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arXiv:cond-mat/0406093 · Physical Review Letters

Interferometric Determination of the s and d -Wave Scattering Amplitudes in Rb87

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

Published Oct 22, 2004• 98 citations
arXivHTMLPDF

Abstract

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%.

DOI
10.1103/physrevlett.93.173202

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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 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 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.
Quantum interference in cold collisions has been predicted to dominate chemical dynamics at low temperatures. However, experimental observations have been largely confined to light-atom systems due to technical challenges. Here, we report direct observation of scattering oscillations in cold ionizing collisions between metastable krypton and rubidium atoms. By combining laser cooling with velocity-mapped ion imaging, we precisely controlled the collision energy from 15 millikelvin to 8 kelvin and detected the ionization products. Below 1 kelvin, pronounced quantum interference between partial waves emerges as the de Broglie wavelength approaches the interaction range. The angular oscillation period scales as [Formula: see text], consistent with a Langevin capture model for van der Waals-dominated collisions. Moreover, interference patterns in the angular distribution-collision temperature spectrum are highly sensitive to the long-range potential shape and reveal subtle shape resonances. These observations were corroborated by theoretical calculations. Our results demonstrate the quantum-classical crossover in heavy-atom systems. This study establishes a versatile platform for studying a wide range of laser-coolable species.
Low energy elastic scattering between clouds of Bose condensed atoms leads to the well known sss-wave halo with atoms emerging in all directions from the collision zone. In this paper we discuss the emergence of Hanbury Brown and Twiss coincidences between atoms scattered in nearly parallel directions. We develop a simple model that explains the observations in terms of an interference involving two pairs of atoms each associated with the elementary sss-wave scattering process.
The low-energy two-body scattering S- and P-wave parameters, together with a shape-dependent S-wave quantity, which appear in the well-known low-density expansions for the ground-state energy of many-boson and many-fermion systems, are accurately calculated for several central pair potentials for spin-polarized atoms, helium atoms, and nucleons. An integral-equation method allowing accurate determination of the coefficients of the above-mentioned parameters expanded in powers of the attraction strength of the pair potential is presented and applied. The results are needed for perturbation studies of ground-state energies of various quantum many-body systems.
We demonstrate a juggling atomic fountain by launching two laser-cooled balls of 133Cs{}^{133}\mathrm{Cs}133Cs atoms in rapid succession. The atoms collide near the top of the fountain and, by varying the delay between launches, we scan the collision energy from 19 to $150\ensuremath{\mu}\mathrm{K}$. We measure the differential scattering cross section and isolate the contributions from different partial waves including their interferences. We observe the sss-wave energy dependence and the ppp-wave scattering threshold. We infer a triplet sss-wave scattering length of ${\ensuremath{-}400a}_{0}$ and a ppp wave of $({\ensuremath{-}107a}_{0}{)}^{3}$ for ∣F=4,m=4〉+∣3,3〉|F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4,m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4〉+|3,3〉∣F=4,m=4〉+∣3,3〉.