- Letter
- Open Access
Static impurity in a mesoscopic system of fermionic matter waves
Phys. Rev. Research 8, L022015 – Published 15 April, 2026
DOI: https://doi.org/10.1103/tcmp-nf52
Abstract
We investigate the effects of a static impurity, modeled by a localized barrier, in a one-dimensional mesoscopic system comprised of strongly correlated repulsive -symmetric fermions. For a mesoscopic sized ring under the effect of an artificial gauge field, we analyze the energy spectrum, the particle density, and the current flowing through the impurity at varying interaction strengths, barrier heights, and number of components. We find that the physics of the system is governed by the competition between effective single-particle process and the formation of a high-stiffness spin-correlated state associated with the phenomenon of fractionalization of the flux quantum characterizing the -component fermionic system. Our findings provide a route to probe the response of fermions to effective magnetic fields; at the same time, they hold significance for fundamental understanding of localized impurity problems.
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References (76)
- B. L. Altshuler, P. A. Lee, and W. R. Webb, Mesoscopic Phenomena in Solids (Elsevier, Amsterdam, 2012).
- G. L. Timp and R. E. Howard, Quantum mechanical aspects of transport in nanoelectronics, Proc. IEEE 79, 1188 (1991).
- H. Alloul, J. Bobroff, M. Gabay, and P. J. Hirschfeld, Defects in correlated metals and superconductors, Rev. Mod. Phys. 81, 45 (2009).
- A. Kolezhuk, S. Sachdev, R. R. Biswas, and P. Chen, Theory of quantum impurities in spin liquids, Phys. Rev. B 74, 165114 (2006).
- C. L. Kane and M. P. A. Fisher, Transport in a one-channel Luttinger liquid, Phys. Rev. Lett. 68, 1220 (1992).
- C. L. Kane and M. P. A. Fisher, Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas, Phys. Rev. B 46, 15233 (1992).
- J. von Delft and H. Schoeller, Bosonization for beginners—refermionization for experts, Ann. Phys. 510, 225 (1998).
- H. Saleur, Lectures on non perturbative field theory and quantum impurity problems, in Topological Aspects of Low Dimensional Systems: Session LXIX (Springer, Berlin, 2002), p. 473.
- T. Giamarchi, Quantum Physics in One Dimension (Clarendon Press, Oxford, 2003), Vol. 121.
- C. Rylands and N. Andrei, Quantum impurity in a Luttinger liquid: Exact solution of the Kane-Fisher model, Phys. Rev. B 94, 115142 (2016).
- P. Manju, K. S. Hardman, M. A. Sooriyabandara, P. B. Wigley, J. D. Close, N. P. Robins, M. R. Hush, and S. S. Szigeti, Quantum tunneling dynamics of an interacting Bose-Einstein condensate through a Gaussian barrier, Phys. Rev. A 98, 053629 (2018).
- S. Léger, J. Puertas-Martínez, K. Bharadwaj, R. Dassonneville, J. Delaforce, F. Foroughi, V. Milchakov, L. Planat, O. Buisson, C. Naud, et al., Observation of quantum many-body effects due to zero point fluctuations in superconducting circuits, Nat. Commun. 10, 5259 (2019).
- J. Puertas Martínez, S. Léger, N. Gheeraert, R. Dassonneville, L. Planat, F. Foroughi, Y. Krupko, O. Buisson, C. Naud, W. Hasch-Guichard, S. Florense, I. Snyman, and N. Roch, A tunable Josephson platform to explore many-body quantum optics in circuit-qed, npj Quantum Inf. 5, 19 (2019).
- R. Kuzmin, N. Grabon, N. Mehta, A. Burshtein, M. Goldstein, M. Houzet, L. I. Glazman, and V. E. Manucharyan, Inelastic scattering of a photon by a quantum phase slip, Phys. Rev. Lett. 126, 197701 (2021).
- S. Mistakidis and A. Volosniev, Physics of Impurities in Quantum Gases (MDPI, Basel, 2022).
- S. Léger, T. Sépulcre, D. Fraudet, O. Buisson, C. Naud, W. Hasch-Guichard, S. Florens, I. Snyman, D. M. Basko, and N. Roch, Revealing the finite-frequency response of a bosonic quantum impurity, SciPost Phys. 14, 130 (2023).
