We prepare a chemically and thermally one-dimensional (1d) quantum degenerate Bose gas in a single microtrap. We introduce a new interferometric method to distinguish the quasicondensate fraction of the gas from the thermal cloud at finite temperatur
e. We reach temperatures down to $kTapprox 0.5hbaromega_perp$ (transverse oscillator eigenfrequency $omega_perp$) when collisional thermalization slows down as expected in 1d. At the lowest temperatures the transverse momentum distribution exhibits a residual dependence on the line density $n_{1d}$, characteristic for 1d systems. For very low densities the approach to the transverse single particle ground state is linear in $n_{1d}$.
Optical dipole traps and atom chips are two very powerful tools for the quantum manipulation of neutral atoms. We demonstrate that both methods can be combined by creating an optical lattice potential on an atom chip. A red-detuned laser beam is retr
o-reflected using the atom chip surface as a high-quality mirror, generating a vertical array of purely optical oblate traps. We load thermal atoms from the chip into the lattice and observe cooling into the two-dimensional regime where the thermal energy is smaller than a quantum of transverse excitation. Using a chip-generated Bose-Einstein condensate, we demonstrate coherent Bloch oscillations in the lattice.
The probabilistic character of the measurement process is one of the most puzzling and fascinating aspects of quantum mechanics. In many-body systems quantum mechanical noise reveals non-local correlations of the underlying many-body states. Here, we
provide a complete experimental analysis of the shot-to-shot variations of interference fringe contrast for pairs of independently created one-dimensional Bose condensates. Analyzing different system sizes we observe the crossover from thermal to quantum noise, reflected in a characteristic change in the distribution functions from Poissonian to Gumbel-type, in excellent agreement with theoretical predictions based on the Luttinger liquid formalism. We present the first experimental observation of quasi long-range order in one-dimensional atomic condensates, which is a hallmark of quantum fluctuations in one-dimensional systems. Furthermore, our experiments constitute the first analysis of the full distribution of quantum noise in an interacting many-body system.
Low-dimensional systems are beautiful examples of many-body quantum physics. For one-dimensional systems the Luttinger liquid approach provides insight into universal properties. Much is known of the equilibrium state, both in the weakly and strongly
interacting regime. However, it remains a challenge to probe the dynamics by which this equilibrium state is reached. Here we present a direct experimental study of the coherence dynamics in both isolated and coupled degenerate 1d Bose gases. Dynamic splitting is used to create two 1d systems in a phase coherent state. The time evolution of the coherence is revealed in local phase shifts of the subsequently observed interference patterns. Completely isolated 1d Bose gases are observed to exhibit a universal sub-exponential coherence decay in excellent agreement with recent predictions by Burkov et al. [Phys. Rev. Lett. 98, 200404 (2007)]. For two coupled 1d Bose gases the coherence factor is observed to approach a non-zero equilibrium value as predicted by a Bogoliubov approach. This coupled-system decay to finite coherence is the matter wave equivalent of phase locking two lasers by injection. The non-equilibrium dynamics of superfluids plays an important role in a wide range of physical systems, such as superconductors, quantum-Hall systems, superfluid Helium, and spin systems. Our experiments studying coherence dynamics show that 1d Bose gases are ideally suited for investigating this class of phenomena.
