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

International Journal of Modern Physics B

Ultracold Atomic Interactions and Bose–Einstein Condensation

Daniel J. Heinzen

Published Nov 10, 1997• 3 citations
Publisher

Abstract

Atomic interactions play a crucial role in Bose-condensed alkali gases. The condensate self-energy, proportional to the two-body s-wave scattering length, strongly affects the stability and other properties of a condensate. Alkali atom scattering lengths have been determined only during the past few years by a combination of conventional molecular spectroscopy, photoassociation spectroscopy, and ultracold atomic collision studies. In this article, we present a brief review of alkali atom interactions and scattering length determinations.

DOI
10.1142/s0217979297001593

Related papers

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

Ultracold photoassociation spectroscopy: Long-range molecules and atomic scattering

K. M. Jones, Eite Tiesinga, Paul D. Lett +1 more

Photoassociation is the process in which two colliding atoms absorb a photon to form an excited molecule. The development of laser-cooling techniques for producing gases at ultracold $(<1\phantom{\rule{0.3em}{0ex}}\mathrm{mK})$ temperatures allows photoassociation spectroscopy to be performed with very high spectral resolution. Of particular interest is the investigation of molecular states whose properties can be related, with high precision, to the properties of their constituent atoms with the ``complications'' of chemical binding accounted for by a few parameters. These include bound long-range or purely long-range vibrational states in which two atoms spend most or all of their time at large internuclear separations. Low-energy atomic scattering states also share this characteristic. Photoassociation techniques have made important contributions to the study of all of these. This review describes what is special about photoassociation spectroscopy at ultracold temperatures, how it is performed, and a sampling of results including the determination of scattering lengths, their control via optical Feshbach resonances, precision determinations of atomic lifetimes from molecular spectra, limits on photoassociation rates in a Bose-Einstein condensate, and briefly, production of cold molecules. Discussions are illustrated with examples on alkali-metal atoms as well as other species. Progress in the field is already past the point where this review can be exhaustive, but an introduction is provided on the capabilities of photoassociation spectroscopy and the techniques presently in use.

Reviews of Modern Physics•May 22, 2006•873 citations

Collisions in cold atomic gases

Paul S. Julienne

Summary form only given. The collisional interactions between the atoms in an cold, dense atomic gas play a crucial role in determining the dynamics and stability of the gas and the approach to Bose-Einstein condensation. This talk will give simple interpretive physical models of threshold scattering, backed up by full quantum scattering calculations for collisions between extremely cold Na atoms or Rb atoms.

Quantum Electronics and Laser Science Conference•Jun 7, 1996•0 citations

The Bose alkali gases

A. J. Leggett

Abstract This chapter starts with a discussion of the structure and properties of individual alkali atoms, and of trapping and diagnostic techniques. It is shown that under the conditions normally satisfied in practice, it is an excellent approximation to model the interatomic interaction by a delta-function potential with a coefficient derived from the experimentally measured s-wave scattering length. The simplest theory of a Bose-condensed dilute atomic alkali gas, the Gross-Pitaevskii ansatz, is introduced and some of its consequences explored. A number of spectacular phenomena related to the phase coherence of a gas displaying BEC are reviewed. The final two sections examine the behavior of an ultracold Bose gas in an optical lattice, and various signatures of superfluidity in the experimental systems.

•Sep 28, 2006•0 citations

Singlet s-wave scattering lengths of {sup 6}Li and {sup 7}Li

E. Abraham, W. I. McAlexander, Jordan M. Gerton

Ultracold collisional interactions are crucial to both the dynamical evolution and the steady-state behavior of systems designed to observe Bose-Einstein condensation, and are relevant to the advances in high precision measurements, and the creation of more highly accurate atomic clocks based on laser-cooled neutral atoms. An important parameter for understanding these collisions is the s-wave scattering length {alpha}, which can be determined from accurate knowledge of the two-body interaction potential. Photoassociation of ultracold lithium atoms into bound vibrational levels of the A{sup 1}{Sigma}{sub u}{sup +} excited state is used to probe the X{sup 1}{Sigma}{sub g}{sup +} ground state interaction potential of {sup 6}Li{sub 2} and {sup 7}Li{sub 2}. It had been predicted that the s-wave photoassociation signal strength would pass through a minimum as a function of vibrational level for positive scattering length. The authors present the observation of this novel effect, and use the location of the minimum to precisely determine the singlet s-wave scattering length for both isotopes. The sensitivity of this technique is demonstrated by distinguishing the scattering lengths for collisions involving {sup 7}Li atoms in different hyperfine states.

Bulletin of the American Physical Society•May 1, 1996•0 citations

Interactions between atoms

C. J. Pethick, H. Smith

From a theoretical point of view, one of the appealing features of clouds of alkali atom vapours is that particle separations, which are typically of order 10 2 nm, are large compared with the scattering length a which characterizes the strength of interactions. Scattering lengths for alkali atoms are of the order of 100 a 0 , where a 0 , is the Bohr radius, and therefore alkali atom vapours are dilute, in the sense that the dominant effects of interaction are due to two-body encounters. It is therefore possible to calculate properties of the gas reliably from a knowledge of two-body scattering at low energies, which implies that information about atomic scattering is a key ingredient in work on Bose–Einstein condensates. An alkali atom in its electronic ground state has several different hyperfine states, as we have seen in Secs. 3.1 and 3.2. Interatomic interactions give rise to transitions between these states and, as we described in Sec. 4.6, such processes are a major mechanism for loss of trapped atoms. In a scattering process, the internal states of the particles in the initial or final states are described by a set of quantum numbers, such as those for the spin, the atomic species, and their state of excitation. We shall refer to a possible choice of these quantum numbers as a channel.1 At the temperatures of interest for Bose-Einstein condensation, atoms are in their electronic ground states, and the only relevant internal states are therefore the hyperfine states. Because of the existence of several hyperfine states for a single atom, the scattering of cold alkali atoms is a multi-channel problem.