- M. Nadeem, M. S. Fuhrer, and X. Wang, The superconducting diode effect, Nat. Rev. Phys. 5, 558 (2023).
- A. M. Hriscu and Yu. V. Nazarov, Coulomb blockade due to quantum phase slips illustrated with devices, Phys. Rev. B 83, 174511 (2011).
- M. Trahms, L. Melischek, J. F. Steiner, B. Mahendru, I. Tamir, N. Bogdanoff, O. Peters, G. Reecht, C. B. Winkelmann, F. von Oppen, et al., Diode effect in Josephson junctions with a single magnetic atom, Nature (London) 615, 628 (2023).
- C. Ryu, P. W. Blackburn, A. A. Blinova, and M. G. Boshier, Experimental realization of Josephson junctions for an atom SQUID, Phys. Rev. Lett. 111, 205301 (2013).
- D. Aghamalyan, M. Cominotti, M. Rizzi, D. Rossini, F. Hekking, A. Minguzzi, L.-C. Kwek, and L. Amico, Coherent superposition of current flows in an atomtronic quantum interference device, New J. Phys. 17, 045023 (2015).
- G. Valtolina, A. Burchianti, A. Amico, E. Neri, K. Xhani, J. A. Seman, A. Trombettoni, A. Smerzi, M. Zaccanti, M. Inguscio, and G. Roati, Josephson effect in fermionic superfluids across the BEC-BCS crossover, Science 350, 1505 (2015).
- V. P. Singh, J. Polo, L. Mathey, and L. Amico, Shapiro steps in driven atomic Josephson junctions, Phys. Rev. Lett. 133, 093401 (2024).
- C. Ryu, E. C. Samson, and M. G. Boshier, Quantum interference of currents in an atomtronic SQUID, Nat. Commun. 11, 3338 (2020).
- O. Adeniji, C. Henry, S. Thomas, R. C. Sapp, A. Goyal, C. W. Clark, and M. Edwards, Double-target BEC atomtronic rotation sensor, arXiv:2411.06585.
- R. M. Godun, M. B. d’Arcy, G. S. Summy, and K. Burnett, Prospects for atom interferometry, Contemp. Phys. 42, 77 (2001).
- S. A. Haine, Quantum noise in bright soliton matterwave interferometry, New J. Phys. 20, 033009 (2018).
- O. J. Wales, A. Rakonjac, T. P. Billam, J. L. Helm, S. A. Gardiner, and S. L. Cornish, Splitting and recombination of bright-solitary-matter waves, Commun. Phys. 3, 51 (2020).
- P. Naldesi, J. Polo, P. D. Drummond, V. Dunjko, L. Amico, A. Minguzzi, and M. Olshanii, Massive particle interferometry with lattice solitons, SciPost Phys. 15, 187 (2023).
- L. Sonderhouse, C. Sanner, R. B. Hutson, A. Goban, T. Bilitewski, L. Yan, W. R. Milner, A. M. Rey, and J. Ye, Thermodynamics of a deeply degenerate -symmetric Fermi gas, Nat. Phys. 16, 1216 (2020).
- H. Frahm and A. Schadschneider, On the Bethe ansatz soluble degenerate Hubbard model, in The Hubbard Model: Its Physics and Mathematical Physics, edited by D. Baeriswyl, D. K. Campbell, J. M. P. Carmelo, F. Guinea, and E. Louis (Springer US, Boston, MA, 1995), p. 21.
- A. V. Gorshkov, M. Hermele, V. Gurarie, C. Xu, P. S. Julienne, J. Ye, P. Zoller, E. Demler, M. D. Lukin, and A. M. Rey, Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms, Nat. Phys. 6, 289 (2010).
- M. A. Cazalilla and A. M. Rey, Ultracold Fermi gases with emergent SU() symmetry, Rep. Prog. Phys. 77, 124401 (2014).
- S. Capponi, P. Lecheminant, and K. Totsuka, Phases of one-dimensional SU() cold atomic Fermi gases—From molecular Luttinger liquids to topological phases, Ann. Phys. 367, 50 (2016).
- M. Cominotti, D. Rossini, M. Rizzi, F. Hekking, and A. Minguzzi, Optimal persistent currents for interacting bosons on a ring with a gauge field, Phys. Rev. Lett. 113, 025301 (2014).
