A trapped-atom interferometer was demonstrated using gaseous Bose-Einstein condensates coherently split by deforming an optical single-well potential into a double-well potential. The relative phase between the two condensates was determined from the spatial phase of the matter wave interference pattern formed upon releasing the condensates from the separated potential wells. Coherent phase evolution was observed for condensates held separated by $13\mu \mathrm{m}$ for up to 5 ms and was controlled by applying ac Stark shift potentials to either of the two separated condensates.

We measure the relative phase of two Bose-Einstein condensates confined in a radio frequency induced double-well potential on an atom chip. We observe phase coherence between the separated condensates for times up to $\sim 200\mathrm{ms}$ after splitting, a factor of 10 longer than the phase diffusion time expected for a coherent state for our experimental conditions. The enhanced coherence time is attributed to number squeezing of the initial state by a factor of 10. In addition, we demonstrate a rotationally sensitive (Sagnac) geometry for a guided atom interferometer by propagating the split condensates.

Spin-polarized gaseous Bose-Einstein condensates were confined by a combination of gravitational and magnetic forces. The partially condensed atomic vapors were adiabatically decompressed by weakening the gravito-magnetic trap to a mean frequency of 1hertz, then evaporatively reduced in size to 2500 atoms. This lowered the peak condensate density to 5 × 10 ¹⁰ atoms per cubic centimeter and cooled the entire cloud in all three dimensions to a kinetic temperature of 450 ± 80 picokelvin. Such spin-polarized, dilute, and ultracold gases are important for spectroscopy, metrology, and atom optics.

Doubly quantized vortices were topologically imprinted in $|F=1⟩{}^{23}\mathrm{N}\mathrm{a}$ condensates, and their time evolution was observed using a tomographic imaging technique. The decay into two singly quantized vortices was characterized and attributed to dynamical instability. The time scale of the splitting process was found to be longer at higher atom density.