Cambridge University Press eBooks•Nov 29, 2001•0 citations
Atomic interactions play a crucial role in Bose-condensed alkali gases. The condensate self-energy, proportional to the two-body s-wave scattering length, strongly affects the stability and other properties of a condensate. Alkali atom scattering lengths have been determined only during the past few years by a combination of conventional molecular spectroscopy, photoassociation spectroscopy, and ultracold atomic collision studies. In this article, we present a brief review of alkali atom interactions and scattering length determinations.
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
Photoassociation is the process in which two colliding atoms absorb a photon to form an excited molecule. The development of laser-cooling techniques for producing gases at ultracold (<1mK)(<1\phantom{\rule{0.3em}{0ex}}\mathrm{mK})(<1mK) temperatures allows photoassociation spectroscopy to be performed with very high spectral resolution. Of particular interest is the investigation of molecular states whose properties can be related, with high precision, to the properties of their constituent atoms with the ``complications'' of chemical binding accounted for by a few parameters. These include bound long-range or purely long-range vibrational states in which two atoms spend most or all of their time at large internuclear separations. Low-energy atomic scattering states also share this characteristic. Photoassociation techniques have made important contributions to the study of all of these. This review describes what is special about photoassociation spectroscopy at ultracold temperatures, how it is performed, and a sampling of results including the determination of scattering lengths, their control via optical Feshbach resonances, precision determinations of atomic lifetimes from molecular spectra, limits on photoassociation rates in a Bose-Einstein condensate, and briefly, production of cold molecules. Discussions are illustrated with examples on alkali-metal atoms as well as other species. Progress in the field is already past the point where this review can be exhaustive, but an introduction is provided on the capabilities of photoassociation spectroscopy and the techniques presently in use.
Abstract This chapter starts with a discussion of the structure and properties of individual alkali atoms, and of trapping and diagnostic techniques. It is shown that under the conditions normally satisfied in practice, it is an excellent approximation to model the interatomic interaction by a delta-function potential with a coefficient derived from the experimentally measured s-wave scattering length. The simplest theory of a Bose-condensed dilute atomic alkali gas, the Gross-Pitaevskii ansatz, is introduced and some of its consequences explored. A number of spectacular phenomena related to the phase coherence of a gas displaying BEC are reviewed. The final two sections examine the behavior of an ultracold Bose gas in an optical lattice, and various signatures of superfluidity in the experimental systems.
Ultracold collisional interactions are crucial to both the dynamical evolution and the steady-state behavior of systems designed to observe Bose-Einstein condensation, and are relevant to the advances in high precision measurements, and the creation of more highly accurate atomic clocks based on laser-cooled neutral atoms. An important parameter for understanding these collisions is the s-wave scattering length {alpha}, which can be determined from accurate knowledge of the two-body interaction potential. Photoassociation of ultracold lithium atoms into bound vibrational levels of the A{sup 1}{Sigma}{sub u}{sup +} excited state is used to probe the X{sup 1}{Sigma}{sub g}{sup +} ground state interaction potential of {sup 6}Li{sub 2} and {sup 7}Li{sub 2}. It had been predicted that the s-wave photoassociation signal strength would pass through a minimum as a function of vibrational level for positive scattering length. The authors present the observation of this novel effect, and use the location of the minimum to precisely determine the singlet s-wave scattering length for both isotopes. The sensitivity of this technique is demonstrated by distinguishing the scattering lengths for collisions involving {sup 7}Li atoms in different hyperfine states.
From a theoretical point of view, one of the appealing features of clouds of alkali atom vapours is that particle separations, which are typically of order 10 2 nm, are large compared with the scattering length a which characterizes the strength of interactions. Scattering lengths for alkali atoms are of the order of 100 a 0 , where a 0 , is the Bohr radius, and therefore alkali atom vapours are dilute, in the sense that the dominant effects of interaction are due to two-body encounters. It is therefore possible to calculate properties of the gas reliably from a knowledge of two-body scattering at low energies, which implies that information about atomic scattering is a key ingredient in work on Bose–Einstein condensates. An alkali atom in its electronic ground state has several different hyperfine states, as we have seen in Secs. 3.1 and 3.2. Interatomic interactions give rise to transitions between these states and, as we described in Sec. 4.6, such processes are a major mechanism for loss of trapped atoms. In a scattering process, the internal states of the particles in the initial or final states are described by a set of quantum numbers, such as those for the spin, the atomic species, and their state of excitation. We shall refer to a possible choice of these quantum numbers as a channel.1 At the temperatures of interest for Bose-Einstein condensation, atoms are in their electronic ground states, and the only relevant internal states are therefore the hyperfine states. Because of the existence of several hyperfine states for a single atom, the scattering of cold alkali atoms is a multi-channel problem.