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

Ultracold atoms in traps and fountains

Eite Tiesinga

Published Jan 1, 1993• 0 citations
Publisher

Abstract

We study the magnetic field dependence of the cross sections for elastic and inelastic collisions of pairs ofultracold cesium atoms in a magnetic trap, calculated with the coupled-channels method.We pay special attention to atoms in the f = 3, m 1 = -3 weak-field seeking state of the lower hyperfine manifold.The cross sections show a pronounced resonance structure.We discuss its origin, starting from the pure hound singlet and triplet rovibrational Csz states and introducing perturbations due to the hyperfine and Zeeman interactions.We also discuss the role of the centrifugal barrier in the final collision channel in reducing the loss of atoms from the trap due • to transitions induced by the magnetic dipole-dipole interaction.

DOI
10.6100/ir389366

Related papers

Threshold and resonance phenomena in ultracold ground-state collisions

Eite Tiesinga, BOUDEWIJN J. VERHAAR, Henk T. C. Stoof

We study the magnetic-field dependence of the cross sections for elastic and inelastic collisions of pairs of ultracold cesium atoms in a magnetic trap, calculated with the coupled-channels method. We pay special attention to atoms in the f=3, ${\mathit{m}}_{\mathit{f}}$=-3 weak-field seeking state of the lower hyperfine manifold. The cross sections show a pronounced resonance structure. We discuss its origin, starting from the pure bound singlet and triplet rovibrational ${\mathrm{Cs}}_{2}$ states and introducing perturbations due to the hyperfine and Zeeman interactions. We also discuss the role of the centrifugal barrier in the final collision channel in reducing the loss of atoms from the trap due to transitions induced by the magnetic dipole-dipole interaction.

Physical Review A•May 1, 1993•648 citations

Effect of hyperfine interactions on ultracold molecular collisions: NH( 3Σ− ) with Mg( 1 S) in magnetic fields

Maykel Leonardo González-Martínez, Jeremy M. Hutson

We investigate the effect of hyperfine interactions on ultracold molecular collisions in magnetic fields, using ${}^{24}$Mg(${}^{1}S){+}^{14}$NH(${}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}}$) as a prototype system. We explore the energy and magnetic-field dependence of the cross sections, comparing the results with previous calculations that neglected hyperfine interactions [A.O.G. Wallis and J. M. Hutson, Phys. Rev. Lett. 103, 183201 (2009)]. The main effect of hyperfine interactions for spin relaxation cross sections is that the kinetic energy release of the dominant outgoing channels does not reduce to zero at low fields. This results in reduced centrifugal suppression of the cross sections and increased inelastic cross sections at low energy and low field. We also analyze state-to-state cross sections, for various initial states, and show that hyperfine interactions introduce additional mechanisms for spin relaxation. In particular, there are hyperfine-mediated collisions to outgoing channels that are not centrifugally suppressed. However, for $\mathrm{Mg}+\mathit{NH}$ these unsuppressed channels make only small contributions to the total cross sections. We consider the implications of our results for sympathetic cooling of NH by Mg and conclude that the ratio of elastic to inelastic cross sections remains high enough for sympathetic cooling to proceed.

arXiv:1108.4641•Physical Review A•Nov 7, 2011•26 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

Conditions for Bose-Einstein condensation in magnetically trapped atomic cesium

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

We study conditions necessary for the observation of Bose-Einstein condensation in a magnetically trapped sample of atomic Cs gas. These conditions are associated with the value of the elastic scattering length, the rate of elastic scattering events, and the lifetime for decay of the density due to both magnetic dipole relaxation in two-body collisions, as well as recombination to ${\mathrm{Cs}}_{2}$ in three-body collisions. We find that, on the basis of these conditions, 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. In all calculated elastic and inelastic two-body rates we find a pronounced resonance structure, which can be understood in terms of the interplay between the singlet-triplet interaction and the hyperfine, Zeeman, and magnetic dipole interactions. The experimental observation of these resonances may help to eliminate present uncertainties about interaction potentials.

Physical Review A•Aug 1, 1992•235 citations

Elastic and inelastic collisions of 6Li atoms in magnetic and optical traps

M. Houbiers, Henk T. C. Stoof, W. I. McAlexander +1 more

We use a full coupled-channels method to calculate collisional properties of magnetically or optically trapped ultracold ${}^{6}\mathrm{Li}.$ The magnetic-field dependence of the $s$-wave scattering lengths of several mixtures of hyperfine states are determined, as are the decay rates due to exchange collisions. In one case, we find Feshbach resonances at $B=0.08\mathrm{T}$ and $B=1.98\mathrm{T}.$ We show that the exact coupled-channels calculation is well approximated over the entire range of magnetic fields by a simple analytical calculation.

