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arXiv:2508.06493

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 Aug 8, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.17863/cam.134979

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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.
The problem of an impurity particle moving through a bosonic medium plays a fundamental role in physics.However, the canonical scenario of a mobile impurity immersed in a Bose-Einstein condensate (BEC) has not yet been realized.Here, we use radio frequency spectroscopy of ultracold bosonic 39 K atoms to experimentally demonstrate the existence of a well-defined quasiparticle state of an impurity interacting with a BEC.We measure the energy of the impurity both for attractive and repulsive interactions, and find excellent agreement with theories that incorporate three-body correlations, both in the weak-coupling limits and across unitarity.The spectral response consists of a well-defined quasiparticle peak at weak coupling, while for increasing interaction strength, the spectrum is strongly broadened and becomes dominated by the many-body continuum of excited states.Crucially, no significant effects of three-body decay are observed.Our results open up exciting prospects for studying mobile impurities in a bosonic environment and strongly interacting Bose systems in general.
The problem of an impurity particle moving through a bosonic medium plays a fundamental role in physics. However, the canonical scenario of a mobile impurity immersed in a Bose-Einstein condensate (BEC) has not yet been realized. Here, we use radio frequency spectroscopy of ultracold bosonic ^{39}K atoms to experimentally demonstrate the existence of a well-defined quasiparticle state of an impurity interacting with a BEC. We measure the energy of the impurity both for attractive and repulsive interactions, and find excellent agreement with theories that incorporate three-body correlations, both in the weak-coupling limits and across unitarity. The spectral response consists of a well-defined quasiparticle peak at weak coupling, while for increasing interaction strength, the spectrum is strongly broadened and becomes dominated by the many-body continuum of excited states. Crucially, no significant effects of three-body decay are observed. Our results open up exciting prospects for studying mobile impurities in a bosonic environment and strongly interacting Bose systems in general.
We consider a mobile impurity immersed in a Bose gas at finite temperature. Using perturbation theory valid for weak coupling between the impurity and the bosons, we derive analytical results for the energy and damping of the impurity for low and high temperatures, as well as for temperatures close to the critical temperature Tc{T}_{c}Tc​ for Bose-Einstein condensation. These results show that the properties of the impurity vary strongly with temperature. In particular, the energy exhibits a nonmonotonic behavior close to Tc{T}_{c}Tc​, and the damping rises sharply close to Tc{T}_{c}Tc​. We argue that this behavior is generic for impurities immersed in an environment undergoing a phase transition that breaks a continuous symmetry. Finally, we discuss how these effects can be detected experimentally.
When an impurity is immersed in a Bose-Einstein condensate, impurity-boson interactions are expected to dress the impurity into a quasiparticle, the Bose polaron. We superimpose an ultracold atomic gas of ^{87}Rb with a much lower density gas of fermionic ^{40}K impurities. Through the use of a Feshbach resonance and radio-frequency spectroscopy, we characterize the energy, spectral width, and lifetime of the resultant polaron on both the attractive and the repulsive branches in the strongly interacting regime. The width of the polaron in the attractive branch is narrow compared to its binding energy, even as the two-body scattering length diverges.
Predicting the emergent properties of impurities immersed in a quantum bath is a fundamental challenge that can defy quasiparticle treatments. Here, we measure the spectral properties and real-time dynamics of mobile impurities injected into a weakly interacting homogeneous Bose-Einstein condensate, using two broad Feshbach resonances to tune both the impurity-bath and intrabath interactions. For attractive impurity-bath interactions, the impurity spectrum features a single branch, which away from the resonance corresponds to a well-defined attractive polaron; near the resonance, we observe dramatic broadening of this branch, suggesting a breakdown of the quasiparticle picture. For repulsive impurity-bath interactions, the spectrum features two branches: the attractive branch that is dominated by excitations with energy close to that of the Feshbach dimer, but has a many-body character, and the repulsive polaron branch. Our measurements show that the behavior of impurities in weakly interacting baths is remarkably universal, controlled only by the bath density and a single dimensionless interaction parameter.
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.