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Effective two- and three-body interactions between dressed impurities in a tilted double-well potential

F. Theel1,*, A. G. Volosniev2, D. Diplaris1,3, F. Brauneis4, S. I. Mistakidis5, and P. Schmelcher1,3

  • *Contact author: friethjof.theel@uni-hamburg.de
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Phys. Rev. Research 7, 043059 – Published 16 October, 2025

DOI: https://doi.org/10.1103/s6hw-cr5w

Abstract

We explore the impact and scaling of effective interactions between two and three impurity atoms, induced by a bosonic medium, on their density distributions. To facilitate the detection of mediated interactions, we propose a setup where impurities are trapped in a tilted double-well potential, while the medium is confined to a ring. The tilt of the potential breaks the spatial inversion symmetry allowing us to exploit the population of the energetically elevated well as a probe of induced interactions. For two impurities, the interaction with the medium reduces the impurity population at the energetically elevated well, which we interpret as evidence of induced impurity-impurity attraction. Furthermore, the impact of an induced three-body interaction is unveiled by comparing the predictions of an effective three-body model with many-body simulations. We extend our study for induced interactions to a three-component mixture containing distinguishable impurities. Our results suggest pathways to detect and tune induced two- and three-body interactions.

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References (106)

  1. L. D. Landau, Über die bewegung der elektronen in kristalgitter, Phys. Z. Sowjetunion 3, 644 (1933).
  2. S. I. Pekar, Autolocalization of the electron in an inertially polarizable dielectric medium, Zh. Eksp. Teor. Fiz 16, 335 (1946).
  3. F. Chevy and C. Mora, Ultra-cold polarized Fermi gases, Rep. Prog. Phys. 73, 112401 (2010).
  4. P. Massignan, M. Zaccanti, and G. M. Bruun, Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases, Rep. Prog. Phys. 77, 034401 (2014).
  5. F. Scazza, M. Zaccanti, P. Massignan, M. M. Parish, and J. Levinsen, Repulsive Fermi and Bose polarons in quantum gases, Atoms 10, 55 (2022).
  6. F. Grusdt, N. Mostaan, E. Demler, and L. A. P. Ardila, Impurities and polarons in bosonic quantum gases: A review on recent progress, Rep. Prog. Phys. 88, 066401 (2025).
  7. P. Massignan, R. Schmidt, G. E. Astrakharchik, A. İmamoglu, M. Zwierlein, J. J. Arlt, and G. M. Bruun, Polarons in atomic gases and two-dimensional semiconductors, arXiv:2501.09618.
  8. A. Schirotzek, C.-H. Wu, A. Sommer, and M. W. Zwierlein, Observation of Fermi polarons in a tunable Fermi liquid of ultracold atoms, Phys. Rev. Lett. 102, 230402 (2009).
  9. M.-G. Hu, M. J. Van de Graaff, D. Kedar, J. P. Corson, E. A. Cornell, and D. S. Jin, Bose polarons in the strongly interacting regime, Phys. Rev. Lett. 117, 055301 (2016).
  10. N. B. Jørgensen, L. Wacker, K. T. Skalmstang, M. M. Parish, J. Levinsen, R. S. Christensen, G. M. Bruun, and J. J. Arlt, Observation of attractive and repulsive polarons in a Bose-Einstein condensate, Phys. Rev. Lett. 117, 055302 (2016).
  11. M. Cetina, M. Jag, R. S. Lous, J. T. M. Walraven, R. Grimm, R. S. Christensen, and G. M. Bruun, Decoherence of impurities in a Fermi sea of ultracold atoms, Phys. Rev. Lett. 115, 135302 (2015).
  12. M. Cetina, M. Jag, R. S. Lous, I. Fritsche, J. T. M. Walraven, R. Grimm, J. Levinsen, M. M. Parish, R. Schmidt, M. Knap, and E. Demler, Ultrafast many-body interferometry of impurities coupled to a Fermi sea, Science 354, 96 (2016).
