[Courants persistants dans un gaz de bosons à plusieurs composantes en interaction forte sur un anneau]
Nous considérons un mélange de bosons à deux composantes en interaction répulsive infiniment forte dans un piège en anneau unidimensionnel à fort confinement et soumis à un champ de jauge artificiel. En utilisant la forme exacte de la fonction d’onde à corps donnée par l’ansatz de Bethe, nous obtenons l’énergie de l’état fondamental et la valeur des courants persistants jusqu’à quatre particules. Ensuite, en fonction du flux appliqué, nous déterminons quelle est la symétrie de l’état sous l’échange de particules. Nous constatons que l’énergie de l’état fondamental et les courants persistants présentent une périodicité réduite par rapport au cas sans interaction, ce qui correspond à l’obtention d’états avec un moment cinétique fractionnaire par particule. Nous relions cet effet au changement de symétrie de l’état fondamental sous l’effet du champ de jauge artificiel. Nos résultats généralisent ceux précédemment rapportés pour les mélanges fermioniques avec des interactions attractives ou répulsives et mettent en évidence le rôle de la symétrie dans cet effet.
We consider a two-component Bose–Bose mixture at infinitely strong repulsive interactions in a tightly confining, one-dimensional ring trap and subjected to an artificial gauge field. By employing the Bethe Ansatz exact solution for the many-body wavefunction, we obtain the ground state energy and the persistent currents up to four particles. For each value of the applied flux, we then determine the symmetry of the state under particles exchange. We find that the ground-state energy and the persistent currents display a reduced periodicity with respect to the case of non-interacting particles, corresponding to reaching states with fractional angular momentum per particle. We relate this effect to the change of symmetry of the ground state under the effect of the artificial gauge field. Our results generalize the ones previously reported for fermionic mixtures with both attractive and repulsive interactions and highlight the role of symmetry in this effect.
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Mot clés : Atomes froids, gaz quantiques, systèmes unidimensionnels, interactions fortes, champs de jauge artificiels, piège en anneau, solution exacte à $N$ corps
CC-BY 4.0
@article{CRPHYS_2023__24_S3_A6_0,
author = {Giovanni Pecci and Gianni Aupetit-Diallo and Mathias Albert and Patrizia Vignolo and Anna Minguzzi},
title = {Persistent currents in a strongly interacting multicomponent {Bose} gas on a ring},
journal = {Comptes Rendus. Physique},
publisher = {Acad\'emie des sciences, Paris},
year = {2023},
doi = {10.5802/crphys.157},
language = {en},
note = {Online first},
}
TY - JOUR AU - Giovanni Pecci AU - Gianni Aupetit-Diallo AU - Mathias Albert AU - Patrizia Vignolo AU - Anna Minguzzi TI - Persistent currents in a strongly interacting multicomponent Bose gas on a ring JO - Comptes Rendus. Physique PY - 2023 PB - Académie des sciences, Paris N1 - Online first DO - 10.5802/crphys.157 LA - en ID - CRPHYS_2023__24_S3_A6_0 ER -
%0 Journal Article %A Giovanni Pecci %A Gianni Aupetit-Diallo %A Mathias Albert %A Patrizia Vignolo %A Anna Minguzzi %T Persistent currents in a strongly interacting multicomponent Bose gas on a ring %J Comptes Rendus. Physique %D 2023 %I Académie des sciences, Paris %Z Online first %R 10.5802/crphys.157 %G en %F CRPHYS_2023__24_S3_A6_0
Giovanni Pecci; Gianni Aupetit-Diallo; Mathias Albert; Patrizia Vignolo; Anna Minguzzi. Persistent currents in a strongly interacting multicomponent Bose gas on a ring. Comptes Rendus. Physique, Online first (2023), pp. 1-13. doi : 10.5802/crphys.157.
