, W., Partridge, G. & Hulet, R. G. Observation of Fermi pressure in a gas of trapped atoms. Science 291, 2570–2572 (2001).
Tammuz, N. et al. Can a Bose gas be saturated? Phys. Rev. Lett. 106, 230401 (2011).
Kothari, D. S. & Srivasava, B. N. Joule–Thomson effect and quantum statistics. Nature 140, 970–971 (1937).
Tisza, L. Transport phenomena in helium II. Nature 141, 913 (1938).
Landau, L. D. The theory of superfluidity of helium II. Phys. Rev. 60, 356–358 (1941).
Berezinskii, V. L. Destruction of long-range order in one-dimensional and two-dimensional system possessing a continous symmetry group - II. Quantum systems. Sov. Phys. JETP 34, 610 (1971).
Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two dimensional systems. J. Phys. C 6, 1181 (1973).
Nelson, D. R. & Kosterlitz, J. M. Universal jump in the superfluid density of two-dimensional superfluids. Phys. Rev. Lett. 39, 1201–1205 (1977).
Luick, N. et al. An ideal Josephson junction in an ultracold two-dimensional Fermi gas. Science 369, 89–91 (2020).
Sobirey, L. et al. Observation of superfluidity in a strongly correlated two-dimensional Fermi gas. Science 372, 844–846 (2021).
Gauthier, G. et al. Quantitative acoustic models for superfluid circuits. Phys. Rev. Lett. 123, 260402 (2019).
Gotlibovych, I. et al. Observing properties of an interacting homogeneous Bose–Einstein condensate: Heisenberg-limited momentum spread, interaction energy, and free-expansion dynamics. Phys. Rev. A 89, 061604 (2014).
Lopes, R. et al. Quasiparticle energy in a strongly interacting homogeneous Bose–Einstein condensate. Phys. Rev. Lett. 118, 210401 (2017).
Mukherjee, B. et al. Spectral response and contact of the unitary Fermi gas. Phys. Rev. Lett. 122, 203402 (2019).
Yan, Z. et al. Boiling a unitary Fermi liquid. Phys. Rev. Lett. 122, 093401 (2019).
Zou, Y.-Q. et al. Magnetic dipolar interaction between hyperfine clock states in a planar alkali Bose gas. Phys. Rev. Lett. 125, 233604 (2020).
Zou, Y. et al. Tan’s two-body contact across the superfluid transition of a planar Bose gas. Nat. Commun. 12, 760 (2021).
Sagi, Y., Drake, T. E., Paudel, R. & Jin, D. S. Measurement of the homogeneous contact of a unitary Fermi gas. Phys. Rev. Lett. 109, 220402 (2012).
Sagi, Y., Drake, T. E., Paudel, R., Chapurin, R. & Jin, D. S. Breakdown of the Fermi–liquid description for strongly interacting fermions. Phys. Rev. Lett. 114, 075301 (2015).
Ota, M., Tajima, H., Hanai, R., Inotani, D. & Ohashi, Y. Local photoemission spectra and effects of spatial inhomogeneity in the BCS-BEC-crossover regime of a trapped ultracold Fermi gas. Phys. Rev. A 95, 053623 (2017).
Carcy, C. et al. Contact and sum rules in a near-uniform Fermi gas at unitarity. Phys. Rev. Lett. 122, 203401 (2019).
Kozuma, M. et al. Coherent splitting of Bose–Einstein condensed atoms with optically induced Bragg diffraction. Phys. Rev. Lett. 82, 871–875 (1999).
Stenger, J. et al. Bragg spectroscopy of a Bose–Einstein condensate. Phys. Rev. Lett. 82, 4569–4573 (1999).
Zakharov, V. E., L’vov, V. S. & Falkovich, G. Kolmogorov Spectra of Turbulence (Springer, 1992).
Navon, N. et al. Synthetic dissipation and cascade fluxes in a turbulent quantum gas. Science 366, 382–385 (2019).
Gauthier, G. et al. Giant vortex clusters in a two-dimensional quantum fluid. Science 364, 1264–1267 (2019).
Johnstone, S. P. et al. Evolution of large-scale flow from turbulence in a two-dimensional superfluid. Science 364, 1267–1271 (2019).
Stockdale, O. R. et al. Universal dynamics in the expansion of vortex clusters in a dissipative two-dimensional superfluid. Phys. Rev. Res. 2, 033138 (2020).