- J. Polo, P. Naldesi, A. Minguzzi, and L. Amico, The quantum solitons atomtronic interference device, Quantum Sci. Technol. 7, 015015 (2021).
- W. J. Chetcuti, T. Haug, L.-C. Kwek, and L. Amico, Persistent current of SU(N) fermions, SciPost Phys. 12, 33 (2022).
- W. J. Chetcuti, Persistent currents in atomtronic circuits of SU(N) fermions, Ph.D. thesis, University of Catania, 2023.
- O. I. Pâţu and D. V. Averin, Temperature-dependent periodicity of the persistent current in strongly interacting systems, Phys. Rev. Lett. 128, 096801 (2022).
- N. Andrei, K. Furuya, and J. H. Lowenstein, Solution of the Kondo problem, Rev. Mod. Phys. 55, 331 (1983).
- S. Taie, R. Yamazaki, S. Sugawa, and Y. Takahashi, An SU(6) Mott insulator of an atomic Fermi gas realized by large-spin Pomeranchuk cooling, Nat. Phys. 8, 825 (2012).
- G. Pagano, M. Mancini, G. Cappellini, P. Lombardi, F. Schäfer, H. Hu, X.-J. Liu, J. Catani, C. Sias, M. Inguscio, and L. Fallani, A one-dimensional liquid of fermions with tunable spin, Nat. Phys. 10, 198 (2014).
- F. Scazza, C. Hofrichter, M. Höfer, P. C. De Groot, I. Bloch, and S. Fölling, Observation of two-orbital spin-exchange interactions with ultracold -symmetric fermions, Nat. Phys. 10, 779 (2014).
- C. Hofrichter, L. Riegger, F. Scazza, M. Höfer, D. R. Fernandes, I. Bloch, and S. Fölling, Direct probing of the Mott crossover in the SU(N) Fermi-Hubbard model, Phys. Rev. X 6, 021030 (2016).
- S. Taie, E. Ibarra-García-Padilla, N. Nishizawa, Y. Takasu, Y. Kuno, H.-T. Wei, R. T. Scalettar, K. R. A. Hazzard, and Y. Takahashi, Observation of antiferromagnetic correlations in an ultracold Hubbard model, Nat. Phys. 18, 1356 (2022).
- B. Mukherjee, J. M. Hutson, and K. R. A. Hazzard, SU() magnetism with ultracold molecules, New J. Phys. 27, 013013 (2025).
- B. Mukherjee and J. M. Hutson, symmetry with ultracold alkali dimers: Weak dependence of scattering properties on hyperfine state, Phys. Rev. Res. 7, 013099 (2025).
- B. Sutherland, Further results for the many-body problem in one dimension, Phys. Rev. Lett. 20, 98 (1968).
- W. J. Chetcuti, J. Polo, A. Osterloh, P. Castorina, and L. Amico, Probe for bound states of SU(3) fermions and colour deconfinement, Commun. Phys. 6, 128 (2023).
- R. Peierls, Zur Theorie des Diamagnetismus von Leitungselektronen, Z. Phys. 80, 763 (1933).
- L. Amico, M. Boshier, G. Birkl, A. Minguzzi, C. Miniatura, L.-C. Kwek, D. Aghamalyan, V. Ahufinger, D. Anderson, N. Andrei, et al., Roadmap on atomtronics: State of the art and perspective, AVS Quantum Sci. 3, 039201 (2021).
- K. C. Wright, R. B. Blakestad, C. J. Lobb, W. D. Phillips, and G. K. Campbell, Driving phase slips in a superfluid atom circuit with a rotating weak link, Phys. Rev. Lett. 110, 025302 (2013).
- J. Polo, W. J. Chetcuti, T. Haug, A. Minguzzi, K. Wright, and L. Amico, Persistent currents in ultracold gases, Phys. Rep. 1137, 1 (2025).
- A. J. Leggett, Dephasing and non-dephasing collisions in nanostructures, in Granular Nanoelectronics, edited by D. K. Ferry, J. R. Barker, and C. Jacoboni (Springer US, Boston, MA, 1991), p. 297.
- On account of this, such behavior is different from that of bosons, even the ones with attractive interactions where fractionalization is present.