[1] Many-body physics with ultracold gases, Rev. Mod. Phys., Volume 80 (2008) no. 3, pp. 885-964 | DOI
[2] Quantum simulations with ultracold atoms in optical lattices, Science, Volume 357 (2017) no. 6355, pp. 995-1001 | DOI
[3] Ultracold Atoms in Optical Lattices: Simulating quantum many-body systems, OUP Oxford, 2012 | DOI
[4] Feshbach resonances in ultracold gases, Rev. Mod. Phys., Volume 82 (2010) no. 2, pp. 1225-1286 | DOI
[5] Deterministic Preparation of a Tunable Few-Fermion System, Science, Volume 332 (2011) no. 6027, pp. 336-338 | DOI
[6] Tonks–Girardeau gas of ultracold atoms in an optical lattice, Nature, Volume 429 (2004) no. 6989, pp. 277-281 | DOI
[7] Observation of a One-Dimensional Tonks-Girardeau Gas, Science, Volume 305 (2004) no. 5687, pp. 1125-1128 | DOI
[8] A quantum Newton’s cradle, Nature, Volume 440 (2006) no. 7086, pp. 900-903 | DOI
[9] Cold atoms in low dimensions – a laboratory for quantum dynamics (2022) (preprint, arXiv:2202.11071) | DOI
[10] Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State, Phys. Rev., Volume 130 (1963) no. 4, pp. 1605-1616 | DOI | MR | Zbl
[11] Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction, Phys. Rev. Lett., Volume 19 (1967) no. 23, pp. 1312-1315 | DOI | MR | Zbl
[12] The Bethe Wavefunction, Cambridge University Press, 2014 | DOI
[13] Further Results for the Many-Body Problem in One Dimension, Phys. Rev. Lett., Volume 20 (1968) no. 3, pp. 98-100 | DOI
[14] Model for a multicomponent quantum system, Phys. Rev. B, Volume 12 (1975) no. 9, pp. 3795-3805 | DOI
[15] Beautiful models: 70 years of exactly solved quantum many-body problems, World Scientific, 2004 | DOI
[16] Bethe ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions, J. Phys. A, Math. Gen., Volume 39 (2006) no. 5, pp. 1073-1098 | DOI | MR | Zbl
[17] Strongly interacting trapped one-dimensional quantum gases: Exact solution, AVS Quantum Sci., Volume 4 (2022) no. 2, 027102 | DOI
[18] Strongly interacting confined quantum systems in one dimension, Nat. Commun., Volume 5 (2014) no. 1, 5300 | DOI
[19] Quantum magnetism without lattices in strongly interacting one-dimensional spinor gases, Phys. Rev. A, Volume 90 (2014) no. 1, 013611 | DOI
[20] et al. Roadmap on Atomtronics: State of the art and perspective, AVS Quantum Sci., Volume 3 (2021) no. 3, 039201 | DOI
[21] Introduction to the physics of artificial gauge fields, Lecture notes of the International School of Physics “Enrico Fermi” on Quantum Matter at Ultralow Temperatures (Varenna 7 - 15 July 2014) (M. Inguscio; W. Ketterle; S. Stringari et al., eds.), IOS Press, 2016, pp. 1-61 | DOI
[22] Colloquium: Artificial gauge potentials for neutral atoms, Rev. Mod. Phys., Volume 83 (2011) no. 4, pp. 1523-1543 | DOI
[23] Light-induced gauge fields for ultracold atoms, Rep. Prog. Phys., Volume 77 (2014) no. 12, 126401 | DOI
[24] Driving Phase Slips in a Superfluid Atom Circuit with a Rotating Weak Link, Phys. Rev. Lett., Volume 110 (2013) no. 2, 025302 | DOI
[25] Producing superfluid circulation states using phase imprinting, Phys. Rev. A, Volume 97 (2018) no. 4, 043615 | DOI
[26] Persistent currents in one-dimensional systems of strongly correlated electrons, Low Temperature Physics, Volume 21 (1995), pp. 533-555
[27] Quantum rings for beginners: energy spectra and persistent currents, Physica E Low Dimens. Syst. Nanostruct., Volume 21 (2004) no. 1, pp. 1-35 | DOI
[28] Colloquium: Atomtronic circuits: from many-body physics to quantum technologies, Rev. Mod. Phys., Volume 94 (2022), 041001 | DOI
[29] Quantum Many Particle Systems in Ring-Shaped Optical Lattices, Phys. Rev. Lett., Volume 95 (2005) no. 6, 063201 | DOI
[30] Interaction-resistant metals in multicomponent Fermi systems, Phys. Rev. B, Volume 103 (2021) no. 20, 205132 | DOI
[31] Interferometric Measurement of the Current-Phase Relationship of a Superfluid Weak Link, Phys. Rev. X, Volume 4 (2014) no. 3, 031052 | DOI
