Abstract:
We discuss the 2D Mott insulator (MI) state of a 2D array of coupled finite size 1D Bose gases. It is shown that the momentum distribution in the lattice plane is very sensitive to the interaction regime in the 1D tubes. In particular, we find that the disappearance of the interference pattern in time of flight experiments will not be a signature of the MI phase, but a clear consequence of the strongly interacting Tonks-Girardeau regime along the tubes.

Abstract:
We study superradiance in a one-dimensional geometry, where N>>1 atoms are randomly distributed along a line. We present an analytic calculation of the photon escape rates based on the diagonalization of the N x N coupling matrix Uij = cos xij, where xij is the dimensionless random distance between any two atoms. We show that unlike a three-dimensional geometry, for a one- dimensional atomic gas the single-atom limit is never reached and the photon is always localized within the atomic ensemble. This localization originates from long-range cooperative effects and not from disorder as expected on the basis of the theory of Anderson localization.

Abstract:
We present experimental observation of electromagnetically induced transparency (EIT) on a single macroscopic artificial "atom" (superconducting quantum system) coupled to open 1D space of a transmission line. Unlike in a optical media with many atoms, the single atom EIT in 1D space is revealed in suppression of reflection of electromagnetic waves, rather than absorption. The observed almost 100 % modulation of the reflection and transmission of propagating microwaves demonstrates full controllability of individual artificial atoms and a possibility to manipulate the atomic states. The system can be used as a switchable mirror of microwaves and opens a good perspective for its applications in photonic quantum information processing and other fields.

Abstract:
We consider spectroscopies of strongly interacting atomic gases, and we propose a model for describing the coupling between quasiparticles and gapless phonon-like modes. Our model explains features in a wide range of different experiments in both fermionic and bosonic atom gases in various spectroscopic methods.

Abstract:
One exciting progress in recent cold atom experiments is the development of high resolution, in situ imaging techniques for atomic quantum gases [1-3]. These new powerful tools provide detailed information on the distribution of atoms in a trap with resolution approaching the level of single atom and even single lattice site, and complement the well developed time-of-flight method that probes the system in momentum space. In a condensed matter analogy, this technique is equivalent to locating electrons of a material in a snap shot. In situ imaging has offered a new powerful tool to study atomic gases and inspired many new research directions and ideas. In this chapter, we will describe the experimental setup of in situ absorption imaging, observables that can be extracted from the images, and new physics that can be explored with this technique.

Abstract:
We report on local measurements of atom number fluctuations in slices of a single 1D Bose gas with repulsive interactions. For weakly interacting gases, the fluctuations are super-Poissonian at intermediate atomic densities and become sub-Poissonian at high densities once the gas enters into the quantum quasi-condensate regime. At stronger interactions, when approaching the fermionization regime, we no longer observe super-Poissonian statistics; the fluctuations go from Poissonian to sub-Poissonian as the density is increased, as those in a Fermi gas.

Abstract:
We propose a scheme utilising a quantum interference phenomenon to switch the transport of atoms in a 1D optical lattice through a site containing an impurity atom. The impurity represents a qubit which in one spin state is transparent to the probe atoms, but in the other acts as a single atom mirror. This allows a single-shot quantum non-demolition measurement of the qubit spin.

Abstract:
Cold atomic gases have proven capable of emulating a number of fundamental condensed matter phenomena including Bose-Einstein condensation, the Mott transition, Fulde-Ferrell-Larkin-Ovchinnikov pairing and the quantum Hall effect. Cooling to a low enough temperature to explore magnetism and exotic superconductivity in lattices of fermionic atoms remains a challenge. We propose a method to produce a low temperature gas by preparing it in a disordered potential and following a constant entropy trajectory to deliver the gas into a non-disordered state which exhibits these incompletely understood phases. We show, using quantum Monte Carlo simulations, that we can approach the Ne\'el temperature of the three-dimensional Hubbard model for experimentally achievable parameters. Recent experimental estimates suggest the randomness required lies in a regime where atom transport and equilibration are still robust.

Abstract:
van Hove's theory of scattering of probe particles by a macroscopic target is generalized so as to relate the differential cross section for atomic ejection via stimulated Raman transitions to one-particle momentum-time correlations and momentum distributions of 1D trapped gases. This method is well suited to probing the longitudinal momentum distributions of 1D gases in situ, and examples are given for bosonic and fermionic atoms.