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

Physical Review Letters

Negative scattering length of ultracold Li7 gas

A. J. Moerdijk, William C. Stwalley, Randall G. Hulet, BOUDEWIJN J. VERHAAR

Published Jan 3, 1994• 81 citations
Publisher

Abstract

We have improved the theoretical triplet ground-state potential of $^{7}\mathrm{Li}_{2}$ by means of an inverse perturbation analysis, and find that the diatomic scattering length for $^{7}\mathrm{Li}$ atoms in the F=2, ${\mathit{m}}_{\mathit{F}}$=2 ground-state hyperfine level is negative. The consequences of this result for achieving Bose-Einstein condensation in a trapped ultracold $^{7}\mathrm{Li}$ gas sample are addressed.

DOI
10.1103/physrevlett.72.40

Related papers

Prospects for Bose-Einstein Condensation in Atomic Li7 and Na23

A. J. Moerdijk, BOUDEWIJN J. VERHAAR

We have determined the scattering length of the ground state $^{7}\mathrm{Li}$ + $^{7}\mathrm{Li}$ singlet potential from spectroscopic data on the highest $S=0$ bound states. Combining this with a previously obtained triplet value we find the first example of an alkali atom hyperfine state (the $^{7}\mathrm{Li}$ $F=1$, ${M}_{F}=\ensuremath{-}1$ state) for which the scattering length is positive. This implies a stable Bose condensate in future attempts to realize Bose-Einstein condensation in a magnetically trapped ultracold gas sample. We also predict magnetic-field-dependent resonances in the collision between atoms in the hyperfine state studied.

Physical Review Letters•Jul 25, 1994•64 citations

Spectroscopic determination of the s-wave scattering length of lithium

E. Abraham, W. L. McAlexander, Charles A. Sackett +1 more

Two-photon photoassociation of colliding ultracold ${}^{7}$Li atoms is used to probe the $^{3}\ensuremath{\Sigma}_{u}^{+}(a)$ ground state of ${}^{7}$L${\mathrm{i}}_{2}$. The binding energy of the least-bound state of this triplet potential, $\ensuremath{\upsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10$, is found to be $12.47\ifmmode\pm\else\textpm\fi{}0.04$ GHz. This spectroscopic information establishes that the $s$-wave scattering length for ${}^{7}$Li atoms in the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$, ${m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ state is $(\ensuremath{-}27.3\ifmmode\pm\else\textpm\fi{}0.8){a}_{0}$. The negative sign of the scattering length has important implications as to whether atoms at this doubly spin-polarized state can undergo a Bose-Einstein condensation.

Quantum Electronics and Laser Science Conference•May 22, 1995•5 citations

Ground state of a weakly interacting Bose gas of atoms in a tight trap

Maciej Lewenstein, Li You

We study properties of the ground state of a bosonic gas of atoms in a tight trap. The atoms interact via model molecular potentials that may have either positive or negative scattering lengths. We discuss the possibility of Bose-Einstein condensation in such a system. We show that when the size of the trap becomes comparable to the correlation length of the condensate, stable Bose-Einstein condensation might occur independent of the sign of the scattering length. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Feb 1, 1996•23 citations

Spectroscopic Determination of the s -Wave Scattering Length of Lithium

E. R. I. Abraham, W. I. McAlexander, Charles A. Sackett +1 more

Two-photon photoassociation of colliding ultracold ${}^{7}$Li atoms is used to probe the $^{3}\ensuremath{\Sigma}_{u}^{+}(a)$ ground state of ${}^{7}$L${\mathrm{i}}_{2}$. The binding energy of the least-bound state of this triplet potential, $\ensuremath{\upsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10$, is found to be $12.47\ifmmode\pm\else\textpm\fi{}0.04$ GHz. This spectroscopic information establishes that the $s$-wave scattering length for ${}^{7}$Li atoms in the $F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$, ${m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ state is $(\ensuremath{-}27.3\ifmmode\pm\else\textpm\fi{}0.8){a}_{0}$. The negative sign of the scattering length has important implications as to whether atoms at this doubly spin-polarized state can undergo a Bose-Einstein condensation.

