Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

Ultracold collisions for Bose—Einstein condensation

L. S. Butcher, Derek N. Stacey, Christopher J. Foot, Keith R. Burnett

Published May 15, 1999• 4 citations
Publisher

Abstract

We describe the low–energy scattering theory relevant to the description of the Bose–Einstein condensed gases recently produced using evaporative cooling. We examine the validity range of the approximations being used to describe the ultracold interactions in the context of the interaction between caesium atoms at the temperatures produced by evaporation in a magnetic trap. We discuss the prospects for future developments in the field.

DOI
10.1098/rsta.1999.0382

Related papers

Collisions at nanokelvin temperatures in Bose-Einstein condensates

Wolfgang Ketterle

Bose-Einstein condensed atomic gases are a new class of quantum fluids. They are produced by cooling a dilute atomic gas to nanokelvin temperatures using laser and evaporative cooling techniques. In this paper we review developments in Bose-Einstein condensation, emphasizing how this new quantum fluid has become a laboratory for the study of collisions at ultralow energy and of collective effects in light-atom and atom-atom interactions. Magnetic fields have been used to modify the scattering length for atomic collisions. Spinor condensates were created, with a spin structure determined by spin relaxation collisions and external magnetic fields. We have used light scattering to study collective excitations and observed superradiant light emission. Dissipation was studied by dragging a repulsive, blue-detuned laser beam through the fluid, as well as by inducing collisions between condensates.

AIP conference proceedings•Jan 1, 2000•0 citations

Ultra-cold Collisions and Evaporative Cooling of Caesium in a Magnetic Trap

Angharad Mair Thomas

Ultra-cold Collisions and Evaporative Cooling of Caesium in a Magnetic Trap Angharad Mair Thomas, Jesus College, Oxford University DPhil Thesis, Hilary Term 2004 Caesium-133 atoms have been evaporatively cooled in a magnetic trap to temperatures as low as 8 nK producing a final phase-space density within a factor of 4 of that required for the onset of Bose-Einstein condensation. At the end of the forced radio-frequency evaporation, 1500 atoms in the F = 3,mF = −3 state remain in the magnetic trap. A decrease in the one-dimensional evaporative cooling efficiency at very low temperatures is observed as the trapped sample enters the collisionally thick (hydrodynamic) regime. Different evaporation trajectories are experimentally studied leading to a greater understanding of one-dimensional evaporation, inelastic collisions and the hydrodynamic regime. A theoretical simulation accurately reproduces the experimental data and indicates that the reduction in the evaporative cooling efficiency as the cloud enters the hydrodynamic regime is the main obstacle to the realization of Bose-Einstein condensation in the F = 3,mF = −3 state. In addition, we report measurements of the two-body inelastic collision rate coefficient for caesium atoms as a function of magnetic field and collision energy. The positions of three previously identified resonances are confirmed, with reduced uncertainties, at magnetic fields of 108.87(6), 118.46(3) and 133.52(3) Gauss. The resonance centred at 118.46Gauss is also investigated as a function of temperature, thus demonstrating the dependence of the inelastic Feshbach resonance on collision energy. The importance of including partial waves of a higher basis in theoretical

•Jan 1, 2004•4 citations

Collisional dynamics of ultra-cold atomic gases

Jean Dalibard, Jean Dalibard

Collision physics plays a key role in understanding the properties of ultracold gases. First, collisions ensure thermalization in trapped atomic samples, which is essential for the success of evaporative cooling. Second, interactions between atoms determine the equilibrium shape and the dynamics of the condensate once it is formed. Finally collisions limit the achievable spatial densities via inelastic processes, which ultimately determine whether a given atomic species may lead to Bose-Einstein condensation. The purpose of the following lectures is to give a basic introduction to collision physics with a special emphasis on the low temperature aspect of these interactions. We will consider here only binary interactions between atoms since one of the remarkable prop-erties of the physics of ultra-cold dilute gases is that all the macroscopic properties of the system can be directly deduced from the two-body interaction potential. In particular the essential concept of scattering length will be introduced and developped for some simple potentials, using as practical examples experimental results obtained on atomic cesium and rubidium. The present lectures are complementary to the ones given by D. Heinzen where a detailed comparison between the collisional properties of the various alkali atoms will be found, together with explanations of the spectroscopic approaches used in the precise determination of interatomic potentials. 1. – Scattering theory: a brief reminder 1.1. Collision between two particles. – We consider here an elementary collision process between two particles 1 and 2 with the same mass M, interacting through the potential

