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We investigate quantum phase transitions occurring in a system of strongly interacting ultracold bosons in a 1D optical lattice. After discussing the commensurate-incommensurate transition, we focus on the phases appearing at incommensurate…
In this paper, we present evidence for a liquid-like phase in systems of many interacting Bosons at intermediate densities. The interacting Bose gas has been studied extensively in the low and high density regimes, in which interactions do…
We review recent developments concerning non-equilibrium quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues. We start with quantum impurity models summarizing the effect of dissipation and…
Ultracold atoms trapped in laser-generated optical lattices serve as a versatile platform for quantum simulations. However, as these lattices are infinitely stiff, they do not allow to emulate phonon degrees of freedom. This restriction can…
We present the general lattice model for a multi-component atomic Bose-Einstein system in the optical lattice. Using the model, we analytically study the quantum phase transition between Mott insulator and superfluid. A mean-field theory is…
The collapses and revivals of a coherent matter wave field of interacting particles can serve as a sensitive interferometric probe of the interactions and the number statistics of the underlying quantum field. Here we show how the ability…
The interaction between the electromagnetic field inside a cavity and natural or artificial atoms has played a crucial role in developing our understanding of light-matter interaction, and is central to various quantum technologies.…
A particular superconducting quantum interference device (SQUID)qubit, indicated as double SQUID qubit, can be manipulated by rapidly modifying its potential with the application of fast flux pulses. In this system we observe coherent…
We analyze interacting one-dimensional bosons in the continuum, subject to a periodic sinusoidal potential of arbitrary depth. Variation of the lattice depth tunes the system from the Bose-Hubbard limit for deep lattices, through the…
We consider bosonic atoms loaded into optical lattices with cavity-mediated infinite-range interactions. Competing short- and global-range interactions cultivates a rich phase diagram. With a systematic field-theoretical perspective, we…
An ultracold gas of coupled two-component atoms in an optical field is studied. Due to the internal two-level structure of the atoms, three competing energy terms exist; atomic kinetic, atomic internal, and atom-atom interaction energies. A…
We study two models realized by two-component Fermi gases loaded in optical lattices. We clarify that multi-band effects inevitably caused by the optical lattices generate a rich structure, when the systems crossover from the region of…
Advances in pure optical trapping techniques now allow the creation of degenerate Bose gases with internal degrees of freedom. Systems such as ${}^{87}$Rb, $^{39}$K or ${}^{23}$Na in the $F=1$ hyperfine state offer an ideal platform for…
We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard…
A trapped 87Rb Bose-Einstein condensate is initially put into a superposition of two internal states. Under the effect of gravity and by means of a second transition, we prepare two vertically displaced condensates in the same internal…
In the emerging field of quantum computation and quantum information, superconducting devices are promising candidates for the implementation of solid-state quantum bits or qubits. Single-qubit operations, direct coupling between two…
Many-body systems with strong interactions often exhibit macroscopic behavior markedly absent in single-particle or noninteracting limits. Such emergent phenomena are well exemplified in lattice Hubbard models, where the interplay between…
We examine the quench dynamics across quantum phase transitions from a Mott insulator (MI) to a superfluid (SF) phase in a two-component bosonic mixture in an optical lattice. We show that two-component Bose mixtures exhibit qualitatively…
We show that off-site processes and multi-orbital physics have a crucial impact on the phase diagram of quantum gas mixtures in optical lattices. In particular, we discuss Bose-Fermi mixtures where the intra- and interspecies interactions…
We review recent theoretical and experimental progresses in the coherent multiple scattering of weakly interacting disordered Bose gases. These systems have allowed, in the recent years, a characterization of weak and strong localization…