Rapidly scanning magnetic and optical dipole traps have been widely utilized to form time-averaged potentials for ultracold quantum gas experiments. Here we theoretically and experimentally characterize the dynamic properties of Bose-Einstein condensates in ring-shaped potentials that are formed by scanning an optical dipole beam in a circular trajectory. We find that unidirectional scanning leads to a nontrivial phase profile of the condensate that can be approximated analytically using the concept of phase imprinting. While the phase profile is not accessible through in-trap imaging, time-of-flight expansion manifests clear density signatures of an in-trap phase step in the condensate, coincident with the instantaneous position of the scanning beam. The phase step remains significant even when scanning the beam at frequencies 2 orders of magnitude larger than the characteristic frequency of the trap. We map out the phase and density properties of the condensate in the scanning trap, both experimentally and using numerical simulations, and find excellent agreement. Furthermore, we demonstrate that bidirectional scanning flattens the phase profile, rendering the system more suitable for coherent matter-wave interferometry.
Rapidly scanning magnetic and optical dipole traps have been widely utilized to form time-averaged potentials for ultracold quantum gas experiments. Here we theoretically and experimentally characterize the dynamic properties of Bose-Einstein condensates in ring-shaped potentials that are formed by scanning an optical dipole beam in a circular trajectory. We find that unidirectional scanning leads to a nontrivial phase profile of the condensate that can be approximated analytically using the concept of phase imprinting. While the phase profile is not accessible through in-trap imaging, time-of-flight expansion manifests clear density signatures of an in-trap phase step in the condensate, coincident with the instantaneous position of the scanning beam. The phase step remains significant even when scanning the beam at frequencies 2 orders of magnitude larger than the characteristic frequency of the trap. We map out the phase and density properties of the condensate in the scanning trap, both experimentally and using numerical simulations, and find excellent agreement. Furthermore, we demonstrate that bidirectional scanning flattens the phase profile, rendering the system more suitable for coherent matter-wave interferometry.
Interferometric measurements with matter waves are established techniques for sensitive gravimetry, rotation sensing, and measurement of surface interactions, but compact interferometers will require techniques based on trapped geometries. In a step towards the realisation of matter wave interferometers in toroidal geometries, we produce a large, smooth ring trap for Bose–Einstein condensates using rapidly scanned time-averaged dipole potentials. The trap potential is smoothed by using the atom distribution as input to an optical intensity correction algorithm. Smooth rings with a diameter up to 300 μ m are demonstrated. We experimentally observe and simulate the dispersion of condensed atoms in the resulting potential, with good agreement serving as an indication of trap smoothness. Under time of flight expansion we observe low energy excitations in the ring, which serves to constrain the lower frequency limit of the scanned potential technique. The resulting ring potential will have applications as a waveguide for atom interferometry and studies of superfluidity.
This paper reports the results of a theoretical and experimental study of how the initial circulation of ring-shaped Bose-Einstein condensates (BECs) can be probed by time-of-flight (TOF) images. We have studied the dynamics of a BEC after release from a toroidal trap potential by solving the three-dimensional Gross-Pitaevskii (GP) equation. The trap and condensate characteristics matched those of a recent experiment. The circulation, experimentally imparted to the condensate by stirring, was simulated by imprinting a linear azimuthal phase on the initial condensate wave function. The simulated TOF images were in good agreement with the experimental data. We find that upon release the dynamics of the ring-shaped condensate proceeds in two distinct phases. First, the condensate expands rapidly inward, filling in the initial hole until it reaches a minimum radius that depends on the initial circulation. In the second phase, the density at the inner radius increases to a maximum after which the hole radius begins slowly to expand. During this second phase a series of concentric rings appears due to the interference of ingoing and outgoing matter waves from the inner radius. The results of the GP equation predict that the hole area is a quadratic function of the initial circulation when the condensate is released directly from the trap in which it was stirred and is a linear function of the circulation if the trap is relaxed before release. These scalings matched the data. Thus hole size after TOF can be used as a reliable probe of initial condensate circulation. This connection between circulation and hole size after TOF will facilitate future studies of atomtronic systems that are implemented in ultracold quantum gases.
