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.

Nov 10, 202119 citations

Fate of the Bose polaron at finite temperature

Bernard Field, Jesper Levinsen, Meera M. Parish

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.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.

arXiv:1910.02620Physical Review AJan 21, 202049 citations

Finite-temperature behavior of the Bose polaron

Jesper Levinsen, Meera M. Parish, Rasmus Søgaard Christensen +2 more

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.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.

arXiv:1708.09172Physical Review ADec 28, 201752 citations

Impurity in a Bose-Einstein condensate: Study of the attractive and repulsive branch using quantum Monte Carlo methods

Luis A. Peña Ardila, S. Giorgini

We investigate the properties of an impurity immersed in a dilute Bose gas at zero temperature using quantum Monte Carlo methods. The interactions between bosons are modeled by a hard-sphere potential with scattering length $a$ , whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length $b$ can be varied by adjusting the well depth. We characterize the attractive and the repulsive polaron branch by calculating the binding energy and the effective mass of the impurity. Furthermore, we investigate the structural properties of the bath, such as the impurity-boson contact parameter and the change of the density profile around the impurity. At the unitary limit of the impurity-boson interaction, we find that the effective mass of the impurity remains smaller than twice its bare mass, while the binding energy scales with ${\ensuremath{\hbar}}^{2}{n}^{2/3}/m$, where $n$ is the density of the bath and $m$ is the common mass of the impurity and the bosons in the bath. The implications for the phase diagram of binary Bose-Bose mixtures at low concentrations are also discussed.We investigate the properties of an impurity immersed in a dilute Bose gas at zero temperature using quantum Monte Carlo methods. The interactions between bosons are modeled by a hard-sphere potential with scattering length $a$, whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length $b$ can be varied by adjusting the well depth. We characterize the attractive and the repulsive polaron branch by calculating the binding energy and the effective mass of the impurity. Furthermore, we investigate the structural properties of the bath, such as the impurity-boson contact parameter and the change of the density profile around the impurity. At the unitary limit of the impurity-boson interaction, we find that the effective mass of the impurity remains smaller than twice its bare mass, while the binding energy scales with ${\ensuremath{\hbar}}^{2}{n}^{2/3}/m$, where $n$ is the density of the bath and $m$ is the common mass of the impurity and the bosons in the bath. The implications for the phase diagram of binary Bose-Bose mixtures at low concentrations are also discussed.

arXiv:1507.07427Physical Review ASep 15, 2015200 citations

Bose Polarons at Finite Temperature and Strong Coupling

Nils-Eric Guenther, Pietro Massignan, Maciej Lewenstein +1 more

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.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.

arXiv:1708.08861Physical Review LettersFeb 1, 201893 citations

The Bose polaron as thermometer of a trapped Bose gas: a quantum Monte Carlo study

