Impurities in ultracold quantum gases: from polaron formation to mediated interactions
File(s)
Author(s)
Jager, Jonas Hugo
Type
Thesis
Abstract
In this thesis, we investigate the properties of Bose polarons in various settings. The overarching
theme of this work is that, in contrast to many existing treatments of the Bose polaron, we apply
semi-classical methods from first principles. Most of this thesis is based on [JJ1,JJ2,JJ3,JJ4].
Our first result addresses the Bose polaron in one dimension. We develop a primarily
analytical treatment of the one-dimensional Bose polaron, which takes the impurity condensate
interaction into account already on the mean-field level. Additionally, we show how to include
first-order quantum corrections. Our results show excellent agreement with quasi-exact Quantum
Monte Carlo simulations.
Motivated by the success of using semi-classical methods, we develop a truncated Wigner
like approximation to address out of equilibrium settings. Using the Keldysh path integral
formalism, we arrive at a set of differential equations with stochastic initial conditions. This
enables us to incorporate quantum fluctuations up to first order and study the impurity dynamics
and polaron formation after a sudden quench of the impurity-boson interaction.
Subsequently, we turn our attention to a three-dimensional system and again rely on semiclassical approximations to study the condensate mediated interaction between two impurities.
The two impurities can form a bound state called the bipolaron for sufficiently large mediated
interactions. We discuss how standard methods lead to inadequate results and show how these
limitations can be remedied by correctly accounting for boson-boson interaction. We calculate
the shape of the mediated interaction potential and the ground state of the two impurities, thus
characterising the bipolaron formation.
Thereafter, we point out the similarities between the semi-classical approximations of the
polaron problem considered so far and colloids interacting with a fluctuating field. We develop
a general framework that perturbatively treats a broad class of field theories and arrive at an
effective action only depending on the impurity degrees of freedom. We apply this approach to
model A and find good agreement with simulations of the full system in the perturbative regime.
theme of this work is that, in contrast to many existing treatments of the Bose polaron, we apply
semi-classical methods from first principles. Most of this thesis is based on [JJ1,JJ2,JJ3,JJ4].
Our first result addresses the Bose polaron in one dimension. We develop a primarily
analytical treatment of the one-dimensional Bose polaron, which takes the impurity condensate
interaction into account already on the mean-field level. Additionally, we show how to include
first-order quantum corrections. Our results show excellent agreement with quasi-exact Quantum
Monte Carlo simulations.
Motivated by the success of using semi-classical methods, we develop a truncated Wigner
like approximation to address out of equilibrium settings. Using the Keldysh path integral
formalism, we arrive at a set of differential equations with stochastic initial conditions. This
enables us to incorporate quantum fluctuations up to first order and study the impurity dynamics
and polaron formation after a sudden quench of the impurity-boson interaction.
Subsequently, we turn our attention to a three-dimensional system and again rely on semiclassical approximations to study the condensate mediated interaction between two impurities.
The two impurities can form a bound state called the bipolaron for sufficiently large mediated
interactions. We discuss how standard methods lead to inadequate results and show how these
limitations can be remedied by correctly accounting for boson-boson interaction. We calculate
the shape of the mediated interaction potential and the ground state of the two impurities, thus
characterising the bipolaron formation.
Thereafter, we point out the similarities between the semi-classical approximations of the
polaron problem considered so far and colloids interacting with a fluctuating field. We develop
a general framework that perturbatively treats a broad class of field theories and arrive at an
effective action only depending on the impurity degrees of freedom. We apply this approach to
model A and find good agreement with simulations of the full system in the perturbative regime.
Version
Open Access
Date Issued
2022-05
Date Awarded
2022-09
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Barnett, Ryan
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
Grant EP/R513052/1
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)