•Jan 1, 1998•13 citations

Strong evaporative cooling towards Bose Einstein condensation of a magnetically trapped caesium gas

A M Thomas, S. A. Hopkins, Simon L. Cornish +1 more

We have evaporatively cooled caesium atoms in a magnetic trap to temperatures as low as 8 nK and produced a final phase space density within a factor of four of that required for the onset of Bose–Einstein condensation. At the end of the forced radio-frequency evaporation, 1500 atoms in the F = 3, m F = −3 state remain in the magnetic trap. We observe a decrease in the one-dimensional evaporative cooling efficiency at very low temperatures as the trapped sample enters the collisionally thick (hydrodynamic) regime. To alleviate this problem we propose a modified trapping scheme where three-dimensional evaporation is possible. In addition, we report measurements of the two-body inelastic collision rates for caesium atoms as a function of magnetic field. We confirm the positions, with reduced uncertainties, of three previously identified resonances at magnetic fields of 108.87(6), 118.46(3) and 133.52(3) G.

Journal of Optics B Quantum and Semiclassical Optics•Apr 1, 2003•12 citations

Bose–Einstein condensation of ultracold atomic gases

Wolfgang Ketterle, Michael R. Andrews, Kendall B. Davis +4 more

Bose–Einstein condensation in a dilute gas of sodium atoms has been observed. The atoms were trapped in an optically plugged magnetic trap or in a cloverleaf magnetic trap. Rf induced evaporative cooling increased the phase-space density by six orders of magnitude. We summarize the different techniques used, and discuss recent studies of properties of Bose condensates with an outlook on future developments.

Physica Scripta•Jan 1, 1996•21 citations

Bose–Einstein Condensation in an Ultracold Gas

Carl Wieman

Bose–Einstein condensation in a gas has now been achieved. Atoms are cooled to the point of condensation using laser cooling and trapping, followed by magnetic trapping and evaporative cooling. These techniques are explained, as well as the techniques by which we observe the cold atom samples. Three different signatures of Bose–Einstein condensation are described. A number of properties of the condensate, including collective excitations, distortions of the wave function by interactions, and the fraction of atoms in the condensate versus temperature, have also been measured.