Since the first Bose-Einstein Condensate (BEC) was demonstrated in a dilute atomic gas [1], rotating BECs have been of interest to researchers due to their quantized circulation. We propose a new method of creating controlled vortices in a BEC. Atoms are held in the focus of a scanning beam that rapidly scans to produce a time-averaged potential [2]. We have made theoretical calculations to measure the heating caused by a scanning beam trap and to find the regime where a scanning beam produces a time-averaged potential. The scanning beam splits the BEC into four parts then imprints a relative phase on each part such that, when the parts recombine, a vortex forms. We have simulated such a system using the Gross-Pitaevskii equation and have demonstrated the laser scanning pattern using a two-dimensional acousto-optic modulator (AOM). The optics for the scanning beam trap have been designed and the experimental trap dimensions are used in our simulations. To carry out the experimental part of this project, we are currently building and testing an all-optical BEC apparatus: we have made a magneto-optical trap (MOT) which cools the 87Rb atomsto 30uK. We are currently setting up an optical dipole trap to perform the final stages of cooling.
There is a pressing need for robust and straightforward methods to create potentials for trapping Bose–Einstein condensates (BECs) that are simultaneously dynamic, fully arbitrary and sufficiently stable to not heat the ultracold gas. We show here how to accomplish these goals, using a rapidly moving laser beam that 'paints' a time-averaged optical dipole potential in which we create BECs in a variety of geometries, including toroids, ring lattices and square lattices. Matter wave interference patterns confirm that the trapped gas is a condensate. As a simple illustration of dynamics, we show that the technique can transform a toroidal condensate into a ring lattice and back into a toroid. The technique is general and should work with any sufficiently polarizable low-energy particles.
We report the experimental realization of a versatile ring trap for ultracold atoms. The ring geometry is created by the time-averaged adiabatic potential resulting from the application of an oscillating magnetic bias field to a rf-dressed quadrupole trap. Lifetimes for a Bose-Einstein condensate in the ring exceed 11s and the ring radius was continuously varied from $50 \ensuremath{\mu}\text{m}$ to $262 \ensuremath{\mu}\text{m}$. An efficient method of loading the ring from a conventional time-averaged orbiting potential trap is presented together with a rotation scheme which introduces angular momentum into the system. The ring presents an opportunity to study the superfluid properties of a condensate in a multiply connected geometry and also has applications for matter-wave interferometry.
This thesis reports the final stages of construction and performance of a high atom number rubidium-87 Bose-Einstein condensate (BEC) apparatus, and the generation of time-averaged optical potentials geared towards interferometric applications. A detailed description of the hybrid trap used in our experiment is given, which comprises magnetic confinement from a quadrupole field, and optical trapping from a focussed 1064 nm laser beam. We present the typical temperatures of atom clouds at all stages of cooling, from the 3D magneto-optical trap, through to the onset of condensation in the hybrid trap. Our trap typically realises nearly-pure BECs of 1.5–2.0×106 atoms, at temperatures of (217 ± 6) nK, over duty cycles of 16–25 s. The implementation of a time-averaged optical potential is also discussed, as a means of generating versatile, planar potentials for BECs. In this work, we focus on the generation of large, ring- shaped potentials, which have trapping frequencies in the ranges 2π×(110–140,35–55) Hz vertically and radially, respectively. The details of a feed forward algorithm are presented, which allows for the realisation of smooth ring structures up to 150 μm in radius, which enclose areas ten times larger than optical ring traps created previously. These larger rings are promising candidates for interferometric measurements of the rotation-induced Sagnac phase, with the device sensitivity proportional to the enclosed area. We typically retain 2.5–3.0×106 atoms in these large traps, after evaporatively cooling to temperatures of (44 ± 9) nK. The measured lifetimes in the trap are on the order of 16 s. These ring condensates are expected to be fully phase coherent, despite their reduced dimensionality, as a result of high atom numbers, weak confinement, and low temperatures. We present preliminary data demonstrating these coherence properties, and outlay future plans for a comprehensive study of this coherence, probing both fully coherent rings, and those expected to fall within the phase-fluctuating regime. The control afforded using our time-averaged optical potentials is demonstrated through the generation of acoustic waves propagating around the ring condensates. The dispersion is linear for low driving frequencies, and allows for a determination of the speed of sound, and the chemical potential, found here to be cs =1.34 mm.s-1, and μ=kB×18nK respectively.