We discuss the regimes of quantum degeneracy in a trapped 1D gas and obtain the diagram of states. Three regimes have been identified: the Bose-Einstein condensation (BEC) regimes of a true condensate and quasicondensate, and the regime of a trapped Tonks gas (gas of impenetrable bosons). The presence of a sharp crossover to the BEC regime requires extremely small interaction between particles. We discuss how to distinguish between true and quasicondensates in phase coherence experiments.

Influence of nearly resonant light on the scattering length in low-temperature atomic gases Fedichev, P.; Kagan, Y.M.; Shlyapnikov, G.V.; Walraven, J.T.M.

The fastest possible collective response of a quantum many-body system is related to its excitations at the highest possible energy. In condensed-matter systems, the corresponding timescale is typically set by the Fermi energy. Taking advantage of fast and precise control of interactions between ultracold atoms, we report on the observation of ultrafast dynamics of impurities coupled to an atomic Fermi sea. Our interferometric measurements track the non-perturbative quantum evolution of a fermionic many-body system, revealing in real time the formation dynamics of quasiparticles and the quantum interference between attractive and repulsive states throughout the full depth of the Fermi sea. Ultrafast time-domain methods to manipulate and investigate strongly interacting quantum gases open up new windows on the dynamics of quantum matter under extreme nonequilibrium conditions.Non-equilibrium dynamics of fermionic systems is at the heart of many problems in science and technology, from the physics of neutron stars and heavy ion collisions to the operation of electronic devices. The wide range of energy scales, spanning the low energies of excitations near the Fermi surface up to high energies of excitations from deep within the Fermi sea, challenges our understanding of the quantum dynamics in such fundamental systems. The Fermi energy E F sets the shortest response time for the collective response of a fermionic many-body system through the Fermi time τ F =h/E F , whereh is the reduced Planck constant. In a metal, i.e. a Fermi sea of electrons, E F is in the range of a few electronvolts, which corresponds to τ F on the order of 100 attoseconds. Dynamics in condensed matter systems on this timescale can be recorded by attosecond streaking techniques [1] and the initial applications were demonstrated by probing photoelectron emission from a surface [2]. However, despite these spectacular advances, the direct observation of the coherent evolution of a fermionic many-body system on the Fermi timescale has remained beyond reach.In atomic quantum gases, the fermions are much heavier and the densities far lower, which brings τ F into the experimentally accessible range of typically a few microseconds. Furthermore, the powerful techniques of atom interferometry [3] now offer the exciting opportunity to probe and manipulate the real-time coherent evolution of a fermionic quantum many-body system. Such techniques have been successfully used, e.g. to measure bosonic Hanbury-Brown-Twiss correlations [4], demonstrate topological bands [5], probe quantum and thermal fluctuations in low-dimensional condensates [6,7], and to measure demagnetization dynamics of a fermionic gas [8,9]. Impurities coupled to a quantum gas provide a novel and unique probe of the many-body state. Strikingly, they allow direct access to the system's wave function when the internal states of the impurities are manipulated using a Ramsey atom-interferometric technique [10,11].We employ dilute 40 K atoms in a 6 Li Fermi sea to measure the response of the ...