The variational Feynman formalism for the polaron, extended to an all-coupling treatment of bipolarons, is applied for two impurity atoms in a Bose-Einstein condensate. This shows that if the polaronic coupling strength is large enough the impurities
will form a bound state (the bipolaron). As a function of the mutual repulsion between the impurities two types of bipolaron are distinguished: a tightly bound bipolaron at weak repulsion and a dumbbell bipolaron at strong repulsion. Apart from the binding energy, also the evolution of the bipolaron radius and its effective mass are examined as a function of the strength of the repulsive interaction between the impurities and of the polaronic cupling strength. We then apply the strong-coupling formalism to multiple impuritiy atoms in a condensate which leads to the prediction of multi-polaron formation in the strong coupling regime. The results of the two formalisms are compared for two impurities in a condensate which results in a general qualitative agreement and a quantitative agreement at strong coupling. Typically the system of impurity atoms in a Bose-Einstein condensate is expected to exhibit the polaronic weak coupling regime. However, the polaronic coupling strength is in principle tunable with a Feshbach resonance.
The polaron optical conductivity is derived within the strong-coupling expansion, which is asymptotically exact in the strong-coupling limit. The polaron optical conductivity band is provided by the multiphonon optical transitions. The polaron optica
l conductivity spectra calculated within our analytic strong-coupling approach and the numerically accurate Diagrammatic Quantum Monte Carlo (DQMC) data are in a good agreement with each other at large $alpha gtrapprox 9$.
Using time-dependent Ginzburg-Landau theory we demonstrate that the Aharonov-Bohm (AB) effect, resulting from a Berry phase shift of the (macroscopic) wavefunction, is revealed through the dynamics of topological phase defects present in that same wa
vefunction. We study vortices and antivortices on the surface of a hollow superconducting cylinder, moving on circular orbits as they are subjected to the force from the current flowing parallel to the cylinder axis. Due to the AB effect the orbit deflections, caused by a magnetic field component along the cylinder axis, become periodic as a function of field, leading to strong and robust resistance oscillations.
