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Ultracold atoms in optical lattices undergo a quantum phase transition from a superfluid to a Mott insulator as the lattice potential depth is increased. We describe an approximate theory of interacting bosons in optical lattices which…
We show that one-dimensional quasi-periodic optical lattice systems can exhibit edge states and topological phases which are generally believed to appear in two-dimensional systems. When the Fermi energy lies in gaps, the Fermi system on…
Topological materials exhibit protected edge modes that have been proposed for applications in for example spintronics and quantum computation. While a number of such systems exist, it would be desirable to be able to test theoretical…
Standard optical potentials use off-resonant laser standing wave induced AC-Stark shift. In a recent development [Phys. Rev. Lett. {\bf 117}, 233001 (2016)] a three-level scheme in $\Lambda$ configuration coupled coherently by resonant…
The regular structures obtained by optical lattice technology and their behaviour are analysed from the quantum information perspective. Initially, we demonstrate that a triangular optical lattice of two atomic species, bosonic or…
We consider a realistic model, i.e., ultracold atoms in a driven optical lattice, to realize phase space crystals [Phys. Rev. Lett. 111, 205303 (2013)]. The corresponding lattice structure in phase space is more complex and contains rich…
Topological pumps offer a promising route to operate as connecting buses, supplying efficient and robust connectivity between non-neighboring elements in a network. Here, we investigate a finite quasiperiodic Fibonacci-type photonic chain…
The effects of frustration on extended supersolid states is a largely unexplored subject in the realm of cold-atom systems. In this work, we explore the impact of quasicrystalline lattices on the supersolid phases of dipolar bosons. Our…
Ultracold gases in optical lattices are of great interest, because these systems bear a great potential for applications in quantum simulations and quantum information processing, in particular when using particles with a long-range…
We have studied interacting and non-interacting quantum degenerate Fermi gases in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Due to…
The recent experimental advancement to realise ultracold gases scattering off an eight-fold optical potential [Phys. Rev. Lett. 122, 110404 (2019)] heralds the beginning of a new technique to study the properties of quasicrystalline…
Here, we propose a platform based on ultra-cold fermionic molecules trapped in optical lattices to simulate nonadiabatic effects, as they appear in certain molecular dynamical problems. The idea consists of a judicious choice of two…
Fermionic atoms in optical lattices provide a native implementation of Fermi-Hubbard (FH) models that can be used as analog quantum simulators of many-body fermionic systems. Recent experimental advances include the time-dependent local…
We analyse nonlinear wave propagation and cascaded self-focusing due to second-harmonic generation in Fibbonacci optical superlattices and introduce a novel concept of nonlinear physics, the quasiperiodic soliton, which describes spatially…
We theoretically analyze the spectrum of phonons of a one-dimensional quasiperiodic lattice. We simulate the quasicrystal from the classic system of spring-bound atoms with a force constant modulated by the Aubry-Andr\'e model, so that its…
We propose the use of photonic crystal structures to design subwavelength optical lattices in two dimensions for ultracold atoms by using both Guided Modes and Casimir-Polder forces. We further show how to use Guided Modes for…
We report on the study of a polariton gas confined in a quasi-periodic one dimensional cavity, described by a Fibonacci sequence. Imaging the polariton modes both in real and reciprocal space, we observe features characteristic of their…
We study the ground-state properties of ultracold bosonic atoms in a state-dependent graphene-like honeycomb optical lattice, where the degeneracy between the two triangular sublattices A and B can be lifted. We discuss the various…
The dynamics of quasicrystals is characterized by the existence of phason excitations in addition to the usual phonon modes. In order to investigate their interplay on an elementary level we resort to various one-dimensional model systems.…
Two discrete N-level alternatives to the popular imaginary cubic oscillator are proposed and studied. In a certain domain ${\cal D}$ of parameters $a$ and $z$ of the model, the spectrum of energies is shown real (i.e., potentially,…