  13. M. G. Skou, T. G. Skov, N. B. Jørgensen, K. K. Nielsen, A. Camacho-Guardian, T. Pohl, G. M. Bruun, and J. J. Arlt, Non-equilibrium quantum dynamics and formation of the Bose polaron, Nat. Phys. 17, 731 (2021).
  14. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  15. J. Catani, G. Lamporesi, D. Naik, M. Gring, M. Inguscio, F. Minardi, A. Kantian, and T. Giamarchi, Quantum dynamics of impurities in a one-dimensional Bose gas, Phys. Rev. A 85, 023623 (2012).
  16. A. N. Wenz, G. Zürn, S. Murmann, I. Brouzos, T. Lompe, and S. Jochim, From few to many: Observing the formation of a Fermi sea one atom at a time, Science 342, 457 (2013).
  17. C. Charalambous, M. A. Garcia-March, A. Lampo, M. Mehboud, and M. Lewenstein, Two distinguishable impurities in BEC: Squeezing and entanglement of two Bose polarons, SciPost Phys. 6, 010 (2019).
  18. R. Paredes, G. Bruun, and A. Camacho-Guardian, Interactions mediated by atoms, photons, electrons, and excitons, Phys. Rev. A 110, 030101 (2024).
  19. Y. Kuramoto, Quantum Many-Body Physics: A Perspective on Strong Correlations (Springer Japan, Tokyo, 2020).
  20. A. Recati, J. N. Fuchs, C. S. Peça, and W. Zwerger, Casimir forces between defects in one-dimensional quantum liquids, Phys. Rev. A 72, 023616 (2005).
  21. M. Bruderer, A. Klein, S. R. Clark, and D. Jaksch, Polaron physics in optical lattices, Phys. Rev. A 76, 011605 (2007).
  22. M. Schecter and A. Kamenev, Phonon-mediated casimir interaction between mobile impurities in one-dimensional quantum liquids, Phys. Rev. Lett. 112, 155301 (2014).
  23. F. Brauneis, H.-W. Hammer, M. Lemeshko, and A. Volosniev, Impurities in a one-dimensional Bose gas: The flow equation approach, SciPost Phys. 11, 008 (2021).
  24. A. Petković and Z. Ristivojevic, Mediated interaction between polarons in a one-dimensional Bose gas, Phys. Rev. A 105, L021303 (2022).
  25. D. Huber, H.-W. Hammer, and A. G. Volosniev, In-medium bound states of two bosonic impurities in a one-dimensional Fermi gas, Phys. Rev. Res. 1, 033177 (2019).
  26. M. Will, G. E. Astrakharchik, and M. Fleischhauer, Polaron interactions and bipolarons in one-dimensional Bose gases in the strong coupling regime, Phys. Rev. Lett. 127, 103401 (2021).
  27. Y. Guo and H. Tajima, Medium-induced bosonic clusters in a Bose-Fermi mixture: Toward simulating cluster formations in neutron-rich matter, Phys. Rev. A 109, 013319 (2024).
  28. S. Dutta and E. J. Mueller, Variational study of polarons and bipolarons in a one-dimensional Bose lattice gas in both the superfluid and the Mott-insulator regimes, Phys. Rev. A 88, 053601 (2013).
  29. M. Pasek and G. Orso, Induced pairing of fermionic impurities in a one-dimensional strongly correlated Bose gas, Phys. Rev. B 100, 245419 (2019).
  30. K. Keiler, S. I. Mistakidis, and P. Schmelcher, Doping a lattice-trapped bosonic species with impurities: From ground state properties to correlated tunneling dynamics, New J. Phys. 22, 083003 (2020).
  31. F. Isaule, A. Rojo-Francàs, and B. Juliá-Díaz, Bound impurities in a one-dimensional Bose lattice gas: Low-energy properties and quench-induced dynamics, SciPost Phys. Core 7, 049 (2024).
  32. A. S. Dehkharghani, A. G. Volosniev, and N. T. Zinner, Coalescence of two impurities in a trapped one-dimensional Bose gas, Phys. Rev. Lett. 121, 080405 (2018).
