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arXiv:2412.09372 · Physical Review A

Transition from spontaneous to explicit symmetry breaking in a finite-sized system: Bosonic bound states of an impurity

L. Chergui, Fabian Brauneis, T. Arnone Cardinale, M. Schubert, Artem G. Volosniev, S. M. Reimann

Published May 12, 2025• 1 citation
arXivHTMLPDF

Abstract

The presence of a single attractive impurity in an ultracold repulsive bosonic system can drive a transition from a homogeneous to a localized state, as we here show for a one-dimensional ring system. In the few-body limit, the localization of the bosons around the impurity, as seen in the pair correlations, is accompanied by low-lying modes that resemble finite-sized precursors of Higgs-Anderson- and Nambu-Goldstone-like modes. Tuning the impurity-boson mass ratio allows for the exploration of the transition from a spontaneous to an explicit breaking of the continuous rotational symmetry of the Hamiltonian. We compare the minimum of the Higgs-Anderson-like mode as a marker of the onset of localization in the few-body limit to mean-field predictions of binding. We find improved agreement between the few-body exact-diagonalization results and mean-field predictions of binding with increasing boson-boson repulsion.

DOI
10.1103/physreva.111.053307

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Abstract We report a comprehensive study of the ground-state properties of one and two bosonic impurities immersed in small one-dimensional optical lattices loaded with a few interacting bosons. We model the system with a two-component Bose–Hubbard model and solve the problem numerically by means of the exact diagonalization method. We report binding energies of one and two impurities across the superfluid (SF) to Mott-insulator transition and confirm the formation of two-body bound states of impurities induced by repulsive interactions. In particular, we found that an insulator bath induces tightly bound di-impurity dimers, whereas a SF bath induces shallower bound states.
The existence of a self-localization transition in the polaron problem has been under an active debate ever since Landau suggested it 84 years ago. Here we reveal the self-localization transition for the rotational analog of the polaron---the angulon quasiparticle. We show that, unlike for the polarons, self-localization of angulons occurs at finite impurity-bath coupling already at the mean-field level. The transition is accompanied by the spherical-symmetry breaking of the angulon ground state and a discontinuity in the first derivative of the ground-state energy. Moreover, the type of symmetry breaking is dictated by the symmetry of the microscopic impurity-bath interaction, which leads to a number of distinct self-localized states. The predicted effects can potentially be addressed in experiments on cold molecules trapped in superfluid helium droplets and ultracold quantum gases, as well as on electronic excitations in solids and Bose-Einstein condensates.
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