We predict a strong enhancement of the critical temperature in a conventional Bardeen-Cooper-Schrieffer (BCS) superconductor in the presence of a bosonic condensate of exciton polaritons. The effect depends strongly on the ratio of the cutoff frequencies for phonon and exciton-polariton mediated BCS superconductivity, respectively. We also discuss a possible design of hybrid semiconductor-superconductor structures suitable for the experimental observation of such an effect.

We consider a model of interacting Bose-Einstein condensates on small Sierpiński gaskets. We study eigenstates which are characterized by cyclic supercurrents for each triangular plaquette (loop states). For noninteracting systems we find at least three classes of loop eigenmodes: standard, chaotic, and periodic. Standard modes are those inherited from the basic three-site ring of condensates with phase differences locked to $2\pi /3$. Standard modes become unstable in the interacting system but only when the interaction exceeds a certain critical value $u_c$. Chaotic modes are characterized by very different circular currents per plaquette, so the usual symmetry of loop currents is broken. Circular supercurrents associated with chaotic modes become chaotic for any finite interaction, signaling the loss of coherence between the condensates. Periodic modes are described by alternating populations and two different phase differences. The modes are self-similar and are present in all generations of Sierpiński gasket. When the interaction is included, the circular current of such a mode becomes periodic in time with the amplitude growing linearly with the interaction. Above a critical interaction the amplitude saturates, signaling a transition to a macroscopic self-trapping state originally known from a usual Bose-Josephson junction. We perform a systematic analysis of this rich physics.

We study the temporal expansion of an ultracold Bose gas in two-dimensional square optical lattices. The gas is described by the Bose-Hubbard model deep in the superfluid regime, with initially all bosons condensed in the central site of the lattice. We use the previously developed nonequilibrium propagator method for capturing the time evolution of an interacting bosonic system, where the many-body Hamiltonian is represented in an appropriate local basis and the corresponding field operators are separated into the classical [Bose-Einstein condensate (BEC)] part and quantum mechanical fluctuations. After a quench, i.e., after a sudden switch of the lattice nearest-neighbor hopping, the expanding bosonic cloud separates spatially into a fast ballistic forerunner and a slowly expanding central part controlled by self-trapping. We show that the forerunner expansion is driven by the coherent dynamics of the BEC and that its velocity is consistent with the Lieb-Robinson bound. For smaller lattices we analyze how quasiparticle collisions lead to enhanced condensate depletion and oscillation damping.

One of the fundamental problems of quantum statistical physics is how an ideally isolated quantum system can ever reach thermal equilibrium behavior despite the unitary time evolution of quantum-mechanical systems. Here, we study, via explicit time evolution for the generic model system of an interacting, trapped Bose gas with discrete single-particle levels, how the measurement of one or more observables subdivides the system into observed and non-observed Hilbert subspaces and the tracing over the non-measured quantum numbers defines an effective, thermodynamic bath, induces the entanglement of the observed Hilbert subspace with the bath, and leads to a bi-exponential approach of the entanglement entropy and of the measured observables to thermal equilibrium behavior as a function of time. We find this to be more generally fulfilled than in the scenario of the eigenstate thermalization hypothesis (ETH), namely for both local particle occupation numbers and non-local density correlation functions, and independent of the specific initial quantum state of the time evolution.

We study the temporal expansion of an ultracold Bose gas in two-dimensional, square optical lattices. The gas is described by the Bose-Hubbard model deep in the superfluid regime, with initially all bosons condensed in the central site of the lattice. We use the previously developed nonequilibrium propagator method for capturing the time evolution of an interacting bosonic system, where the many-body Hamiltonian is represented in an appropriate local basis and the corresponding field operators are separated into the classical [Bose-Einstein condensate (BEC)] part and quantum mechanical fluctuations. After a quench, i.e. after a sudden switch of the lattice nearest-neighbor hopping, the expanding, bosonic cloud separates spatially into a fast, ballistic forerunner and a slowly expanding central part controlled by selftrapping. We show that the forerunner expansion is driven by the coherent dynamics of the BEC and that its velocity is consistent with the Lieb-Robinson bound. For smaller lattices we analyze how quasiparticle collisions lead to enhanced condensate depletion and oscillation damping.

We consider large rings of weakly-coupled Bose-Einstein condensates, analyzing their transition to chaotic dynamics and loss of coherence. Initially, a ring is considered to be in an eigenstate, i.e. in a commensurate configuration with equal site fillings and equal phase differences between neighboring sites. Such a ring should exhibit a circulating current whose value will depend on the initial, non-zero phase difference. The appearance of such currents is a signature of an established coherence along the ring. If phase difference falls between $\pi/2$ and $3\pi/2$ and interparticle interaction in condensates exceeds a critical interaction value $u_c$, the coherence is supposed to be quickly destroyed because the system enters a chaotic regime due to inherent instabilities. This is, however, only a part of the story. It turns out that chaotic dynamics and resulting averaging of circular current to zero is generally offset by a critical time-scale $t_c$, which is almost two orders of magnitude larger than the one expected from the linear stability analysis. We study the critical time-scale in detail in a broad parameter range.