Physical Review Letters•Feb 20, 1995•218 citations

BEC in Ultra-cold Cesium: Collisional Constraints

Eite Tiesinga, A. J. Moerdijk, BOUDEWIJN J. VERHAAR +1 more

We study necessary conditions for the observation of Bose–Einstein condensation in a magnetically trapped sample of atomic cesium gas. These constraints are due to interatomic collisions in the sample. We show that the prospects for observing Bose–Einstein condensation are favorable for a gas of ground-state Cs atoms in the highest state of the lowest hyperfine manifold. An interesting aspect of the calculations is that the scattering length for this f = 3, m f = −3 hyperfine state shows pronounced resonance structures as a function of applied magnetic field leading to variations of two orders of magnitude. Most importantly, the scattering length can change sign near the resonances. This suggests a controllable means to change the behavior of the Bose condensate because for negative values a condensate is unstable and other (quantum-)collective effects might be observed. The origin of the resonances is understood from the bound singlet and triplet rovibrational Cs 2 states which are perturbed due to the hyperfine and Zeeman interactions. It is a long standing goal to achieve quantum-collective effects in atomic Fermi- or Bose gases. The prominent reasons are that for a relatively simple system with low density, a microscopic theoretical treatment of the phase transition is still feasible, and to have an experimental testing ground for more complicated quantum-coherent effects such as superfluidity in 4 He and superconductivity in metals. Here, we focus on atomic species which behave as (composite) bosons.

Cambridge University Press eBooks•Apr 6, 1995•1 citation

Bose-Einstein Condensation in Trapped Atomic Gases

Yu. Kagan, Georgy V. Shlyapnikov, Jook T. M. Walraven

We discuss Bose-Einstein condensation in a trapped atomic gas and analyze how the sign of the scattering length a and the ratio \ensuremath{\eta} of the interaction between particles to the level spacing in the trap influence the behavior of the condensate wave function ${\ensuremath{\psi}}_{0}$. We find that for $a<0$ and $\ensuremath{\eta}\ensuremath{\ll}1$ it is possible to form a metastable Bose condensate, with a long characteristic lifetime with respect to contraction and transitions of particles to excited trap states. For $\ensuremath{\eta}\ensuremath{\gg}1$ a negative scattering length prevents the formation of the condensate. If $a>0$, then an increase of density is accompanied by the evolution of ${\ensuremath{\psi}}_{0}$ to a comparatively wide quasihomogeneous distribution.

