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Bose-Einstein condensation and macroscopic interference with atomic tunnel arrays

Brian P. Anderson

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

Bose-Einstein condensation in a dilute vapor of magnetically trapped Rb was achieved, and the condensed atoms were used to observe de Broglie-wave interference due to atom tunneling between the barriers of an array of traps. The condensed atoms were loaded into a vertically-oriented one-dimensional optical lattice formed by a retro-reflected laser beam, creating the trap array. In the limit of negligible interactions between atoms, the energy difference between adjacent array sites was determined by the gravitational potential energy shift between the sites. This energy difference initiated an oscillating atom mass current similar to an electric current in the ac Josephson effect for two coupled superconductors. In the optical lattice, de Broglie-wave interference occurred between atoms in localized lattice states, and the interference was observed as a train of falling pulses of atoms. In a separate experiment, using a dilute vapor of lithium, enhanced loading of a Li magneto-optic trap with spectrally-broadened cooling and trapping light was demonstrated. By placing the Li oven nozzle near the trap, the Li atoms could be efficiently captured from an atomic beam without using a pre-cooling stage. The trapped atoms were transferred into a three-dimensional optical lattice, formed by four intersecting and interfering beams of far-off-resonant laser light, and adiabatic cooling and velocity selection in three dimensions was demonstrated.