International Journal of Modern Physics B•Nov 10, 1997•0 citations
We describe the low–energy scattering theory relevant to the description of the Bose–Einstein condensed gases recently produced using evaporative cooling. We examine the validity range of the approximations being used to describe the ultracold interactions in the context of the interaction between caesium atoms at the temperatures produced by evaporation in a magnetic trap. We discuss the prospects for future developments in the field.
Bose-Einstein condensed atomic gases are a new class of quantum fluids. They are produced by cooling a dilute atomic gas to nanokelvin temperatures using laser and evaporative cooling techniques. In this paper we review developments in Bose-Einstein condensation, emphasizing how this new quantum fluid has become a laboratory for the study of collisions at ultralow energy and of collective effects in light-atom and atom-atom interactions. Magnetic fields have been used to modify the scattering length for atomic collisions. Spinor condensates were created, with a spin structure determined by spin relaxation collisions and external magnetic fields. We have used light scattering to study collective excitations and observed superradiant light emission. Dissipation was studied by dragging a repulsive, blue-detuned laser beam through the fluid, as well as by inducing collisions between condensates.
Ultra-cold Collisions and Evaporative Cooling of Caesium in a Magnetic Trap Angharad Mair Thomas, Jesus College, Oxford University DPhil Thesis, Hilary Term 2004 Caesium-133 atoms have been evaporatively cooled in a magnetic trap to temperatures as low as 8 nK producing a final phase-space density within a factor of 4 of that required for the onset of Bose-Einstein condensation. At the end of the forced radio-frequency evaporation, 1500 atoms in the F = 3,mF = −3 state remain in the magnetic trap. A decrease in the one-dimensional evaporative cooling efficiency at very low temperatures is observed as the trapped sample enters the collisionally thick (hydrodynamic) regime. Different evaporation trajectories are experimentally studied leading to a greater understanding of one-dimensional evaporation, inelastic collisions and the hydrodynamic regime. A theoretical simulation accurately reproduces the experimental data and indicates that the reduction in the evaporative cooling efficiency as the cloud enters the hydrodynamic regime is the main obstacle to the realization of Bose-Einstein condensation in the F = 3,mF = −3 state. In addition, we report measurements of the two-body inelastic collision rate coefficient for caesium atoms as a function of magnetic field and collision energy. The positions of three previously identified resonances are confirmed, with reduced uncertainties, at magnetic fields of 108.87(6), 118.46(3) and 133.52(3) Gauss. The resonance centred at 118.46Gauss is also investigated as a function of temperature, thus demonstrating the dependence of the inelastic Feshbach resonance on collision energy. The importance of including partial waves of a higher basis in theoretical
Collision physics plays a key role in understanding the properties of ultracold gases. First, collisions ensure thermalization in trapped atomic samples, which is essential for the success of evaporative cooling. Second, interactions between atoms determine the equilibrium shape and the dynamics of the condensate once it is formed. Finally collisions limit the achievable spatial densities via inelastic processes, which ultimately determine whether a given atomic species may lead to Bose-Einstein condensation. The purpose of the following lectures is to give a basic introduction to collision physics with a special emphasis on the low temperature aspect of these interactions. We will consider here only binary interactions between atoms since one of the remarkable prop-erties of the physics of ultra-cold dilute gases is that all the macroscopic properties of the system can be directly deduced from the two-body interaction potential. In particular the essential concept of scattering length will be introduced and developped for some simple potentials, using as practical examples experimental results obtained on atomic cesium and rubidium. The present lectures are complementary to the ones given by D. Heinzen where a detailed comparison between the collisional properties of the various alkali atoms will be found, together with explanations of the spectroscopic approaches used in the precise determination of interatomic potentials. 1. – Scattering theory: a brief reminder 1.1. Collision between two particles. – We consider here an elementary collision process between two particles 1 and 2 with the same mass M, interacting through the potential
We have evaporatively cooled caesium atoms in a magnetic trap to temperatures as low as 8 nK and produced a final phase space density within a factor of four of that required for the onset of Bose–Einstein condensation. At the end of the forced radio-frequency evaporation, 1500 atoms in the F = 3, m F = −3 state remain in the magnetic trap. We observe a decrease in the one-dimensional evaporative cooling efficiency at very low temperatures as the trapped sample enters the collisionally thick (hydrodynamic) regime. To alleviate this problem we propose a modified trapping scheme where three-dimensional evaporation is possible. In addition, we report measurements of the two-body inelastic collision rates for caesium atoms as a function of magnetic field. We confirm the positions, with reduced uncertainties, of three previously identified resonances at magnetic fields of 108.87(6), 118.46(3) and 133.52(3) G.
Bose–Einstein condensation in a gas has now been achieved. Atoms are cooled to the point of condensation using laser cooling and trapping, followed by magnetic trapping and evaporative cooling. These techniques are explained, as well as the techniques by which we observe the cold atom samples. Three different signatures of Bose–Einstein condensation are described. A number of properties of the condensate, including collective excitations, distortions of the wave function by interactions, and the fraction of atoms in the condensate versus temperature, have also been measured.