  33. S. I. Mistakidis, G. C. Katsimiga, G. M. Koutentakis, and P. Schmelcher, Repulsive Fermi polarons and their induced interactions in binary mixtures of ultracold atoms, New J. Phys. 21, 043032 (2019).
  34. S. I. Mistakidis, A. G. Volosniev, and P. Schmelcher, Induced correlations between impurities in a one-dimensional quenched Bose gas, Phys. Rev. Res. 2, 023154 (2020).
  35. S. I. Mistakidis, G. M. Koutentakis, G. C. Katsimiga, T. Busch, and P. Schmelcher, Many-body quantum dynamics and induced correlations of Bose polarons, New J. Phys. 22, 043007 (2020).
  36. T. D. Anh-Tai, T. Fogarty, S. de María-García, T. Busch, and M. A. García-March, Engineering impurity Bell states through coupling with a quantum bath, Phys. Rev. Res. 6, 043042 (2024).
  37. B. J. DeSalvo, K. Patel, G. Cai, and C. Chin, Observation of fermion-mediated interactions between bosonic atoms, Nature (London) 568, 61 (2019).
  38. A. L. Gaunt, T. F. Schmidutz, I. Gotlibovych, R. P. Smith, and Z. Hadzibabic, Bose-Einstein condensation of atoms in a uniform potential, Phys. Rev. Lett. 110, 200406 (2013).
  39. R. Folman, P. Krüger, D. Cassettari, B. Hessmo, T. Maier, and J. Schmiedmayer, Controlling cold atoms using nanofabricated surfaces: Atom chips, Phys. Rev. Lett. 84, 4749 (2000).
  40. P. Krüger, S. Hofferberth, I. E. Mazets, I. Lesanovsky, and J. Schmiedmayer, Weakly interacting Bose gas in the one-dimensional limit, Phys. Rev. Lett. 105, 265302 (2010).
  41. S. Fölling, S. Trotzky, P. Cheinet, M. Feld, R. Saers, A. Widera, T. Müller, and I. Bloch, Direct observation of second-order atom tunnelling, Nature (London) 448, 1029 (2007).
  42. S. Levy, E. Lahoud, I. Shomroni, and J. Steinhauer, The ac and dc Josephson effects in a Bose–Einstein condensate, Nature (London) 449, 579 (2007).
  43. T. Sowiński and M. Ángel García-March, One-dimensional mixtures of several ultracold atoms: A review, Rep. Prog. Phys. 82, 104401 (2019).
  44. A. Minguzzi and P. Vignolo, Strongly interacting trapped one-dimensional quantum gases: Exact solution, AVS Quantum Sci. 4, 027102 (2022).
  45. S. Mistakidis, A. Volosniev, R. Barfknecht, T. Fogarty, Th. Busch, A. Foerster, P. Schmelcher, and N. Zinner, Few-body Bose gases in low dimensions—A laboratory for quantum dynamics, Phys. Rep. 1042, 1 (2023).
  46. L. Cao, V. Bolsinger, S. I. Mistakidis, G. M. Koutentakis, S. Krönke, J. M. Schurer, and P. Schmelcher, A unified ab initio approach to the correlated quantum dynamics of ultracold fermionic and bosonic mixtures, J. Chem. Phys. 147, 044106 (2017).
  47. L. Cao, S. Krönke, O. Vendrell, and P. Schmelcher, The multi-layer multi-configuration time-dependent Hartree method for bosons: Theory, implementation, and applications, J. Chem. Phys. 139, 134103 (2013).
  48. S. Krönke, L. Cao, O. Vendrell, and P. Schmelcher, Non-equilibrium quantum dynamics of ultra-cold atomic mixtures: The multi-layer multi-configuration time-dependent Hartree method for bosons, New J. Phys. 15, 063018 (2013).
  49. P. R. Johnson, E. Tiesinga, J. V. Porto, and C. J. Williams, Effective three-body interactions of neutral bosons in optical lattices, New J. Phys. 11, 093022 (2009).
