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 A

Properties of cold collisions of K39 atoms and of K41 atoms in relation to Bose-Einstein condensation

H. M. J. M. Boesten, J. M. M. J. Vogels, J. G. C. Tempelaars, BOUDEWIJN J. VERHAAR

Published Nov 1, 1996• 32 citations
Publisher

Abstract

We have determined properties of cold $^{39}\mathrm{K}$+$^{39}\mathrm{K}$ and $^{41}\mathrm{K}$+$^{41}\mathrm{K}$ collisions by a multichannel inverted perturbation approach applied to spectroscopic data of highly excited $^{39}\mathrm{K}$ singlet and triplet bound states. We predict positive scattering lengths for the $^{39}\mathrm{K}$+$^{39}\mathrm{K}$ and $^{41}\mathrm{K}$+$^{41}\mathrm{K}$ singlet potentials, as well as for the $^{41}\mathrm{K}$+$^{41}\mathrm{K}$ triplet potential, and a negative value for $^{39}\mathrm{K}$+$^{39}\mathrm{K}$ triplet scattering. From a study of the magnetic field dependence we conclude that $^{41}\mathrm{K}$ may be a bosonic atom with a Feshbach resonance in the magnetic field range where these atoms can be trapped in the $f=1$, ${m}_{f}=\ensuremath{-}1$ hyperfine state, thus providing a possibility to switch between stable and instable condensates in a Bose-Einstein condensation experiment.

DOI
10.1103/physreva.54.r3726

Related papers

Collisional properties of ultracold potassium: Consequences for degenerate Bose and Fermi gases

John L. Bohn, James P. Burke, Chris H. Greene +3 more

The hyperfine-state-selected scattering properties of potassium atoms at ultralow temperatures are calculated using interaction potentials gleaned from an analysis of recent photoassociation data. We predict that the small, probably negative value of the ${}^{39}\mathrm{K}$ triplet scattering length will hamper efforts to produce a Bose-Einstein condensate, unless experiments utilize a broad, accessible magnetic Feshbach resonance. The large positive value calculated for the ${}^{41}\mathrm{K}$ triplet scattering length makes it a better candidate for condensation at zero magnetic field. The fermionic isotope ${}^{40}\mathrm{K}$ is also predicted to have a large, positive scattering length for elastic collisions between spin states of experimental interest, implying that it can be efficiently evaporatively cooled to the quantum degenerate regime. In addition, certain spin states possess Feshbach resonances that may enable tuning of its interatomic interactions, possibly leading to the formation of Cooper pairs.

Physical Review A•May 1, 1999•53 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

Feshbach resonances and transition rates for cold homonuclear collisions between K39 and K41 atoms

Marius Lysebo, Leif Veseth

We report results from close-coupling calculations for homonuclear ultracold collisions between potassium atoms, using the most up-to-date Born-Oppenheimer potential curves. The present study includes both of the bosonic isotopes $^{39}\mathrm{K}$ and $^{41}\mathrm{K}$. The $s$-wave scattering lengths as functions of the magnetic field strength for collisions between atoms in identical and different hyperfine states are obtained. Several Feshbach resonances are located and characterized for both isotopes. Comparison with experiments, where such data are available, show excellent agreement. We also study weakly bound molecular states of the ${\mathrm{K}}_{2}$ molecule in close relation to the calculated Feshbach resonances. Another objective of the present work is to study inelastic collisions in which the hyperfine states of the colliding atoms are changed. From this type of calculation we obtain transition rates as functions of the magnetic field strength. Finally, we discuss how such transition rates might be of importance for experimental work.

