- Letter
- Open Access
Superfluid transition of a ferromagnetic Bose gas
Phys. Rev. Research 6, L022030 – Published 3 May, 2024
DOI: https://doi.org/10.1103/PhysRevResearch.6.L022030
Abstract
The strongly ferromagnetic spin-1 Bose-Einstein condensate has recently been realized with atomic . It was predicted that a strong ferromagnetic interaction can drive the normal gas into a magnetized phase at a temperature above the superfluid transition, and likely satisfies the criterion. We reexamine this theoretical proposal employing the two-particle-irreducible effective potential, and conclude that there exists no stable normal magnetized phase for a dilute ferromagnetic Bose gas. For , we predict that the normal gas undergoes a joint first-order transition and jumps directly into a state with finite condensate density and magnetization. We estimate the size of the first-order jump and examine how a partial spin polarization in the initial sample affects the first-order transition. We propose a qualitative phase diagram at fixed temperature for the trapped gas.
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References (51)
- M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Observation of Bose-Einstein condensation in a dilute atomic vapor, Science 269, 198 (1995).
- K. B. Davis, M. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Bose-Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett. 75, 3969 (1995).
- C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions, Phys. Rev. Lett. 75, 1687 (1995).
- D. M. Stamper-Kurn and M. Ueda, Spinor Bose gases: Symmetries, magnetism, and quantum dynamics, Rev. Mod. Phys. 85, 1191 (2013).
- N. Gross and L. Khaykovich, All-optical production of Bose-Einstein condensation using Feshbach resonances, Phys. Rev. A 77, 023604 (2008).
- S. E. Pollack, D. Dries, M. Junker, Y. P. Chen, T. A. Corcovilos, and R. G. Hulet, Extreme tunability of interactions in a Bose-Einstein condensate, Phys. Rev. Lett. 102, 090402 (2009).
- S. J. Huh, K. Kim, K. Kwon, and J.-Y. Choi, Observation of a strongly ferromagnetic spinor Bose-Einstein condensate, Phys. Rev. Res. 2, 033471 (2020).
- E. R. I. Abraham, W. I. McAlexander, J. M. Gerton, R. G. Hulet, R. Côté, and A. Dalgarno, Triplet -wave resonance in collisions and scattering lengths of and , Phys. Rev. A 55, R3299 (1997).
- P. S. Julienne and J. M. Hutson, Contrasting the wide Feshbach resonances in and , Phys. Rev. A 89, 052715 (2014).
- T.-L. Ho, Spinor Bose condensates in optical traps, Phys. Rev. Lett. 81, 742 (1998).
- T. Ohmi and K. Machida, Bose-Einstein condensation with internal degrees of freedom in alkali atom gases, J. Phys. Soc. Jpn. 67, 1822 (1998).
- W. Zhang, S. Yi, and L. You, Bose-Einstein condensation of trapped interacting spin-1 atoms, Phys. Rev. A 70, 043611 (2004).
- Y. Kawaguchi, N. T. Phuc, and P. B. Blakie, Finite-temperature phase diagram of a spin-1 Bose gas, Phys. Rev. A 85, 053611 (2012).
- G. Lang and E. Witkowska, Thermodynamics of a spin-1 Bose gas with fixed magnetization, Phys. Rev. A 90, 043609 (2014).
- S. S. Natu and E. J. Mueller, Pairing, ferromagnetism, and condensation of a normal spin-1 Bose gas, Phys. Rev. A 84, 053625 (2011).
- P. Nozières and D. Saint James, Particle vs. pair condensation in attractive Bose liquids, J. Phys. France 43, 1133 (1982).
- M. J. Rice and Y. R. Wang, Superconductivity in a quasi-two-dimensional Bose gas, Phys. Rev. B 37, 5893 (1988).
- M. Y. Kagan and D. V. Efremov, Two-particle pairing and phase separation in a two-dimensional Bose gas with one or two sorts of bosons, Phys. Rev. B 65, 195103 (2002).
- A. Kuklov, N. Prokof'ev, and B. Svistunov, Commensurate two-component bosons in an optical lattice: Ground state phase diagram, Phys. Rev. Lett. 92, 050402 (2004).
- E. Babaev, A. Sudbø, and N. W. Ashcroft, A superconductor to superfluid phase transition in liquid metallic hydrogen, Nature (London) 431, 666 (2004).
- A. B. Kuklov, M. Matsumoto, N. V. Prokof'ev, B. V. Svistunov, and M. Troyer, Deconfined criticality: Generic first-order transition in the SU(2) symmetry case, Phys. Rev. Lett. 101, 050405 (2008).
- T. A. Bojesen, E. Babaev, and A. Sudbø, Time reversal symmetry breakdown in normal and superconducting states in frustrated three-band systems, Phys. Rev. B 88, 220511(R) (2013).
- M. H. Fischer and E. Berg, Fluctuation and strain effects in a chiral -wave superconductor, Phys. Rev. B 93, 054501 (2016).