Reeves, M. T. et al. Emergence of off-axis equilibria in a quantum vortex gas. Preprint at https://arxiv.org/abs/2010.10049 (2020).
Onsager, L. Statistical hydrodynamics. Nuovo Cimento 6, 279–287 (1949).
Kwon, W. J. et al. Sound emission and annihilations in a programmable quantum vortex collider. Preprint at https://arxiv.org/abs/2105.15180 (2021).
Kibble, T. W. B. Topology of cosmic domains and strings. J. Phys. A 9, 1387–1398 (1976).
Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985).
del Campo, A. & Zurek, W. H. Universality of phase transition dynamics: topological defects from symmetry breaking. Int. J. Mod. Phys. A 29, 1430018 (2014).
Beugnon, J. & Navon, N. Exploring the Kibble–Zurek mechanism with homogeneous Bose gases. J. Phys. B 50, 022002 (2017).
Aidelsburger, M. et al. Relaxation dynamics in the merging of n independent condensates. Phys. Rev. Lett. 119, 190403 (2017).
Schweigler, T. et al. Decay and recurrence of non-Gaussian correlations in a quantum many-body system. Nat. Phys. 17, 559–563 (2021).
Glidden, J. A. P. et al. Bidirectional dynamic scaling in an isolated Bose gas far from equilibrium. Nat. Phys. 17, 457–461 (2021).
Eigen, C. et al. Universal scaling laws in the dynamics of a homogeneous unitary Bose gas. Phys. Rev. Lett. 119, 250404 (2017).
Eigen, C. et al. Universal prethermal dynamics of Bose gases quenched to unitarity. Nature 563, 221–224 (2018).
Bakkali-Hassani, B. et al. Realization of a Townes soliton in a two-component planar Bose gas. Phys. Rev. Lett. 127, 023603 (2021).
Chen and C.-L. Hung, C.-A. Observation of universal quench dynamics and Townes soliton formation from modulational instability in two-dimensional Bose gases. Phys. Rev. Lett. 125, 250401 (2020).
Chen, C.-A. & Hung, C.-L. Observation of scale invariance in two-dimensional matter-wave Townes solitons. Phys. Rev. Lett. 127, 023604 (2021).
Zou, Y.-Q. et al. Optical control of the density and spin spatial profiles of a planar Bose gas. J. Phys. B 54, 08LT01 (2021).
Zhang, Z., Chen, L., Yao, K. & Chin, C. Transition from an atomic to a molecular Bose–Einstein condensate. Nature 592, 708–711 (2021).
Eigen, C. et al. Observation of weak collapse in a Bose–Einstein condensate. Phys. Rev. X 6, 041058 (2016).
Clark, L. W., Gaj, A., Feng, L. & Chin, C. Collective emission of matter-wave jets from driven Bose–Einstein condensates. Nature 551, 356–359 (2017).
Fu, H. et al. Density waves and jet emission asymmetry in Bose fireworks. Phys. Rev. Lett. 121, 243001 (2018).
Zhang, Z., Yao, K.-X., Feng, L., Hu, J. & Chin, C. Pattern formation in a driven Bose–Einstein condensate. Nat. Phys. 16, 652–656 (2020).
Chen, C.-A., Khlebnikov, S. & Hung, C.-L. Observation of quasiparticle pair production and quantum entanglement in atomic quantum gases quenched to an attractive interaction. Phys. Rev. Lett. 127, 060404 (2021).
Mathey, L. & Polkovnikov, A. Light cone dynamics and reverse Kibble–Zurek mechanism in two-dimensional superfluids following a quantum quench. Phys. Rev. A 81, 033605 (2010).
Jelić, A. & Cugliandolo, L. F. Quench dynamics of the 2d XY model. J. Stat. Mech. 2011, 02032 (2011).
Mathey, L., Günter, K. J., Dalibard, J. & Polkovnikov, A. Dynamic Kosterlitz–Thouless transition in two-dimensional Bose mixtures of ultracold atoms. Phys. Rev. A 95, 053630 (2017).
Comaron, P., Larcher, F., Dalfovo, F. & Proukakis, N. P. Quench dynamics of an ultracold two-dimensional Bose gas. Phys. Rev. A 100, 033618 (2019).
Brown, K., Bland, T., Comaron, P. & Proukakis, N. P. Periodic quenches across the Berezinskii-Kosterlitz–Thouless phase transition. Phys. Rev. Res. 3, 013097 (2021).