Physical Review A•Mar 10, 2010•56 citations

Determination of collisional properties of cold Na atoms from analysis of bound-state photoassociation and Feshbach resonance field data

Frank A. van Abeelen, BOUDEWIJN J. VERHAAR

We review the information on the interactions between cold ground-state Na atoms following from ${\mathrm{Na}}_{2}$ bound states, a Na photoassociation experiment, and a recent observation of field-induced Feshbach resonances in a Na Bose condensate. We obtain a set of Na interaction parameters that is in excellent agreement with all these experimental data. The existing discrepancy between different values for the scattering length ${a}_{1,\ensuremath{-}1}$ of Na atoms in the $|1,\ensuremath{-}1〉$ hyperfine state is resolved. The present interaction parameters enable us to give accurate predictions for the singlet and triplet scattering lengths ${a}_{S}$ and ${a}_{T},$ ${a}_{1,\ensuremath{-}1},$ scattering lengths for collisions between Na atoms in other hyperfine states, and resonance fields of several yet unobserved Feshbach resonances. We find ${a}_{S}=(19.1\ifmmode\pm\else\textpm\fi{}{2.1)a}_{0},{a}_{T}=(65.3\ifmmode\pm\else\textpm\fi{}{0.9)a}_{0},$ and ${a}_{1,\ensuremath{-}1}(B=0)=(55.4\ifmmode\pm\else\textpm\fi{}{1.2)a}_{0}.$

Physical Review A•Jan 1, 1999•54 citations

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

Multichannel scattering and Feshbach resonances: Effective theory, phenomenology, and many-body effects

Georg M. Bruun, Andrew David Jackson, Evgeni E. Kolomeitsev

A low-energy effective theory based on a microscopic multichannel description of the atom-atom interaction is derived for the scattering of alkali-metal atoms in different hyperfine states. This theory describes all scattering properties, including medium effects, in terms of the singlet and triplet scattering lengths and the range of the atom-atom potential and provides a link between a microscopic description of Feshbach scattering and more phenomenological approaches. It permits the calculation of medium effects on the resonance coming from the occupation of closed channel states. The examination of such effects is demonstrated to be of particular relevance to an experimentally important Feshbach resonance for $^{40}\mathrm{K}$ atoms. We analyze a recent rethermalization rate experiment on $^{40}\mathrm{K}$ and demonstrate that a measurement of the temperature dependence of this rate can determine the magnetic moment of the Feshbach molecule. Finally, the energy dependence of the Feshbach interaction is shown to introduce a negative effective range inversely proportional to the width of the resonance. Since our theory is based on a microscopic multichannel picture, it allows the explicit calculation of corrections to commonly used approximations such as the neglect of the effective range and the treatment of the Feshbach molecule as a point boson.

