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arXiv:1910.02620 · Physical Review A

Fate of the Bose polaron at finite temperature

Bernard Field, Jesper Levinsen, Meera M. Parish

Published Jan 21, 2020• 49 citations
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Abstract

We consider an impurity immersed in a Bose-Einstein condensate with tunable boson-impurity interactions. Such a Bose polaron has recently been predicted to exhibit an intriguing energy spectrum at finite temperature, where the ground-state quasiparticle evenly splits into two branches as the temperature is increased from zero [Guenther et al., Phys. Rev. Lett. 120, 050405 (2018)]. To investigate this theoretical prediction, we employ a recently developed variational approach that systematically includes multibody correlations between the impurity and the finite-temperature medium, thus allowing us to go beyond previous finite-temperature methods. Crucially, we find that the number of quasiparticle branches is simply set by the number of hole excitations of the thermal cloud, such that including up to one hole yields one splitting, two holes yields two splittings, and so on. Moreover, this effect is independent of the impurity mass. We thus expect that the exact ground-state quasiparticle will evolve into a single broad peak for temperatures $T>0$, with a broadening that scales as ${T}^{3/4}$ at low temperatures and sufficiently weak boson-boson interactions. In the zero-temperature limit, we show that our calculated ground-state polaron energy is in excellent agreement with recent quantum Monte Carlo results and with experiments.

DOI
10.1103/physreva.101.013623

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We consider an impurity immersed in a Bose-Einstein condensate with tunable boson-impurity interactions. Such a Bose polaron has recently been predicted to exhibit an intriguing energy spectrum at finite temperature, where the ground-state quasiparticle evenly splits into two branches as the temperature is increased from zero [Guenther et al., Phys. Rev. Lett. 120, 050405 (2018)]. To investigate this theoretical prediction, we employ a recently developed variational approach that systematically includes multibody correlations between the impurity and the finite-temperature medium, thus allowing us to go beyond previous finite-temperature methods. Crucially, we find that the number of quasiparticle branches is simply set by the number of hole excitations of the thermal cloud, such that including up to one hole yields one splitting, two holes yields two splittings, and so on. Moreover, this effect is independent of the impurity mass. We thus expect that the exact ground-state quasiparticle will evolve into a single broad peak for temperatures T>0T>0T>0, with a broadening that scales as T3/4{T}^{3/4}T3/4 at low temperatures and sufficiently weak boson-boson interactions. In the zero-temperature limit, we show that our calculated ground-state polaron energy is in excellent agreement with recent quantum Monte Carlo results and with experiments.
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.
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.
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.
An impurity particle interacting with a Bose-Einstein condensate (BEC) leads to the formation of a quasiparticle known as the Bose polaron. We investigate the properties of the two-dimensional Bose polaron, applying a variational ansatz that contains up to three Bogoliubov excitations of the BEC. Similar to its three-dimensional counterpart, we observe the existence of two quasiparticle branches, namely, the attractive and the repulsive polarons, at different coupling strengths. We find that their energies agree well with recent quantum Monte Carlo calculations. In particular, we observe that the inclusion of three excitations is crucial to capture the attractive polaron energy towards the regime of strong attraction, where the quasiparticle properties are dominated by few-body correlations. We also calculate the attractive polaron effective mass and residue, where we find significant differences between considering a weakly interacting Bose medium and taking the noninteracting limit, signaling enhanced impurity dressing by excitations in the latter case. By contrast, the spectral weight of the metastable repulsive polaron is largely insensitive to the interactions in the BEC and the number of Bogoliubov excitations. Our model may be experimentally realized in dilute atomic vapors and atomically thin semiconductors.
Abstract The properties of a Bose polaron immersed in a dilute two-dimensional medium at finite temperatures are discussed. Assuming that the impurity is weakly coupled to bath particles, we have perturbatively calculated the polaron energy, effective mass, quasiparticle residue and damping rate. The parameters of the impurity spectrum are found to be well-defined in the whole temperature region whereas the pole structure of the impurity Green’s function is visible only at absolute zero. At any finite temperatures the quasiparticle residue is logarithmically-divergent signalling of the branch-cut behavior of the polaron propagator.
Mobile impurity atoms immersed in Bose–Einstein condensates provide a new platform for exploring Bose polarons. Recent experimental advances in the field of ultracold atoms make it possible to realize such systems with highly tunable microscopic parameters and to explore equilibrium and dynamical properties of polarons using a rich toolbox of atomic physics. In this paper we present a detailed theoretical analysis of Bose polarons in one-dimensional systems of ultracold atoms. By combining a non-perturbative renormalization group approach with numerically exact diffusion Monte Carlo calculations we obtain not only detailed numerical results over a broad range of parameters but also qualitative understanding of different regimes of the system. We find that an accurate description of Bose polarons requires the inclusion of two-phonon scattering terms which go beyond the commonly used Fröhlich model. Furthermore we show that when the Bose gas is in the strongly interacting regime, one needs to include interactions between the phonon modes. We use several theoretical approaches to calculate the polaron energy and its effective mass. The former can be measured using radio-frequency spectroscopy and the latter can be studied experimentally using impurity oscillations in a harmonic trapping potential. We compare our theoretical results for the effective mass to the experiments by Catani et al (2012 Phys. Rev. A 85 023623). In the weak-to-intermediate coupling regimes we obtain excellent quantitative agreement between theory and experiment, without any free fitting parameter. We supplement our analysis by full dynamical simulations of polaron oscillations in a shallow trapping potential. We also use our renormalization group approach to analyze the full phase diagram and identify regions that support repulsive and attractive polarons, as well as multi-particle bound states.