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Bose-Einstein condensation in a dilute vapor of magnetically trapped Rb was achieved, and the condensed atoms were used to observe de Broglie-wave interference due to atom tunneling between the barriers of an array of traps. The condensed atoms were loaded into a vertically-oriented one-dimensional optical lattice formed by a retro-reflected laser beam, creating the trap array. In the limit of negligible interactions between atoms, the energy difference between adjacent array sites was determined by the gravitational potential energy shift between the sites. This energy difference initiated an oscillating atom mass current similar to an electric current in the ac Josephson effect for two coupled superconductors. In the optical lattice, de Broglie-wave interference occurred between atoms in localized lattice states, and the interference was observed as a train of falling pulses of atoms. In a separate experiment, using a dilute vapor of lithium, enhanced loading of a Li magneto-optic trap with spectrally-broadened cooling and trapping light was demonstrated. By placing the Li oven nozzle near the trap, the Li atoms could be efficiently captured from an atomic beam without using a pre-cooling stage. The trapped atoms were transferred into a three-dimensional optical lattice, formed by four intersecting and interfering beams of far-off-resonant laser light, and adiabatic cooling and velocity selection in three dimensions was demonstrated.
Interference of atomic de Broglie waves tunneling from a vertical array of macroscopically populated traps has been observed. The traps were located in the antinodes of an optical standing wave and were loaded from a Bose-Einstein condensate. Tunneling was induced by acceleration due to gravity, and interference was observed as a train of falling pulses of atoms. In the limit of weak atomic interactions, the pulse frequency is determined by the gravitational potential energy difference between adjacent potential wells. The effect is closely related to the ac Josephson effect observed in superconducting electronic systems.
In this thesis, I present the first experimental implementation of a Josephson junction for Bose-Einstein condensates. The weak link between two BECs constitutes the nonlinear generalization of the well known Josephson junction of weakly-coupled superconductors that are separated by a thin insulating barrier. In our experiment, the required overlap of two macroscopic wavefunctions is provided by loading a BEC into an optical double well potential. It is realized by a superposition of a one-dimensional optical lattice with a focused laser beam optical dipole trap. The tunneling dynamics between the two potential wells exhibits two distinct dynamical regimes. For small initial population imbalances of the two wells we observe nearly sinusoidal Josephson tunneling oscillations, which are characterized by an oscillating population and relative phase. The situation changes drastically, if the initial population imbalance is chosen above a critical value. In this case, resonant tunneling between the two wells is prohibited because the difference between the on-site particle interaction energies in the two wells exceeds the tunneling energy splitting. As a consequence, the atomic distribution becomes self-locked and the relative phase evolves unbound in time. This regime of prohibited tunneling, which has no analogon in superconducting Josephson junctions, is called “macroscopic quantum self-trapping”.
We report on the direct observation of an oscillating atomic current in a one-dimensional array of Josephson junctions realized with an atomic Bose-Einstein condensate. The array is created by a laser standing wave, with the condensates trapped in the valleys of the periodic potential and weakly coupled by the interwell barriers. The coherence of multiple tunneling between adjacent wells is continuously probed by atomic interference. The square of the small-amplitude oscillation frequency is proportional to the microscopic tunneling rate of each condensate through the barriers and provides a direct measurement of the Josephson critical current as a function of the intermediate barrier heights. Our superfluid array may allow investigation of phenomena so far inaccessible to superconducting Josephson junctions and lays a bridge between the condensate dynamics and the physics of discrete nonlinear media.
This thesis includes both experimental and theoretical investigations, presented in a series of eight papers. The experimental part ranges from the construction procedures of an apparatus for Bose-Einstein condensates, to full scale experiments using three different set-ups for ultracold atoms in optical lattices. As one of the main themes of the thesis, an experimental apparatus for production of Bose-Einstein Condensates is under construction. A magneto-optically trapped sample, hosting more than 200 million 87Rb atoms, have successfully been loaded into a magnetic trap with high transfer rate. The lifetime of the sample in the magnetic trap is in the range of 9 s, and the atoms have been shown to respond to evaporative cooling. The experiment is ready for optimization of the magnetic trap loading, and evaporative cooling parameters, which are the final steps for reaching Bose-Einstein condensation. The set-up is designed to host experiments including variable geometry optical lattices, and includes the possibility to align laser beams with high angular precision for this purpose. The breakdown of Bloch waves in a Bose-Einstein condensate is studied, attributed to the effect of energetic and dynamical instability. This experimental study is performed using a Bose-Einstein condensate in a moving one-dimensional optical lattice at LENS, Florence Italy. The optical lattice parameters, and the thermal distribution of the atomic sample required to trigger the instabilities, are detected, and compared with a theoretical model developed in parallel with the experiments. In close connection with these one-dimensional lattice studies, an experimental survey to characterize regimes of superradiant Rayleigh scattering and Bragg scattering is presented. Tunneling properties of repulsively bound atom pairs in double well potentials are characterized in an experiment at Johannes Gutenberg University, Mainz Germany. A three-dimensional optical lattice, producing an array of double wells with tunable properties is let to interact with a Bose-Einstein condensate. Pairs of ultracold atoms are produced on one side in the double wells, and their tunneling behavior, dependent on potential barrier and repulsion properties, is studied. A theoretical study of the crossover between one- and two-dimensional systems has been performed. The simulations were made for a two-dimensional array of atoms, where the behavior for different tunneling probabilities and atom-atom repulsion strengths was studied. Scaling relations for systems of variable sizes have been examined in detail, and numerical values for the involved variables have been found.
We report on the observation of interference of a series of atom lasers. A comblike array of atomic beams is generated by outcoupling atoms from distinct Bose-Einstein condensates confined in the different sites of a mesoscopic optical lattice. The observed interference signal arises from the spatial beating of the overlapped atom laser beams, which is monitored over a range corresponding to 2ms2\phantom{\rule{0.3em}{0ex}}\mathrm{ms}2ms of freefall time. The relative de Broglie frequencies and phases of the atom lasers were measured.
Summary form only given.We have established an experimental and theoretical program focused on understanding photon atom interactions in condensates with the aim of probing the properties of condensates as well as testing our models of the interactions themselves. With a combination of laser and evaporative cooling, we are routinely creating million atom Bose-Einstein condensates of sodium atoms in the newly designed 4D magnet. Our experimental setup incorporates a candlestick atomic beam source, which provides for recirculation of uncollimated sodium atoms, The laser cooling step involves a zero-crossing Zeeman slower, magneto-optic trap, and polarization gradient cooling. The laser-cooled atom cloud is loaded into the 4D magnetic trap and adiabatically compressed to high density and an evaporative cooling process is initiated. Using a RF magnetic resonance technique, hot atoms are ejected through magnetic spin flips. After formation of the condensate in the tightly confining trap, we manipulate the condensate by adiabatically changing the trapping potential and through interaction with photons. We have developed a technique for probing the condensates directly inside the trap using near-resonant absorption imaging. This imaging technique gives high sensitivity to details of the condensate wavefunction and to its surface structure. Images of pure condensates are compared to calculations of the condensate wavefunction based on a Hartree mean field description of the two-body interaction between condensate atoms.