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Physical Review Letters

Fate of an impurity strongly interacting with a thermal Bose gas

Jiří Etrych, Sebastian J. Morris, Simon M. Fischer, Gevorg Martirosyan, C. J. Ho, Moritz Drescher, Manfred Salmhofer B, Zoran Hadzibabic, Tilman Enss, Christoph Eigen

Published Sep 28, 2026• 0 citations
Publisher
DOI
10.1103/g8gh-vsyq

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We spectroscopically study mobile impurities immersed in a homogeneous bosonic bath (a box-trapped Bose gas), varying the bath temperature and the strength of impurity-bath interactions. We compare our results to those for a quasipure Bose–Einstein condensate (BEC), and find that for strong impurity-bath interactions, the spectra narrow with increasing temperature, while the impurity energy shift is suppressed. Near the critical temperature for condensation, many-body effects still play an important role, and only for a nondegenerate bath the system approaches the classical Boltzmann-gas behavior. The key spectral features are reproduced within the theory of the ideal Bose polaron.
Using near-exact numerical simulations, we study the propagation of an impurity through a one-dimensional Bose lattice gas for varying bosonic interaction strengths and filling factors at zero temperature. The impurity is coupled to the Bose gas and confined to a separate tilted lattice. The precise nature of the transport of the impurity is specific to the excitation spectrum of the Bose gas, which allows one to measure properties of the Bose gas nondestructively, in principle, by observing the impurity; here we focus on the spatial and momentum distributions of the impurity as well as its reduced density matrix. For instance, we show it is possible to determine whether the Bose gas is commensurately filled as well as the bandwidth and gap in its excitation spectrum. Moreover, we show that the impurity acts as a witness to the crossover of its environment from the weakly to the strongly interacting regime, i.e., from a superfluid to a Mott insulator or Tonks-Girardeau lattice gas, and the effects on the impurity in both of these strongly interacting regimes are clearly distinguishable. Finally, we find that the spatial coherence of the impurity is related to its propagation through the Bose gas.
A mobile impurity coupled to a weakly interacting Bose gas, a Bose polaron, displays several interesting effects. While a single attractive quasiparticle is known to exist at zero temperature, we show here that the spectrum splits into two quasiparticles at finite temperatures for sufficiently strong impurity-boson interaction. The ground state quasiparticle has minimum energy at T_{c}, the critical temperature for Bose-Einstein condensation, and it becomes overdamped when T≫T_{c}. The quasiparticle with higher energy instead exists only below T_{c}, since it is a strong mixture of the impurity with thermally excited collective Bogoliubov modes. This phenomenology is not restricted to ultracold gases, but should occur whenever a mobile impurity is coupled to a medium featuring a gapless bosonic mode with a large population for finite temperature.