Tomasz Wasak, Gerard Pascual, Gregory E. Astrakharchik +2 more

Quantum impurities interacting with quantum environments offer unique insights into many-body systems. Here, we explore the thermometric potential of a neutral impurity immersed in a harmonically trapped bosonic quantum gas below the Bose-Einstein condensation critical temperature $T_c$ . Using ab-initio Path Integral Monte Carlo simulations at finite temperatures, we analyze the impurity's sensitivity to temperature changes by exploiting experimentally accessible observables such as its spatial distribution. Our results, covering a temperature range of $-1.1 \leqslant T/T_c \leqslant 0.9$ , reveal that the impurity outperforms estimations based on a one-species bath at lower temperatures, achieving relative precision of 3-4\% for 1000 measurement repetitions. While non-zero boson-impurity interaction strength $g_{BI}$ slightly reduces the accuracy, the impurity's performance remains robust, especially in the low-temperature regime $T/T_c \lesssim 0.45$ withing the analyzed interaction strengths $0 \leqslant g_{BI}/g \leqslant 5$ , where $g$ is the boson-boson coupling. We confirm that quantum optical models can capture rather well the dependence of the temperature sensor on the impurity-gas interaction. Although our findings are in qualitative agreement with previous studies, our Monte Carlo simulations offer improved precision. We find that the maximum likelihood estimation protocol approaches the precision comparable to the limit set by the Quantum Fisher Information bound. Finally, using the Hellinger distance method, we directly extract the Fisher information and find that, by exploiting the extremum order statistics, impurities far from the trap center are more sensitive to thermal effects than those close to the trap center.Quantum impurities interacting with quantum environments offer unique insights into many-body systems. Here, we explore the thermometric potential of a neutral impurity immersed in a harmonically trapped bosonic quantum gas below the Bose-Einstein condensation critical temperature $T_c$. Using ab-initio Path Integral Monte Carlo simulations at finite temperatures, we analyze the impurity's sensitivity to temperature changes by exploiting experimentally accessible observables such as its spatial distribution. Our results, covering a temperature range of $-1.1 \leqslant T/T_c \leqslant 0.9$, reveal that the impurity outperforms estimations based on a one-species bath at lower temperatures, achieving relative precision of 3-4\% for 1000 measurement repetitions. While non-zero boson-impurity interaction strength $g_{BI}$ slightly reduces the accuracy, the impurity's performance remains robust, especially in the low-temperature regime $T/T_c \lesssim 0.45$ withing the analyzed interaction strengths $0 \leqslant g_{BI}/g \leqslant 5$, where $g$ is the boson-boson coupling. We confirm that quantum optical models can capture rather well the dependence of the temperature sensor on the impurity-gas interaction. Although our findings are in qualitative agreement with previous studies, our Monte Carlo simulations offer improved precision. We find that the maximum likelihood estimation protocol approaches the precision comparable to the limit set by the Quantum Fisher Information bound. Finally, using the Hellinger distance method, we directly extract the Fisher information and find that, by exploiting the extremum order statistics, impurities far from the trap center are more sensitive to thermal effects than those close to the trap center.

arXiv:2503.04553Mar 6, 20250 citations

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.

{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.

a

, whereas the interactions between the impurity and the bosons are modeled by a short-range, square-well potential where both the sign and the strength of the scattering length

b

can be varied by adjusting the well depth. We characterize the attractive and the repulsive polaron branch by calculating the binding energy and the effective mass of the impurity. Furthermore, we investigate the structural properties of the bath, such as the impurity-boson contact parameter and the change of the density profile around the impurity. At the unitary limit of the impurity-boson interaction, we find that the effective mass of the impurity remains smaller than twice its bare mass, while the binding energy scales with ${\ensuremath{\hbar}}^{2}{n}^{2/3}/m$, where

n

is the density of the bath and

m

is the common mass of the impurity and the bosons in the bath. The implications for the phase diagram of binary Bose-Bose mixtures at low concentrations are also discussed.

T_c

. Using ab-initio Path Integral Monte Carlo simulations at finite temperatures, we analyze the impurity's sensitivity to temperature changes by exploiting experimentally accessible observables such as its spatial distribution. Our results, covering a temperature range of

-1.1 \leqslant T/T_c \leqslant 0.9

, reveal that the impurity outperforms estimations based on a one-species bath at lower temperatures, achieving relative precision of 3-4\% for 1000 measurement repetitions. While non-zero boson-impurity interaction strength

g_{BI}

slightly reduces the accuracy, the impurity's performance remains robust, especially in the low-temperature regime

T/T_c \lesssim 0.45

withing the analyzed interaction strengths

0 \leqslant g_{BI}/g \leqslant 5

, where

g

is the boson-boson coupling. We confirm that quantum optical models can capture rather well the dependence of the temperature sensor on the impurity-gas interaction. Although our findings are in qualitative agreement with previous studies, our Monte Carlo simulations offer improved precision. We find that the maximum likelihood estimation protocol approaches the precision comparable to the limit set by the Quantum Fisher Information bound. Finally, using the Hellinger distance method, we directly extract the Fisher information and find that, by exploiting the extremum order statistics, impurities far from the trap center are more sensitive to thermal effects than those close to the trap center.