Abstract:
We present the implementation of tailored trapping potentials for ultracold gases on an atom chip. We realize highly elongated traps with box-like confinement along the long, axial direction combined with conventional harmonic confinement along the two radial directions. The design, fabrication and characterization of the atom chip and the box traps is described. We load ultracold ($\lesssim1 \mu$K) clouds of $^{87}$Rb in a box trap, and demonstrate Bose-gas focusing as a means to characterize these atomic clouds in arbitrarily shaped potentials. Our results show that box-like axial potentials on atom chips are very promising for studies of one-dimensional quantum gases.

Abstract:
We present experiments with Bose-Einstein condensates on a combined atom chip. The combined structure consists of a large-scale "carrier chip" and smaller "atom-optics chips", containing micron-sized elements. This allows us to work with condensates very close to chip surfaces without suffering from fragmentation or losses due to thermally driven spin flips. Precise three-dimensional positioning and transport with constant trap frequencies are described. Bose-Einstein condensates were manipulated with submicron accuracy above atom-optics chips. As an application of atom chips, a direction sensitive magnetic field microscope is demonstrated.

Abstract:
Atom chips provide a versatile `quantum laboratory on a microchip' for experiments with ultracold atomic gases. They have been used in experiments on diverse topics such as low-dimensional quantum gases, cavity quantum electrodynamics, atom-surface interactions, and chip-based atomic clocks and interferometers. A severe limitation of atom chips, however, is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. Such techniques enable chip-based studies of entangled many-body systems and are a key prerequisite for atom chip applications in quantum simulations, quantum information processing, and quantum metrology. Here we report experiments where we generate multi-particle entanglement on an atom chip by controlling elastic collisional interactions with a state-dependent potential. We employ this technique to generate spin-squeezed states of a two-component Bose-Einstein condensate and show that they are useful for quantum metrology. The observed 3.7 dB reduction in spin noise combined with the spin coherence imply four-partite entanglement between the condensate atoms and could be used to improve an interferometric measurement by 2.5 dB over the standard quantum limit. Our data show good agreement with a dynamical multi-mode simulation and allow us to reconstruct the Wigner function of the spin-squeezed condensate. The techniques demonstrated here could be directly applied in chip-based atomic clocks which are currently being set up.

Abstract:
We review our recent and ongoing work with Fermi gases on an atom chip. After reviewing some statistical and thermodynamic properties of the ideal, non-interacting Fermi gas, and a brief description of our atom chip and its capabilities, we discuss our experimental approach to producing a potassium-40 degenerate Fermi gas (DFG) using sympathetic cooling by a rubidium-87 Bose-Einstein condensate on an atom chip. In doing so, we describe the factors affecting the loading efficiency of the atom chip microtrap. This is followed by a discussion of species selectivity in radio frequency manipulation of the Bose-Fermi mixture, which we explore in the context of sympathetic evaporative cooling and radio-frequency dressed adiabatic double-well potentials. Next, we describe the incorporation of a crossed-beam dipole trap into the atom chip setup, in which we generate and manipulate strongly interacting spin mixtures of potassium-40. Finally, we conclude with a brief discussion of future research directions with DFGs and atom chips.

Abstract:
Divergence-free pseudopotentials for spatially even and odd-wave interactions in spinor Fermi gases in tight atom waveguides are derived. The Fermi-Bose mapping method is used to relate the effectively one-dimensional fermionic many-body problem to that of a spinor Bose gas. Depending on the relative magnitudes of the even and odd-wave interactions, the N-atom ground state may have total spin S=0, S=N/2, and possibly also intermediate values, the case S=N/2 applying near a p-wave Feshbach resonance, where the N-fermion ground state is space-antisymmetric and spin-symmetric. In this case the fermionic ground state maps to the spinless bosonic Lieb-Liniger gas. An external magnetic field with a longitudinal gradient causes a Stern-Gerlach spatial separation of the corresponding trapped Fermi gas with respect to various values of $S_z$.

Abstract:
In an atomic gas near a Feshbach resonance, the energy of two colliding atoms is close to the energy of a bound state, i.e., a molecular state, in a closed channel that is coupled to the incoming open channel. Due to the different spin arrangements of the atoms in the open channel and the atoms in the molecular state, the energy difference between the bound state and the two-atom continuum threshold is experimentally accessible by means of the Zeeman interaction of the atomic spins with a magnetic field. As a result, it is in principle possible to vary the scattering length to any value by tuning the magnetic field. This level of experimental control has opened the road for many beautiful experiments, which recently led to the demonstration of coherence between atoms and molecules. This is achieved by observing coherent oscillations between atoms and molecules, analogous to coherent Rabi oscillations that occur in ordinary two-level systems. We review the many-body theory that describes coherence between atoms and molecules in terms of an effective quantum field theory for Feshbach-resonant interactions. The most important feature of this effective quantum field theory is that it incorporates the two-atom physics of the Feshbach resonance exactly, which turns out to be necessary to fully explain experiments with Bose-Einstein condensed atomic gases.

Abstract:
The relative importance of density and phase fluctuations in ultracold one dimensional atomic Bose gases is investigated. By defining appropriate characteristic temperatures for their respective onset, a broad experimental regime is found, where density fluctuations set in at a lower temperature than phase fluctuations. This is in stark contrast to the usual experimental regime explored up to now, in which phase fluctuations are largely decoupled from density fluctuations, a regime also recovered in this work as a limiting case. Observation of the novel regime of dominant density fluctuations is shown to be well within current experimental capabilities for both $^{23}Na$ and $^{87}Rb$, requiring relatively low temperatures, small atom numbers and moderate aspect ratios.

Abstract:
We show that previously observed large disorder potentials in magnetic microtraps for neutral atoms are reduced by about two orders of magnitude when using atom chips with lithographically fabricated high quality gold layers. Using one dimensional Bose-Einstein condensates, we probe the remaining magnetic field variations at surface distances down to a few microns. Measurements on a 100 um wide wire imply that residual variations of the current flow result from local properties of the wire.

Abstract:
One-dimensional Bose gases are considered, interacting either through the hard-core potentials or through the contact delta potentials. Interest in these gases gained momentum because of the recent experimental realization of quasi-one-dimensional Bose gases in traps with tightly confined radial motion, achieving the Tonks-Girardeau (TG) regime of strongly interacting atoms. For such gases the Fermi-Bose mapping of wavefunctions is applicable. The aim of the present communication is to give a brief survey of the problem and to demonstrate the generality of this mapping by emphasizing that: (i) It is valid for nonequilibrium wavefunctions, described by the time-dependent Schr\"odinger equation, not merely for stationary wavefunctions. (ii) It gives the whole spectrum of all excited states, not merely the ground state. (iii) It applies to the Lieb-Liniger gas with the contact interaction, not merely to the TG gas of impenetrable bosons.

Abstract:
We show that current in a two-dimensional electron gas (2DEG) can trap ultracold atoms $<1 \mu$m away with orders of magnitude less spatial noise than a metal trapping wire. This enables the creation of hybrid systems, which integrate ultracold atoms with quantum electronic devices to give extreme sensitivity and control: for example, activating a single quantized conductance channel in the 2DEG can split a Bose-Einstein condensate (BEC) for atom interferometry. In turn, the BEC offers unique structural and functional imaging of quantum devices and transport in heterostructures and graphene.