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Vortex states in the mixture of ultracold atomic clouds of bosons and fermions are investigated using the effective Hamiltonian for the Bose subsystem. A stability of the Bose system in the case of attractive interaction between components…
A grand-canonical system of interacting bosons is considered to study phase transitions of ultracold atoms in an optical lattice. The phase diagram is discussed in terms of a matrix-like order parameter, representing a symmetric phase (Mott…
Systems with two species of active molecular motors moving on (cytoskeletal) filaments into opposite directions are studied theoretically using driven lattice gas models. The motors can unbind from and rebind to the filaments. Two motors…
We describe interacting mixtures of ultracold bosonic and fermionic atoms in harmonically confined optical lattices. For a suitable choice of parameters we study the emergence of superfluid and Fermi liquid (non-insulating) regions out of…
We consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions, such as Na-23, in optical lattices. We show that spin-exchange interactions give rise to several distinct phases, which differ in their spin…
Microresonators are micron-scale optical systems that confine light using total internal reflection. These optical systems have gained interest in the last two decades due to their compact sizes, unprecedented measurement capabilities, and…
A mixture of light and heavy spin-polarized fermionic atoms in an optical lattice is considered. Tunneling of the heavy atoms is neglected such that they are only subject to thermal fluctuations. This results in a complex interplay between…
We present a review of properties of ultracold atomic Fermi-Bose mixtures in inhomogeneous and random optical lattices. In the strong interacting limit and at very low temperatures, fermions form, together with bosons or bosonic holes, {\it…
We develop a model of a binary fermionic mixture, consisting of large number of atoms, applicable at nonzero temperatures, in the normal phase. We use this approach to study dynamics of degenerate Fermi systems under various perturbations.…
Symmetry breaking of light states is of interest for the understanding of nonlinear optics, photonic circuits, telecom applications and optical pulse generation. Here we demonstrate 4-fold symmetry breaking of the resonances of ring…
We study the internal dynamics of bosonic atoms in an optical lattice. Within the regime in which the atomic crystal is a Mott insulator with one atom per well, the atoms behave as localized spins which interact according to some spin…
Recent experimental progress have revealed Meissner and Vortex phases in low-dimensional ultracold atoms systems. Atomtronic setups can realize ring ladders, while explicitly taking the finite size of the system into account. This enables…
We propose the creation and investigation of a system of spin-one fermions in the presence of artificial spin-orbit coupling, via the interaction of three hyperfine states of fermionic atoms to Raman laser fields. We explore the emergence…
Phase transitions are commonly held to occur only in the thermodynamical limit of large number of system components. Here we exemplify at the hand of the exactly solvable Jaynes-Cummings (JC) model and its generalization to finite…
Recent mean-field calculations suggest that the superconducting state of twisted bilayer graphene exhibits either a nematic order or a spontaneous breakdown of the time-reversal symmetry. The two-dimensional character of the material and…
This review describes quantum systems of bosonic particles moving on a lattice. These models are relevant in statistical physics, and have natural ties with probability theory. The general setting is recalled and the main questions about…
Exchange processes are responsible for the stability of elementary boson condensates with respect to their possible fragmentation. This remains true for composite bosons when single fermion exchanges are included but spin degrees of freedom…
Fermionic atoms in optical lattices have served as a compelling model system to study and emulate the physics of strongly-correlated matter. Driven by the advances of high-resolution microscopy, the recent focus of research has been on…
We investigate phase transitions towards frequency entrainment in large, locally coupled networks of limit cycle oscillators. Specifically, we simulate two-dimensional lattices of pulse-coupled oscillators with random natural frequencies,…
Recent years have seen the discovery of a chiral spin liquid state - a bosonic analogue of a fractional Quantum Hall state first put forward by Kalmeyer and Laughlin in 1987 - in several deformations of the Heisenberg model on the Kagome…