Physical Review Letters•Apr 8, 1996•171 citations
We have improved the theoretical triplet ground-state potential of 7Li2^{7}\mathrm{Li}_{2}7Li2​ by means of an inverse perturbation analysis, and find that the diatomic scattering length for 7Li^{7}\mathrm{Li}7Li atoms in the F=2, mF{\mathit{m}}_{\mathit{F}}mF​=2 ground-state hyperfine level is negative. The consequences of this result for achieving Bose-Einstein condensation in a trapped ultracold 7Li^{7}\mathrm{Li}7Li gas sample are addressed.
We have determined the scattering length of the ground state 7Li^{7}\mathrm{Li}7Li + 7Li^{7}\mathrm{Li}7Li singlet potential from spectroscopic data on the highest S=0S=0S=0 bound states. Combining this with a previously obtained triplet value we find the first example of an alkali atom hyperfine state (the 7Li^{7}\mathrm{Li}7Li F=1F=1F=1, ${M}_{F}=\ensuremath{-}1$ state) for which the scattering length is positive. This implies a stable Bose condensate in future attempts to realize Bose-Einstein condensation in a magnetically trapped ultracold gas sample. We also predict magnetic-field-dependent resonances in the collision between atoms in the hyperfine state studied.
Two-photon photoassociation of colliding ultracold 7{}^{7}7Li atoms is used to probe the $^{3}\ensuremath{\Sigma}_{u}^{+}(a)$ ground state of 7{}^{7}7Li2{\mathrm{i}}_{2}i2​. The binding energy of the least-bound state of this triplet potential, $\ensuremath{\upsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10$, is found to be $12.47\ifmmode\pm\else\textpm\fi{}0.04$ GHz. This spectroscopic information establishes that the sss-wave scattering length for 7{}^{7}7Li atoms in the F=2F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2F=2, mF=2{m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2mF​=2 state is $(\ensuremath{-}27.3\ifmmode\pm\else\textpm\fi{}0.8){a}_{0}$. The negative sign of the scattering length has important implications as to whether atoms at this doubly spin-polarized state can undergo a Bose-Einstein condensation.
We study properties of the ground state of a bosonic gas of atoms in a tight trap. The atoms interact via model molecular potentials that may have either positive or negative scattering lengths. We discuss the possibility of Bose-Einstein condensation in such a system. We show that when the size of the trap becomes comparable to the correlation length of the condensate, stable Bose-Einstein condensation might occur independent of the sign of the scattering length. \textcopyright{} 1996 The American Physical Society.
Two-photon photoassociation of colliding ultracold 7{}^{7}7Li atoms is used to probe the $^{3}\ensuremath{\Sigma}_{u}^{+}(a)$ ground state of 7{}^{7}7Li2{\mathrm{i}}_{2}i2​. The binding energy of the least-bound state of this triplet potential, $\ensuremath{\upsilon}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}10$, is found to be $12.47\ifmmode\pm\else\textpm\fi{}0.04$ GHz. This spectroscopic information establishes that the sss-wave scattering length for 7{}^{7}7Li atoms in the F=2F\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2F=2, mF=2{m}_{F}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2mF​=2 state is $(\ensuremath{-}27.3\ifmmode\pm\else\textpm\fi{}0.8){a}_{0}$. The negative sign of the scattering length has important implications as to whether atoms at this doubly spin-polarized state can undergo a Bose-Einstein condensation.
We study necessary conditions for the observation of Bose–Einstein condensation in a magnetically trapped sample of atomic cesium gas. These constraints are due to interatomic collisions in the sample. We show that the prospects for observing Bose–Einstein condensation are favorable for a gas of ground-state Cs atoms in the highest state of the lowest hyperfine manifold. An interesting aspect of the calculations is that the scattering length for this f = 3, m f = −3 hyperfine state shows pronounced resonance structures as a function of applied magnetic field leading to variations of two orders of magnitude. Most importantly, the scattering length can change sign near the resonances. This suggests a controllable means to change the behavior of the Bose condensate because for negative values a condensate is unstable and other (quantum-)collective effects might be observed. The origin of the resonances is understood from the bound singlet and triplet rovibrational Cs 2 states which are perturbed due to the hyperfine and Zeeman interactions. It is a long standing goal to achieve quantum-collective effects in atomic Fermi- or Bose gases. The prominent reasons are that for a relatively simple system with low density, a microscopic theoretical treatment of the phase transition is still feasible, and to have an experimental testing ground for more complicated quantum-coherent effects such as superfluidity in 4 He and superconductivity in metals. Here, we focus on atomic species which behave as (composite) bosons.
We discuss Bose-Einstein condensation in a trapped atomic gas and analyze how the sign of the scattering length a and the ratio \ensuremath{\eta} of the interaction between particles to the level spacing in the trap influence the behavior of the condensate wave function ${\ensuremath{\psi}}_{0}$. We find that for a<0a<0a<0 and $\ensuremath{\eta}\ensuremath{\ll}1$ it is possible to form a metastable Bose condensate, with a long characteristic lifetime with respect to contraction and transitions of particles to excited trap states. For $\ensuremath{\eta}\ensuremath{\gg}1$ a negative scattering length prevents the formation of the condensate. If a>0a>0a>0, then an increase of density is accompanied by the evolution of ${\ensuremath{\psi}}_{0}$ to a comparatively wide quasihomogeneous distribution.