arXiv:cond-mat/0501407•Physical Review A•May 26, 2005•44 citations
We have determined properties of cold 39K^{39}\mathrm{K}39K+39K^{39}\mathrm{K}39K and 41K^{41}\mathrm{K}41K+41K^{41}\mathrm{K}41K collisions by a multichannel inverted perturbation approach applied to spectroscopic data of highly excited 39K^{39}\mathrm{K}39K singlet and triplet bound states. We predict positive scattering lengths for the 39K^{39}\mathrm{K}39K+39K^{39}\mathrm{K}39K and 41K^{41}\mathrm{K}41K+41K^{41}\mathrm{K}41K singlet potentials, as well as for the 41K^{41}\mathrm{K}41K+41K^{41}\mathrm{K}41K triplet potential, and a negative value for 39K^{39}\mathrm{K}39K+39K^{39}\mathrm{K}39K triplet scattering. From a study of the magnetic field dependence we conclude that 41K^{41}\mathrm{K}41K may be a bosonic atom with a Feshbach resonance in the magnetic field range where these atoms can be trapped in the f=1f=1f=1, mf=\ensuremath−1{m}_{f}=\ensuremath{-}1mf​=\ensuremath−1 hyperfine state, thus providing a possibility to switch between stable and instable condensates in a Bose-Einstein condensation experiment.
The hyperfine-state-selected scattering properties of potassium atoms at ultralow temperatures are calculated using interaction potentials gleaned from an analysis of recent photoassociation data. We predict that the small, probably negative value of the 39K{}^{39}\mathrm{K}39K triplet scattering length will hamper efforts to produce a Bose-Einstein condensate, unless experiments utilize a broad, accessible magnetic Feshbach resonance. The large positive value calculated for the 41K{}^{41}\mathrm{K}41K triplet scattering length makes it a better candidate for condensation at zero magnetic field. The fermionic isotope 40K{}^{40}\mathrm{K}40K is also predicted to have a large, positive scattering length for elastic collisions between spin states of experimental interest, implying that it can be efficiently evaporatively cooled to the quantum degenerate regime. In addition, certain spin states possess Feshbach resonances that may enable tuning of its interatomic interactions, possibly leading to the formation of Cooper pairs.
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 report results from close-coupling calculations for homonuclear ultracold collisions between potassium atoms, using the most up-to-date Born-Oppenheimer potential curves. The present study includes both of the bosonic isotopes 39K^{39}\mathrm{K}39K and 41K^{41}\mathrm{K}41K. The sss-wave scattering lengths as functions of the magnetic field strength for collisions between atoms in identical and different hyperfine states are obtained. Several Feshbach resonances are located and characterized for both isotopes. Comparison with experiments, where such data are available, show excellent agreement. We also study weakly bound molecular states of the K2{\mathrm{K}}_{2}K2​ molecule in close relation to the calculated Feshbach resonances. Another objective of the present work is to study inelastic collisions in which the hyperfine states of the colliding atoms are changed. From this type of calculation we obtain transition rates as functions of the magnetic field strength. Finally, we discuss how such transition rates might be of importance for experimental work.
We review the information on the interactions between cold ground-state Na atoms following from Na2{\mathrm{Na}}_{2}Na2​ bound states, a Na photoassociation experiment, and a recent observation of field-induced Feshbach resonances in a Na Bose condensate. We obtain a set of Na interaction parameters that is in excellent agreement with all these experimental data. The existing discrepancy between different values for the scattering length ${a}_{1,\ensuremath{-}1}$ of Na atoms in the $|1,\ensuremath{-}1〉$ hyperfine state is resolved. The present interaction parameters enable us to give accurate predictions for the singlet and triplet scattering lengths aS{a}_{S}aS​ and aT,{a}_{T},aT​, ${a}_{1,\ensuremath{-}1},$ scattering lengths for collisions between Na atoms in other hyperfine states, and resonance fields of several yet unobserved Feshbach resonances. We find ${a}_{S}=(19.1\ifmmode\pm\else\textpm\fi{}{2.1)a}_{0},{a}_{T}=(65.3\ifmmode\pm\else\textpm\fi{}{0.9)a}_{0},$ and ${a}_{1,\ensuremath{-}1}(B=0)=(55.4\ifmmode\pm\else\textpm\fi{}{1.2)a}_{0}.$
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.
A low-energy effective theory based on a microscopic multichannel description of the atom-atom interaction is derived for the scattering of alkali-metal atoms in different hyperfine states. This theory describes all scattering properties, including medium effects, in terms of the singlet and triplet scattering lengths and the range of the atom-atom potential and provides a link between a microscopic description of Feshbach scattering and more phenomenological approaches. It permits the calculation of medium effects on the resonance coming from the occupation of closed channel states. The examination of such effects is demonstrated to be of particular relevance to an experimentally important Feshbach resonance for 40K^{40}\mathrm{K}40K atoms. We analyze a recent rethermalization rate experiment on 40K^{40}\mathrm{K}40K and demonstrate that a measurement of the temperature dependence of this rate can determine the magnetic moment of the Feshbach molecule. Finally, the energy dependence of the Feshbach interaction is shown to introduce a negative effective range inversely proportional to the width of the resonance. Since our theory is based on a microscopic multichannel picture, it allows the explicit calculation of corrections to commonly used approximations such as the neglect of the effective range and the treatment of the Feshbach molecule as a point boson.