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Laser Spectroscopy

BOSE-EINSTEIN CONDENSATES STUDIED WITH A LINEAR ACCELERATOR

Ch. Buggle, Jérémie Léonard, Wolf von Klitzing, Jook T. M. Walraven

Published Dec 1, 2005• 0 citations
Publisher

Abstract

We present a stand-alone interference method for the determination of the s- and d-wave scattering amplitudes in a quantum gas. Colliding two ultracold atomic clouds we observe the halo of scattered atoms in the rest frame of the collisional center of mass by absorption imaging. The clouds are accelerated up to energies at which the scattering pattern shows the interference between the s- (l = 0) and d- (l = 2) partial waves. With computerized tomography we transform the images to obtain the angular distribution, which is directly proportional to the difierential cross section. This allows us to measure the asymptotic phase shifts of the s- and d-wave scattering channels. The method does not require knowledge of the atomic density. It allows us to infer accurate values for the s- and dwave scattering amplitudes from the zero-energy limit up to the flrst RamsauerTownsend minimum using only the Van der Waals C6 coe‐cient as theoretical input. For the 87 Rb triplet potential, the method yields an accuracy of 6%.

DOI
10.1142/9789812701473_0020

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We present a stand-alone interference method for the determination of the s- and d-wave scattering amplitudes in a quantum gas. Colliding two ultracold atomic clouds we observe the halo of scattered atoms in the rest frame of the collisional center of mass by absorption imaging. The clouds are accelerated up to energies at which the scattering pattern shows the interference between the s- (l = 0) and d- (l = 2) partial waves. With computerized tomography we transform the images to obtain the angular distribution, which is directly proportional to the difierential cross section. This allows us to measure the asymptotic phase shifts of the s- and d-wave scattering channels. The method does not require knowledge of the atomic density. It allows us to infer accurate values for the s- and dwave scattering amplitudes from the zero-energy limit up to the flrst RamsauerTownsend minimum using only the Van der Waals C6 coe‐cient as theoretical input. For the 87 Rb triplet potential, the method yields an accuracy of 6%.
We demonstrate an interference method to determine the low-energy elastic scattering amplitudes of a quantum gas. We linearly accelerate two ultracold atomic clouds up to energies of 1.2 mK and observe the collision halo by direct imaging in free space. From the interference between s- and d- partial waves in the differential scattering pattern we extract the corresponding phase shifts. The method does not require knowledge of the atomic density. This allows us to infer accurate values for the s- and d-wave scattering amplitudes from the zero-energy limit up to the first Ramsauer minimum using only the van der Waals C6 coefficient as theoretical input. For the 87Rb triplet potential, the method reproduces the scattering length with an accuracy of 6%.
We report on the direct imaging of s and d partial-wave interference in cold collisions of atoms. Two ultracold clouds of 87Rb atoms were accelerated by magnetic fields to collide at energies near a d-wave shape resonance. The resulting halos of scattered particles were imaged using laser absorption. By scanning across the resonance we observed a marked evolution of the scattering patterns due to the energy dependent phase shifts for the interfering s and d waves. Since only two partial-wave states are involved in the collision process the scattering yield and angular distributions have a simple interpretation in terms of a theoretical model.
We report on experiments investigating the collisional properties of atoms at ultralow collision energies using an all-optical atom collider. By using a pair of optical tweezers, we can manipulate two ultracold atom clouds and collide them together at energies up to three orders of magnitude larger than their thermal energy. Our experiments measure the scattering of 87 Rb, 40 K, and 40 K- 87 Rb collisions. The versatility of our collider allows us to probe both shape resonances and Feshbach resonances in any partial wave. As examples, we present experiments demonstrating p-wave scattering with indistinguishable fermions, inelastic scattering at non-zero energies near a homonuclear Feshbach resonance, and partial wave interference in heteronuclear collisions.
A method is presented that is able to predict the probability of outcomes of snapshot measurements, such as the images of the instantaneous particle density distribution in a quantum many-body system. It is shown that a gauge-like transformation of the phase of the many-body wave function allows one to construct a probability generating functional, the Fourier transform of which with respect to the “gauge” field returns the joint probability distribution to detect any given number of particles at various locations. The method is applied to the problem of interference of two independent clouds of Bose-Einstein condensates, where the initially separated clouds with fixed boson numbers expand and the density profile image of the overlapping clouds is registered. In the limit of large particle numbers, the probability to observe a particular image of the density profile is shown to be given by a sum of partial probability distributions, each of which corresponds to a noisy image of interference of two matter waves with definite phase difference. In agreement with earlier theoretical arguments, interference fringes are, therefore, expected in any single shot measurement, the fringe pattern randomly varying from run to run. These results conform to the physical picture where the Bose-Einstein clouds are in spontaneously symmetry broken states, the hidden phases of which are revealed by the density profile measurement via the position of the interference fringes.
We demonstrate an interferometric scattering technique that allows highly precise measurements of s-wave scattering phase shifts. We collide two clouds of cesium atoms in a juggling fountain clock. The atoms in one cloud are prepared in a coherent superposition of the two clock states and the atoms in the other cloud in an F,mF state. After the two clouds collide, we detect the scattered part of the clock atom's wavefunction for which the phase of the clock coherence is shifted by the difference of the s-wave phase shifts. In this way, we unambiguously observe the differences of scattering phase shifts. These phase shifts are independent of the atomic density to lowest order, enabling measurements of scattering phase shifts with clock accuracy. Recently, we have observed the changes in scattering phase shifts as a function of magnetic field over a range where Feshbach resonances may be expected and inelastic scattering channels open and close. Measurements like these will tightly constrain our knowledge of cesium-cesium interactions. With such knowledge, future measurements may place stringent limits on the time variation of fundamental constants, such as the electron-proton mass ratio, by precisely probing phase shifts near a Feshbach resonance.