Fialko, O., Opanchuk, B., Sidorov, A. I., Drummond, P. D. & Brand, J. Fate of the false vacuum: towards realization with ultra-cold atoms. Europhys. Lett. 110, 56001 (2015).
Braden, J., Johnson, M. C., Peiris, H. V. & Weinfurtner, S. Towards the cold atom analog false vacuum. J. High Energy Phys. 2018, 14 (2018).
Braden, J., Johnson, M. C., Peiris, H. V., Pontzen, A. & Weinfurtner, S. Nonlinear dynamics of the cold atom analog false vacuum. J. High Energy Phys. 2019, 174 (2019).
Billam, T. P., Gregory, R., Michel, F. & Moss, I. G. Simulating seeded vacuum decay in a cold atom system. Phys. Rev. D 100, 065016 (2019).
Goldman, N., Budich, J. C. & Zoller, P. Topological quantum matter with ultracold gases in optical lattices. Nat. Phys. 12, 639–645 (2016).
Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).
Fletcher, R. J. et al. Geometric squeezing into the lowest Landau level. Science 372, 1318–1322 (2021).
Mancini, M. et al. Observation of chiral edge states with neutral fermions in synthetic Hall ribbons. Science 349, 1510–1513 (2015).
Stuhl, B. K., Lu, H. I., Aycock, L. M., Genkina, D. & Spielman, I. B. Visualizing edge states with an atomic Bose gas in the quantum Hall regime. Science 349, 1514–1518 (2015).
Chalopin, T. et al. Probing chiral edge dynamics and bulk topology of a synthetic Hall system. Nat. Phys. 16, 1017–1021 (2020).
Roccuzzo, S. M., Stringari, S. & Recati, A. Supersolid edge and bulk phases of a dipolar quantum gas in a box. Preprint at https://arxiv.org/abs/2104.01068 (2021).
Böttcher, F. et al. Transient supersolid properties in an array of dipolar quantum droplets. Phys. Rev. X 9, 011051 (2019).
Tanzi, L. et al. Observation of a dipolar quantum gas with metastable supersolid properties. Phys. Rev. Lett. 122, 130405 (2019).
Chomaz, L. et al. Long-lived and transient supersolid behaviors in dipolar quantum gases. Phys. Rev. X 9, 021012 (2019).
Norcia, M. A. et al. Two-dimensional supersolidity in a dipolar quantum gas. Nature 596, 357–361 (2021).
Hertkorn, J. et al. Supersolidity in two-dimensional trapped dipolar droplet arrays. Phys. Rev. Lett. 127, 155301 (2021).
Böttcher, F. et al. New states of matter with fine-tuned interactions: quantum droplets and dipolar supersolids. Rep. Progr. Phys. 84, 012403 (2021).
Mazurenko, A. et al. A cold-atom Fermi–Hubbard antiferromagnet. Nature 545, 462–466 (2017).
Gall, M., Wurz, N., Samland, J., Chan, C. F. & Köhl, M. Competing magnetic orders in a bilayer Hubbard model with ultracold atoms. Nature 589, 40–43 (2021).
Fulde, P. & Ferrell, R. A. Superconductivity in a strong spin-exchange field. Phys. Rev. 135, A550–A563 (1964).
Larkin, A. I. & Ovchinnikov, Y. N. Nonuniform state of superconductors. Zh. Eksp. Teor. Fiz. 47, 1136–1146 (1964).
Kinnunen, J. J., Baarsma, J. E., Martikainen, J.-P. & Törmä, P. The Fulde–Ferrell–Larkin–Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review. Rep. Progr. Phys. 81, 046401 (2018).
Lee, T. D. & Yang, C. N. Many-body problem in quantum mechanics and quantum statistical mechanics. Phys. Rev. 105, 1119–1120 (1957).
Reppy, J. D. et al. Density dependence of the transition temperature in a homogeneous Bose–Einstein condensate. Phys. Rev. Lett. 84, 2060–2063 (2000).
Arnold, P. & Moore, G. BEC transition temperature of a dilute homogeneous imperfect Bose gas. Phys. Rev. Lett. 87, 120401 (2001).
Kashurnikov, V. A., Prokof’ev, N. V. & Svistunov, B. V. Critical temperature shift in weakly interacting Bose gas. Phys. Rev. Lett. 87, 120402 (2001).
Andersen, J. O. Theory of the weakly interacting Bose gas. Rev. Mod. Phys. 76, 599–639 (2004).
