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arXiv:1708.09172 · Physical Review A

Finite-temperature behavior of the Bose polaron

Jesper Levinsen, Meera M. Parish, Rasmus Søgaard Christensen, J. Arlt, Georg M. Bruun

Published Dec 28, 2017• 52 citations
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Abstract

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 ${T}_{c}$ 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 ${T}_{c}$, and the damping rises sharply close to ${T}_{c}$. 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.

DOI
10.1103/physreva.96.063622

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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.
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The Bose polaron has attracted theoretical and experimental interest because the mobile impurity is surrounded by a bath that undergoes a superfluid-to-normal phase transition. Although many theoretical works have studied this system in its ground state, only a few analyze its behavior at finite temperature. We have studied the effect of temperature on a Bose polaron system performing ab initio path integral Monte Carlo simulations. This method is able to approach the critical temperature without losing accuracy, in contrast with perturbative approximations. We have calculated the polaron energy for the repulsive and attractive branches and we have observed an asymmetric behavior between the two branches. When the potential is repulsive, the polaron energy decreases when the temperature increases, and contrariwise for the attractive branch. Our results for the effective mass and the dynamical structure factor of the polaron show unambiguously that its quasiparticle nature disappears close to the critical temperature, in agreement with recent experimental findings. Finally, we have also estimated the fraction of bosons in the condensate as well as the superfluid fraction, and we have concluded that the impurity hinders the condensation of the rest of bosons.
Abstract The properties of an impurity immersed in a dilute D -dimensional Bose gas at temperatures close to its second-order phase transition point are considered. Particularly by means of the 1/ N -expansion, we calculate the leading-order polaron energy and the damping rate in the limit of vanishing boson–boson interaction. It is shown that the perturbative effective mass and the quasiparticle residue diverge logarithmically in the long-length limit, signalling the non-analytic behavior of the impurity spectrum and pole-free structure of the polaron Green’s function in the infrared region, respectively.
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.
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.