TY  - GEN
N2  - In this thesis, field theoretical and variational methods are applied to few- and
many-body problems of strongly interacting ultracold atomic gases and atomicallythin semiconductors. In strongly interacting mixtures of particles, the renormalizing
effect of one species upon another is investigated to study the competition between
the formation of different quasiparticles and the associated quantum phases related
to the appearance of such particles. Tracing back to the Fermi polaron problem in
which an impurity interacts attractively with a bath of fermionic particles, a majority
of the work presented in this thesis may be understood in the context of a transition
between the molecule state, in which a bath particle binds tightly to the impurity,
and a quasiparticle best described as an impurity dressed by a cloud of bath particles. Going from a few to many impurities, due to the small energy gap between
these quasiparticles, insights obtained in the Fermi polaron problem are leveraged
to study the phase diagram of Fermi-Fermi and Bose-Fermi mixtures. First, the
phase diagram of two- and three-dimensional Bose-Fermi mixtures is studied using
the functional renormalization group (fRG). Three-body correlations are considered,
and the approach is suited to treat finite-density populations of both bosons and
fermions to study the molecular phase. Concurrently, experimental data are analyzed
to characterize the superfluid-to-normal transition encountered in three-dimensional
Bose-Fermi mixtures. A self-consistent, frequency- and momentum-resolved fRG approach is used to predict the transition point. This fRG method is then improved
leveraging its analytical structure to obtain Greens functions at arbitrary complex
frequencies using exact analytical continuation at a reduced computational cost. This
is used to study the momentum-dependent decay rates of low-lying excited states, and
predictions for Ramsey and Raman measurements are made. A stochastic variational
approach is used to study bound-state formation in few-body problems. Precursors of
the physics of the Fermi polaron problem are observed, and we find that finite interaction ranges, along with confinement, can greatly enhance trimer formation, relating to
superfluid p-wave pairing. Finally, insights obtained in the study of strongly coupled
Bose-Fermi mixtures are leveraged to study superconductivity in two-dimensional heterostructures of transition metal dichalcogenides. Here, capturing the strong-coupling
physics of Bose-Fermi mixtures, boson-induced correlations are studied as a means to
induce/enhance superfluid pairing with high critical temperatures.
TI  - Quasiparticle formation and induced correlations in strongly coupled Bose-Fermi mixtures
AV  - public
Y1  - 2024///
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/34437/
CY  - Heidelberg
ID  - heidok34437
A1  - Milczewski, Jonas von
ER  -