  50. H.-W. Hammer, A. Nogga, and A. Schwenk, Colloquium: Three-body forces: From cold atoms to nuclei, Rev. Mod. Phys. 85, 197 (2013).
  51. G. Panochko and V. Pastukhov, Two- and three-body effective potentials between impurities in ideal BEC, J. Phys. A: Math. Theor. 54, 085001 (2021).
  52. H. Tajima, E. Nakano, and K. Iida, Tunable Fujita-Miyazawa-type three-body force in ultracold atoms, arXiv:2505.19117.
  53. M. Olshanii, Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons, Phys. Rev. Lett. 81, 938 (1998).
  54. D. R. Dounas-Frazer, A. M. Hermundstad, and L. D. Carr, Ultracold bosons in a tilted multilevel double-well potential, Phys. Rev. Lett. 99, 200402 (2007).
  55. L. D. Carr, D. R. Dounas-Frazer, and M. A. Garcia-March, Dynamical realization of macroscopic superposition states of cold bosons in a tilted double well, Europhys. Lett. 90, 10005 (2010).
  56. J. Erdmann, S. I. Mistakidis, and P. Schmelcher, Correlated tunneling dynamics of an ultracold Fermi-Fermi mixture confined in a double well, Phys. Rev. A 98, 053614 (2018).
  57. C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Rev. Mod. Phys. 82, 1225 (2010).
  58. V. Dunjko, M. G. Moore, T. Bergeman, and M. Olshanii, Confinement-induced resonances, Advances in Atomic, Molecular, and Optical Physics, edited by E. Arimondo, P. R. Berman, C. C. Lin (Academic Press, New York, 2011), pp. 461–510.
  59. T. M. Bersano, V. Gokhroo, M. A. Khamehchi, J. D'Ambroise, D. J. Frantzeskakis, P. Engels, and P. G. Kevrekidis, Three-component soliton states in spinor F = 1 Bose-Einstein condensates, Phys. Rev. Lett. 120, 063202 (2018).
  60. S. Lannig, C.-M. Schmied, M. Prüfer, P. Kunkel, R. Strohmaier, H. Strobel, T. Gasenzer, P. G. Kevrekidis, and M. K. Oberthaler, Collisions of three-component vector solitons in Bose-Einstein condensates, Phys. Rev. Lett. 125, 170401 (2020).
  61. A. Romero-Ros, G. C. Katsimiga, S. I. Mistakidis, S. Mossman, G. Biondini, P. Schmelcher, P. Engels, and P. G. Kevrekidis, Experimental realization of the peregrine soliton in repulsive two-component Bose-Einstein condensates, Phys. Rev. Lett. 132, 033402 (2024).
  62. B. E. Sherlock, M. Gildemeister, E. Owen, E. Nugent, and C. J. Foot, Time-averaged adiabatic ring potential for ultracold atoms, Phys. Rev. A 83, 043408 (2011).
  63. T. A. Bell, J. A. P. Glidden, L. Humbert, M. W. J. Bromley, S. A. Haine, M. J. Davis, T. W. Neely, M. A. Baker, and H. Rubinsztein-Dunlop, Bose–Einstein condensation in large time-averaged optical ring potentials, New J. Phys. 18, 035003 (2016).
  64. M. Egorov, B. Opanchuk, P. Drummond, B. V. Hall, P. Hannaford, and A. I. Sidorov, Measurement of s-wave scattering lengths in a two-component Bose-Einstein condensate, Phys. Rev. A 87, 053614 (2013).
  65. L. D. Landau and E. M. Lifshitz, in Quantum mechanics, 3rd ed., edited by J. Menzies (Butterworth-Heinemann, Oxford, 1981).
  66. P. Naidon, Two Impurities in a Bose–Einstein condensate: From Yukawa to Efimov attracted polarons, J. Phys. Soc. Jpn. 87, 043002 (2018).
  67. G. Panochko and V. Pastukhov, Static impurities in a weakly interacting Bose gas, Atoms 10, 19 (2022).
  68. J. Jager and R. Barnett, The effect of Boson–Boson interaction on the bipolaron formation, New J. Phys. 24, 103032 (2022).