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/tcmp-nf52 for additional derivations and data, which includes Refs. [73, 74, 75, 76].
- A. Osterloh, J. Polo, W. J. Chetcuti, and L. Amico, Exact one-particle density matrix for SU() fermionic matter waves in the strong repulsive limit, SciPost Phys. 15, 006 (2023).
- G. Pecci, G. Aupetit-Diallo, M. Albert, P. Vignolo, and A. Minguzzi, Persistent currents in a strongly interacting multicomponent Bose gas on a ring, C. R. Phys. 24, 87 (2023).
- Note that the representation can be different, which would generally be indicated by a different . However, for some the different representations can share the same .
- M. Ogata and H. Shiba, Bethe-ansatz wave function, momentum distribution, and spin correlation in the one-dimensional strongly correlated Hubbard model, Phys. Rev. B 41, 2326 (1990).
- The barrier is the least effective versus interactions at . In this case, the density at the impurity site coincides with that of a bosonic system of the same . Such a behavior reflects the lack of a meaningful Pauli exclusion principle in the system.
- A. Litvinov, P. Bataille, E. Maréchal, P. Pedri, O. Gorceix, M. Robert-De-Saint-Vincent, and B. Laburthe-Tolra, Measuring densities of cold atomic clouds smaller than the resolution limit, Phys. Rev. A 104, 033309 (2021).
- W. J. Chetcuti, A. Osterloh, L. Amico, and J. Polo, Interference dynamics of matter-waves of SU(N) fermions, SciPost Phys. 15, 181 (2023).
- T. Botzung and P. Nataf, Exact diagonalization of Fermi-Hubbard models, Phys. Rev. Lett. 132, 153001 (2024).
- A. Weichselbaum, QSpace—An open-source tensor library for Abelian and non-Abelian symmetries, SciPost Phys. Codebases 40 (2024).
- A. Seidel and D.-H. Lee, The Luther-Emery liquid: Spin gap and anomalous flux period, Phys. Rev. B 71, 045113 (2005).
- F. V. Kusmartsev, Aharonov-Bohm effect in the Luttinger liquid, JETP Lett. 60, 639 (1994).
- A. O. Gogolin, A. A. Nersesyan, and A. M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge University Press, Cambridge, 2004).
- A. Amaricci, A. Richaud, M. Capone, N. D. Oppong, and F. Scazza, Engineering the Kondo impurity problem with alkaline-earth atom arrays, Phys. Rev. A 112, 043301 (2025).
- L. Amico, D. Anderson, M. Boshier, J.-P. Brantut, L.-C. Kwek, A. Minguzzi, and W. von Klitzing, Colloquium: Atomtronic circuits: From many-body physics to quantum technologies, Rev. Mod. Phys. 94, 041001 (2022).
- J. Polo, W. J. Chetcuti, E. C. Domanti, P. Kitson, A. Osterloh, F. Perciavalle, V. P. Singh, and L. Amico, Perspective on new implementations of atomtronic circuits, Quantum Sci. Technol. 9, 030501 (2024).
- P. Naldesi, J. Polo, V. Dunjko, H. Perrin, M. Olshanii, L. Amico, and A. Minguzzi, Enhancing sensitivity to rotations with quantum solitonic currents, SciPost Phys. 12, 138 (2022).
- S. D. Huber, B. Theiler, E. Altman, and G. Blatter, Amplitude mode in the quantum phase model, Phys. Rev. Lett. 100, 050404 (2008).
- N. Yu and M. Fowler, Persistent current of a Hubbard ring threaded with a magnetic flux, Phys. Rev. B 45, 11795 (1992).
- M. Consiglio, W. J. Chetcuti, C. Bravo-Prieto, S. Ramos-Calderer, A. Minguzzi, J. I. Latorre, L. Amico, and T. J. G. Apollaro, Variational quantum eigensolver for fermions, J. Phys. A 55, 265301 (2022).
- G. Del Pace, K. Xhani, A. Muzi Falconi, M. Fedrizzi, N. Grani, D. Hernandez Rajkov, M. Inguscio, F. Scazza, W. J. Kwon, and G. Roati, Imprinting persistent currents in tunable fermionic rings, Phys. Rev. X 12, 041037 (2022).