[32] Quench-Induced Supercurrents in an Annular Bose Gas, Phys. Rev. Lett., Volume 113 (2014) no. 13, 135302 | DOI
[33] Self-heterodyne detection of the in situ phase of an atomic superconducting quantum interference device, Phys. Rev. A, Volume 92 (2015) no. 3, 033602 | DOI
[34] Persistent Currents in Rings of Ultracold Fermionic Atoms, Phys. Rev. Lett., Volume 128 (2022) no. 15, 150401 | DOI
[35] Imprinting persistent currents in tunable fermionic rings, Phys. Rev. X, Volume 12 (2022) no. 4, 041037 | DOI
[36] Interference dynamics of matter-waves of SU() fermions (2022) (preprint, arXiv:2206.02807) | DOI
[37] Theoretical Considerations Concerning Quantized Magnetic Flux in Superconducting Cylinders, Phys. Rev. Lett., Volume 7 (1961) no. 2, pp. 46-49 | DOI
[38] Some Considerations Related to the Quantization of Charge in Mesoscopic Systems, Granular Nanoelectronics (C. W. J. Beenakker et al., eds.) (NATO Science Series B: Physics), Volume 251, Plenum Press, New York, 1991, pp. 343-358 | DOI
[39] Enhancing sensitivity to rotations with quantum solitonic currents, SciPost Phys., Volume 12 (2022), 138 | DOI
[40] Persistent Currents in One Dimension: The Counterpart of Leggett’s Theorem, Phys. Rev. Lett., Volume 101 (2008) no. 10, 106804 | DOI
[41] Probing the BCS-BEC crossover with persistent currents, Phys. Rev. Res., Volume 3 (2021) no. 3, L032064 | DOI
[42] Persistent current of a Hubbard ring threaded with a magnetic flux, Phys. Rev. B, Volume 45 (1992) no. 20, pp. 11795-11804 | DOI
[43] Persistent current of SU(N) fermions, SciPost Phys., Volume 12 (2022), 033 | DOI | MR
[44] Exact results of the ground state and excitation properties of a two-component interacting Bose system, Eur. Phys. Lett., Volume 61 (2003) no. 3, pp. 368-374 | DOI
[45] Exactly solvable case of a one-dimensional Bose–Fermi mixture, Phys. Rev. A, Volume 73 (2006) no. 2, 021602 | DOI
[46] Applications of exact solution for strongly interacting one-dimensional Bose-–Fermi mixture: Low-temperature correlation functions, density profiles, and collective modes, Ann. Phys., Volume 321 (2006) no. 10, pp. 2390-2437 | DOI | MR | Zbl
[47] The One-Dimensional Hubbard Model, Cambridge University Press, 2005 | DOI
[48] Bethe-ansatz wave function, momentum distribution, and spin correlation in the one-dimensional strongly correlated Hubbard model, Phys. Rev. B, Volume 41 (1990) no. 4, pp. 2326-2338 | DOI
[49] Zur theorie der metalle. I. Eigenwerte und Eigenfunktionen der linearen Atomkette, Z. Phys., Volume 71 (1931) no. 3, pp. 205-226 | Zbl
[50] et al. An introduction to integrable techniques for one-dimensional quantum systems, Springer, 2017 | MR
[51] Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension, J. Math. Phys., Volume 1 (1960) no. 6, pp. 516-523 | DOI | MR | Zbl
[52] Exact density profiles and symmetry classification for strongly interacting multi-component Fermi gases in tight waveguides, New J. Phys., Volume 18 (2016) no. 5, 055011 | DOI
[53] Solution of the Kondo problem, Rev. Mod. Phys., Volume 55 (1983) no. 2, pp. 331-402 | DOI | MR
[54] Quantum rings for beginners II: Bosons versus fermions, Physica E Low Dimens. Syst. Nanostruct., Volume 46 (2012), pp. 119-132 | DOI
[55] Superfluidity in a Ring, Phys. Rev. A, Volume 7 (1973) no. 6, pp. 2187-2191 | DOI
[56] Algebraic Bethe ansatz for singular solutions, J. Phys. A, Math. Theor., Volume 46 (2013) no. 32, 325002 | DOI | MR | Zbl
[57] Singular solutions to the Bethe ansatz equations and rigged configurations, J. Phys. A, Math. Theor., Volume 47 (2014) no. 20, 205207 | DOI | MR | Zbl
[58] High-momentum tails as magnetic-structure probes for strongly correlated fermionic mixtures in one-dimensional traps, Phys. Rev. A, Volume 94 (2016) no. 5, 053614 | DOI
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