Transistor-Like Behavior of a Bose-Einstein Condensate in a Triple Well Potential

In the last several years considerable efforts have been devoted to developing Bose-Einstein Condensate (BEC)-based devices for applications such as fundamental research, precision measurements and integrated atom optics. Such devices capable of complex functionality can be designed from simpler building blocks as is done in microelectronics. One of the most important components of microelectronics is a transistor. We demonstrate that Bose-Einstein condensate in a three well potential structure where the tunneling of atoms between two wells is controlled by the population in the third, shows behavior similar to that of an electronic field effect transistor. Namely, it exhibits switching and both absolute and differential gain. The role of quantum fluctuations is analyzed, estimates of switching time and parameters for the potential are presented.Comment: 12 pages, 12 figure

Atomic population distribution in the output ports of cold-atom interferometers with optical splitting and recombination

Cold-atom interferometers with optical splitting and recombination use off-resonant laser beams to split a cloud of Bose-Einstein condensate (BEC) into two clouds that travel along different paths and are then recombined again using optical beams. After the recombination, the BEC in general populates both the cloud at rest and the moving clouds. Measuring relative number of atoms in each of these clouds yields information about the relative phase shift accumulated by the atoms in the two moving clouds during the interferometric cycle. We derive the expression for the probability of finding any given number of atoms in each of the clouds, discuss features of the probability density distribution, analyze its dependence on the relative accumulated phase shift as a function of the strength of the interatomic interactions, and compare our results with experiment.Comment: 25 pages, 7 figure

Increasing the coherence time of Bose-Einstein-condensate interferometers with optical control of dynamics

Atom interferometers using Bose-Einstein condensate that is confined in a waveguide and manipulated by optical pulses have been limited by their short coherence times. We present a theoretical model that offers a physically simple explanation for the loss of contrast and propose the method for increasing the fringe contrast by recombining the atoms at a different time. A simple, quantitatively accurate, analytical expression for the optimized recombination time is presented and used to place limits on the physical parameters for which the contrast may be recovered.Comment: 34 Pages, 8 Figure

Theoretical analysis of a single and double reflection atom interferometer in a weakly-confining magnetic trap

The operation of a BEC based atom interferometer, where the atoms are held in a weakly-confining magnetic trap and manipulated with counter-propagating laser beams, is analyzed. A simple analytic model is developed to describe the dynamics of the interferometer. It is used to find the regions of parameter space with high and low contrast of the interference fringes for both single and double reflection interferometers. We demonstrate that for a double reflection interferometer the coherence time can be increased by shifting the recombination time. The theory is compared with recent experimental realizations of these interferometers.Comment: 25 pages, 6 figure

Revealing buried information: Statistical processing techniques for ultracold gas image analysis

The techniques of principal and independent component analysis are applied to images of ultracold atoms. As an illustrative example, we present the use of these model-independent methods to rapidly determine the differential phase of a BEC interferometer from large sets of images of interference patterns. These techniques have been useful in the calibration of the experiment and in the investigation of phase randomization. The details of the algorithms are provided.Comment: v2: Many changes made to answer reviewer comments and improve clarity. 29 pages, 9 figures v3: Small change to emphasize role of models in result interpretation. 29 pages, 9 figure

A waveguide atom beamsplitter for laser-cooled neutral atoms

A laser-cooled neutral-atom beam from a low-velocity intense source is split into two beams while guided by a magnetic-field potential. We generate our multimode-beamsplitter potential with two current-carrying wires on a glass substrate combined with an external transverse bias field. The atoms bend around several curves over a $10$-cm distance. A maximum integrated flux of $1.5\cdot10^{5} \mathrm{atoms/s}$ is achieved with a current density of $5\cdot10^{4} \mathrm{Ampere/cm^{2}}$ in the 100-$\mathrm{\mu m}$ diameter wires. The initial beam can be split into two beams with a 50/50 splitting ratio

Wave function recombination instability in cold atom interferometers

Cold atom interferometers use guiding potentials that split the wave function of the Bose-Einstein condensate and then recombine it. We present theoretical analysis of the wave function recombination instability that is due to the weak nonlinearity of the condensate. It is most pronounced when the accumulated phase difference between the arms of the interferometer is close to an odd multiple of PI and consists in exponential amplification of the weak ground state mode by the strong first excited mode. The instability exists for both trapped-atom and beam interferometers.Comment: 4 pages, 5 figure