  69. M. Drescher, M. Salmhofer, and T. Enss, Medium-induced interaction between impurities in a Bose-Einstein condensate, Phys. Rev. A 107, 063301 (2023).
  70. Note that here we disregard the long-range part of the potential [22, 71], which is irrelevant for small trapped systems [34].
  71. B. Reichert, Z. Ristivojevic, and A. Petković, The Casimir-like effect in a one-dimensional Bose gas, New J. Phys. 21, 053024 (2019).
  72. A. U. J. Lode, C. Lévêque, L. B. Madsen, A. I. Streltsov, and O. E. Alon, Colloquium: Multiconfigurational time-dependent Hartree approaches for indistinguishable particles, Rev. Mod. Phys. 92, 011001 (2020).
  73. K. Keiler, S. I. Mistakidis, and P. Schmelcher, Polarons and their induced interactions in highly imbalanced triple mixtures, Phys. Rev. A 104, L031301 (2021).
  74. F. Theel, S. I. Mistakidis, and P. Schmelcher, Crossover from attractive to repulsive induced interactions and bound states of two distinguishable Bose polarons, SciPost Phys. 16, 023 (2024).
  75. R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, Quantum entanglement, Rev. Mod. Phys. 81, 865 (2009).
  76. G. Vidal and R. F. Werner, Computable measure of entanglement, Phys. Rev. A 65, 032314 (2002).
  77. M. B. Plenio, Logarithmic negativity: A full entanglement monotone that is not convex, Phys. Rev. Lett. 95, 090503 (2005).
  78. E. Schmidt, Zur Theorie der linearen und nichtlinearen Integralgleichungen: I. Teil: Entwicklung willkürlicher Funktionen nach Systemen vorgeschriebener, Math. Ann. 63, 433 (1907).
  79. A. Ekert and P. L. Knight, Entangled quantum systems and the Schmidt decomposition, Am. J. Phys. 63, 415 (1995).
  80. S. I. Mistakidis, F. Grusdt, G. M. Koutentakis, and P. Schmelcher, Dissipative correlated dynamics of a moving impurity immersed in a Bose–Einstein condensate, New J. Phys. 21, 103026 (2019).
  81. F. Theel, K. Keiler, S. I. Mistakidis, and P. Schmelcher, Entanglement-assisted tunneling dynamics of impurities in a double well immersed in a bath of lattice trapped bosons, New J. Phys. 22, 023027 (2020).
  82. M. Pyzh and P. Schmelcher, Breathing dynamics of the few-body Bose polaron in a species-selective harmonic trap, Phys. Rev. A 105, 043304 (2022).
  83. For a given Mpr, ML-MCTDHX is numerically exact when dσ=Mpr and Dσ equals the number of bosonic configurations, i.e., Nσ+dσ−1dσ−1.
  84. A. Camacho-Guardian and G. M. Bruun, Landau effective interaction between quasiparticles in a Bose-Einstein condensate, Phys. Rev. X 8, 031042 (2018).
  85. In the homogeneous case, the induced interaction between two impurities is approximately given by gBBeff−gBB≃−gAB2gAA [45] (see also Sec. 2b). The induced attraction is roughly equal to the internal impurity-impurity repulsion (gBB=gBBeff) when gAB≃gAA. We have checked that the mediated interaction gBBeff determined via the fitting procedure indeed approaches this prediction if (1) gAB≪gAA and (2) the healing length of the Bose gas is much smaller than L.
  86. In fact, the effective model at gAB=0 yields a gBBeff that matches up to the third digit gBB=0.1. This deviation marks the accuracy of the employed exact diagonalization method when fitting to the ML-MCTDHX data.
  87. J. Chen, J. M. Schurer, and P. Schmelcher, Entanglement induced interactions in binary mixtures, Phys. Rev. Lett. 121, 043401 (2018).
  88. K. Sakmann, A. I. Streltsov, O. E. Alon, and L. S. Cederbaum, Reduced density matrices and coherence of trapped interacting bosons, Phys. Rev. A 78, 023615 (2008).