- M. Zeng, L.-H. Hu, H.-Y. Hu, Y.-Z. You, and C. Wu, High-order time-reversal symmetry breaking normal state, Sci. China Phys. Mech. Astron. 67, 237411 (2024).
- Y. Sun, S. Kittaka, T. Sakakibara, K. Machida, J. Wang, J. Wen, X. Xing, Z. Shi, and T. Tamegai, Quasiparticle evidence for the nematic state above in , Phys. Rev. Lett. 123, 027002 (2019).
- C.-W. Cho, J. Shen, J. Lyu, O. Atanov, Q. Chen, S. H. Lee, Y. S. Hor, D. J. Gawryluk, E. Pomjakushina, M. Bartkowiak, M. Hecker, J. Schmalian, and R. Lortz, -vestigial nematic order due to superconducting fluctuations in the doped topological insulators and , Nat. Commun. 11, 3056 (2020).
- G. Röpke, A. Schnell, P. Schuck, and P. Nozières, Four-Particle condensate in strongly coupled fermion systems, Phys. Rev. Lett. 80, 3177 (1998).
- E. Berg, E. Fradkin, and S. A. Kivelson, Charge- superconductivity from pair-density-wave order in certain high-temperature superconductors, Nat. Phys. 5, 830 (2009).
- R. M. Fernandes, P. P. Orth, and J. Schmalian, Intertwined vestigial order in quantum materials: Nematicity and beyond, Annu. Rev. Condens. Matter Phys. 10, 133 (2019).
- R. M. Fernandes and L. Fu, Charge- superconductivity from multicomponent nematic pairing: Application to twisted bilayer graphene, Phys. Rev. Lett. 127, 047001 (2021).
- S.-K. Jian, Y. Huang, and H. Yao, Charge- superconductivity from nematic superconductors in two and three dimensions, Phys. Rev. Lett. 127, 227001 (2021).
- M. Hecker, R. Willa, J. Schmalian, and R. M. Fernandes, Cascade of vestigial orders in two-component superconductors: Nematic, ferromagnetic, -wave charge-, and -wave charge- states, Phys. Rev. B 107, 224503 (2023).
- M. Hecker and J. Schmalian, Vestigial nematic order and superconductivity in the doped topological insulator , npj Quantum Mater. 3, 26 (2018).
- P. T. How and S. K. Yip, Absence of Ginzburg-Landau mechanism for vestigial order in the normal phase above a two-component superconductor, Phys. Rev. B 107, 104514 (2023).
- S. Ashhab, Superfluid vs ferromagnetic behavior in a Bose gas of spin-1/2 atoms, J. Low Temp. Phys. 140, 51 (2005).
- J. Radić, S. S. Natu, and V. Galitski, Stoner ferromagnetism in a thermal pseudospin- Bose gas, Phys. Rev. Lett. 113, 185302 (2014).
- L. He, P. Gao, and Z.-Q. Yu, Normal-Superfluid phase separation in spin-half bosons at finite temperature, Phys. Rev. Lett. 125, 055301 (2020).
- J. Stenger, S. Inouye, D. M. Stamper-Kurn, H.-J. Miesner, A. P. Chikkatur, and W. Ketterle, Spin domains in ground-state Bose–Einstein condensates, Nature (London) 396, 345 (1998).
- J. M. Cornwall, R. Jackiw, and E. Tomboulis, Effective action for composite operators, Phys. Rev. D 10, 2428 (1974).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L022030 for derivation.
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L022030 for estimation.
- B. Van Schaeybroeck, Weakly interacting Bose mixtures at finite temperature, Physica A 392, 3806 (2013).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L022030 for the caveats that may stabilize a vestigial phase.
- J. Zinn-Justin, Quantum Field Theory and Critical Phenomena, 4th ed. (Clarendon Press, Oxford, 2002).
- G. Baym and G. Grinstein, Phase transition in the sigma model at finite temperature, Phys. Rev. D 15, 2897 (1977).
- S. Pankov, G. Kotliar, and Y. Motome, Semiclassical analysis of extended dynamical mean-field equations, Phys. Rev. B 66, 045117 (2002).
- D. Hügel, P. Werner, L. Pollet, and H. U. R. Strand, Bosonic self-energy functional theory, Phys. Rev. B 94, 195119 (2016).
- S. Watabe, Hugenholtz-Pines theorem for multicomponent Bose-Einstein condensates, Phys. Rev. A 103, 053307 (2021).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L022030 for result at a different density.
- F. Gerbier, A. Widera, S. Fölling, O. Mandel, and I. Bloch, Resonant control of spin dynamics in ultracold quantum gases by microwave dressing, Phys. Rev. A 73, 041602(R) (2006).
- S. Huh, K. Mukherjee, K. Kwon, J. Seo, J. Hur, S. I. Mistakidis, H. R. Sadeghpour, and J.-Y. Choi, Universality class of a spinor Bose-Einstein condensate far from equilibrium, Nat. Phys. 20, 402 (2024).