Holzmann, M., Fuchs, J.-N., Baym, G. A., Blaizot, J.-P. & Laloë, F. Bose Einstein transition temperature in a dilute repulsive gas. C. R. Phys. 5, 21–37 (2004).
Ensher, J. R., Jin, D. S., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Bose–Einstein condensation in a dilute gas: measurement of energy and ground-state occupation. Phys. Rev. Lett. 77, 4984–4987 (1996).
Gerbier, F. et al. Critical temperature of a trapped, weakly interacting Bose gas. Phys. Rev. Lett. 92, 030405 (2004).
Meppelink, R. et al. Thermodynamics of Bose–Einstein-condensed clouds using phase-contrast imaging. Phys. Rev. A 81, 053632 (2010).
Smith, R. P., Campbell, R. L. D., Tammuz, N. & Hadzibabic, Z. Effects of interactions on the critical temperature of a trapped Bose gas. Phys. Rev. Lett. 106, 250403 (2011a).
Smith, R. P., Tammuz, N., Campbell, R. L. D., Holzmann, M. & Hadzibabic, Z. Condensed fraction of an atomic Bose gas induced by critical correlations. Phys. Rev. Lett. 107, 190403 (2011).
Giorgini, S., Pitaevskii, L. P. & Stringari, S. Condensate fraction and critical temperature of a trapped interacting Bose gas. Phys. Rev. A 54, R4633–R4636 (1996).
Shkedrov, C., Menashes, M., Ness, G., Vainbaum, A. & Sagi, Y. Absence of heating in a uniform Fermi gas created by periodic driving. Preprint at https://arxiv.org/abs/2102.09506 (2021).
Becker, D. et al. Space-borne Bose–Einstein condensation for precision interferometry. Nature 562, 391–395 (2018).
Aveline, D. C. et al. Observation of Bose–Einstein condensates in an Earth-orbiting research lab. Nature 582, 193–197 (2020).
Frye, K. et al. The Bose–Einstein condensate and cold atom laboratory. EPJ Quantum Technol. 8, 1–38 (2021).
Huang, K. Statistical Mechanics (Wiley, 1987).
Drake, T. E. et al. Direct observation of the Fermi surface in an ultracold atomic gas. Phys. Rev. A 86, 031601 (2012).
Donner, T. et al. Critical behavior of a trapped interacting Bose gas. Science 315, 1556–1558 (2007).
Campostrini, M., Hasenbusch, M., Pelissetto, A. & Vicari, E. Theoretical estimates of the critical exponents of the superfluid transition in 4He by lattice methods. Phys. Rev. B 74, 144506 (2006).
Burovski, E., Prokof’ev, N., Svistunov, B. & Troyer, M. Critical temperature and thermodynamics of attractive fermions at unitarity. Phys. Rev. Lett. 96, 160402 (2006).
Acknowledgements
We thank C. Eigen for help in the preparation of the figures and critical reading of the manuscript. We also thank R. Lopes and S. Nascimbene for comments on the manuscript, and M. Zwierlein, P. Patel, B. Mukherjee, J. Beugnon, J. Dalibard, R. Saint-Jalm, H. Biss, T. Lompe and H. Moritz for sharing their data. This work was supported by the EPSRC (grant numbers EP/N011759/1, EP/P009565/1 and EP/T019913/1), ERC (QBox), QuantERA (NAQUAS, EPSRC grant number EP/R043396/1), NSF CAREER (grant number 1945324) and DARPA (grant number 00010372). N.N. acknowledges support from the David and Lucile Packard Foundation, and the Alfred P. Sloan Foundation. R.P.S. acknowledges support from the Royal Society. Z.H. acknowledges support from the Royal Society Wolfson Fellowship.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Peer review information Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Navon, N., Smith, R.P. & Hadzibabic, Z. Quantum gases in optical boxes. Nat. Phys. 17, 1334–1341 (2021). https://doi.org/10.1038/s41567-021-01403-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41567-021-01403-z
This article is cited by
-
Antiferromagnetic phase transition in a 3D fermionic Hubbard model
Nature (2024)
-
Stabilizing persistent currents in an atomtronic Josephson junction necklace
Nature Communications (2024)
-
Condensate and superfluid fraction of homogeneous Bose gases in a self-consistent Popov approximation
Scientific Reports (2024)
-
Low-dimensional quantum gases in curved geometries
Nature Reviews Physics (2023)
-
Universal equation of state for wave turbulence in a quantum gas
Nature (2023)