  89. S. I. Mistakidis, G. C. Katsimiga, P. G. Kevrekidis, and P. Schmelcher, Correlation effects in the quench-induced phase separation dynamics of a two species ultracold quantum gas, New J. Phys. 20, 043052 (2018).
  90. Note that our three-body interaction term leads to divergences similar to the two-dimensional contact interaction (see Ref.  [91] and Appendix pp7). We renormalize this interaction potential by fitting to a finite Hilbert space.
  91. L. Pricoupenko, Three-body pseudopotential for atoms confined in one dimension, Phys. Rev. A 99, 012711 (2019).
  92. B. Reichert, A. Petković, and Z. Ristivojevic, Field-theoretical approach to the Casimir-like interaction in a one-dimensional Bose gas, Phys. Rev. B 99, 205414 (2019).
  93. E. Timmermans, Phase separation of Bose-Einstein condensates, Phys. Rev. Lett. 81, 5718 (1998).
  94. L. Zschetzsche and R. E. Zillich, Suppression of polaron self-localization by correlations, Phys. Rev. Res. 6, 023137 (2024).
  95. D. Breu, E. Vidal Marcos, M. Will, and M. Fleischhauer, Impurities in a trapped one-dimensional Bose gas of arbitrary interaction strength: Localization-delocalization transition and absence of self-localization, Phys. Rev. A 111, 023326 (2025).
  96. H. Tajima, J. Takahashi, S. Mistakidis, E. Nakano, and K. Iida, Polaron problems in ultracold atoms: Role of a Fermi sea across different spatial dimensions and quantum fluctuations of a Bose medium, Atoms 9, 18 (2021).
  97. C. Baroni, B. Huang, I. Fritsche, E. Dobler, G. Anich, E. Kirilov, R. Grimm, M. A. Bastarrachea-Magnani, P. Massignan, and G. M. Bruun, Mediated interactions between Fermi polarons and the role of impurity quantum statistics, Nat. Phys. 20, 68 (2024).
  98. G. E. Astrakharchik, L. A. P. Ardila, K. Jachymski, and A. Negretti, Many-body bound states and induced interactions of charged impurities in a bosonic bath, Nat. Commun. 14, 1647 (2023).
  99. F. Theel, S. I. Mistakidis, K. Keiler, and P. Schmelcher, Counterflow dynamics of two correlated impurities immersed in a bosonic gas, Phys. Rev. A 105, 053314 (2022).
  100. T. D. Anh-Tai, M. A. García-March, T. Busch, and T. Fogarty, Quantum correlations and spatial localization in trapped one-dimensional ultra-cold Bose–Bose–Bose mixtures, New J. Phys. 27, 073201 (2025).
  101. S. I. Mistakidis, A. G. Volosniev, N. T. Zinner, and P. Schmelcher, Effective approach to impurity dynamics in one-dimensional trapped Bose gases, Phys. Rev. A 100, 013619 (2019).
  102. M. Rontani, G. Eriksson, S. Åberg, and S. Reimann, On the renormalization of contact interactions for the configuration-interaction method in two-dimensions, J. Phys. B: At. Mol. Opt. Phys. 50, 065301 (2017).
  103. S.-L. Nyeo, Regularization methods for delta-function potential in two-dimensional quantum mechanics, Am. J. Phys. 68, 571 (2000).
  104. E. Gross, Motion of foreign bodies in boson systems, Ann. Phys. 19, 234 (1962).
  105. M. D. Girardeau, Reduction of a quantum n-body problem to an (n− 1)-body problem, Phys. Rev. A 28, 3635 (1983).
  106. F. Brauneis, H.-W. Hammer, S. M. Reimann, and A. G. Volosniev, Comparison of renormalized interactions using one-dimensional few-body systems as a testbed, Phys. Rev. A 111, 013303 (2025).

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Phys. Rev. Research 7, 043059– Published 16 October, 2025
  • Received 1 April 2025
  • Accepted 3 September 2025
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