arXiv:cond-mat/9710333•Physical Review A•Mar 1, 1998•152 citations

Theory of ultracold atomic collisions in radio-frequency fields

Daniel J. Owens

This thesis has investigated the dynamics of ultracold atomic collisions in the presence of both static magnetic and oscillating radio-frequency (rf) fields. The bound state structure and scattering length of 39K+133Cs was examined in the presence of only a static magnetic field, where it was found that no Feshbach resonance of suitable width for magnetoassociation existed at a magnetic field where caesium can be cooled to degeneracy. We then showed that zero-energy Feshbach resonances may be engineered using an rf field in places where they did not previously exist. An rf field with frequency 79.9 MHz was chosen to induce a resonance near 21 G. The widths of such rf-induced Feshbach resonances increase quadratically with rf field strength. The resonances presented are lossless with circularly polarized rf, and the molecules created are long-lived even with plane-polarized RF. Collisional losses in rf-dressed magnetic traps were also investigated. An rf-induced loss mechanism that does not exist in the absence of rf radiation was identified. This mechanism is not suppressed by a centrifugal barrier in the outgoing channel, and can be much faster than spin relaxation, which is centrifugally suppressed. We explore the dependence of the rf-induced loss rate on singlet and triplet scattering lengths, hyperfine splittings and the strength of the rf field. The results were interpreted in terms of an adiabatic model of the collision dynamics, and calculate the corresponding nonadiabatic couplings. The loss rate can vary by 10 orders of magnitude as a function of singlet and triplet scattering lengths. 87Rb is a special case, where several factors combine to reduce rf-induced losses; as a result, they are slow compared to spin-relaxation losses. For most other alkali-metal pairs, rf-induced losses are expected to be much faster and may dominate. For heteronuclear mixtures an rf-modified spin-exchange mechanism was identified that results in loss rates orders of magnitude greater than the rf-induced loss rates in homonuclear cases. Fast loss is expected in mixtures where the Lande g-factors differ.

•Jan 1, 2019•0 citations
We study the magnetic field dependence of the cross sections for elastic and inelastic collisions of pairs ofultracold cesium atoms in a magnetic trap, calculated with the coupled-channels method.We pay special attention to atoms in the f = 3, m 1 = -3 weak-field seeking state of the lower hyperfine manifold.The cross sections show a pronounced resonance structure.We discuss its origin, starting from the pure hound singlet and triplet rovibrational Csz states and introducing perturbations due to the hyperfine and Zeeman interactions.We also discuss the role of the centrifugal barrier in the final collision channel in reducing the loss of atoms from the trap due • to transitions induced by the magnetic dipole-dipole interaction.
We study the magnetic-field dependence of the cross sections for elastic and inelastic collisions of pairs of ultracold cesium atoms in a magnetic trap, calculated with the coupled-channels method. We pay special attention to atoms in the f=3, mf{\mathit{m}}_{\mathit{f}}mf​=-3 weak-field seeking state of the lower hyperfine manifold. The cross sections show a pronounced resonance structure. We discuss its origin, starting from the pure bound singlet and triplet rovibrational Cs2{\mathrm{Cs}}_{2}Cs2​ states and introducing perturbations due to the hyperfine and Zeeman interactions. We also discuss the role of the centrifugal barrier in the final collision channel in reducing the loss of atoms from the trap due to transitions induced by the magnetic dipole-dipole interaction.
We investigate the effect of hyperfine interactions on ultracold molecular collisions in magnetic fields, using 24{}^{24}24Mg(1S)+14{}^{1}S){+}^{14}1S)+14NH(${}^{3}{\ensuremath{\Sigma}}^{\ensuremath{-}}$) as a prototype system. We explore the energy and magnetic-field dependence of the cross sections, comparing the results with previous calculations that neglected hyperfine interactions [A.O.G. Wallis and J. M. Hutson, Phys. Rev. Lett. 103, 183201 (2009)]. The main effect of hyperfine interactions for spin relaxation cross sections is that the kinetic energy release of the dominant outgoing channels does not reduce to zero at low fields. This results in reduced centrifugal suppression of the cross sections and increased inelastic cross sections at low energy and low field. We also analyze state-to-state cross sections, for various initial states, and show that hyperfine interactions introduce additional mechanisms for spin relaxation. In particular, there are hyperfine-mediated collisions to outgoing channels that are not centrifugally suppressed. However, for Mg+NH\mathrm{Mg}+\mathit{NH}Mg+NH these unsuppressed channels make only small contributions to the total cross sections. We consider the implications of our results for sympathetic cooling of NH by Mg and conclude that the ratio of elastic to inelastic cross sections remains high enough for sympathetic cooling to proceed.
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 study conditions necessary for the observation of Bose-Einstein condensation in a magnetically trapped sample of atomic Cs gas. These conditions are associated with the value of the elastic scattering length, the rate of elastic scattering events, and the lifetime for decay of the density due to both magnetic dipole relaxation in two-body collisions, as well as recombination to Cs2{\mathrm{Cs}}_{2}Cs2​ in three-body collisions. We find that, on the basis of these conditions, 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. In all calculated elastic and inelastic two-body rates we find a pronounced resonance structure, which can be understood in terms of the interplay between the singlet-triplet interaction and the hyperfine, Zeeman, and magnetic dipole interactions. The experimental observation of these resonances may help to eliminate present uncertainties about interaction potentials.
We use a full coupled-channels method to calculate collisional properties of magnetically or optically trapped ultracold 6Li.{}^{6}\mathrm{Li}.6Li. The magnetic-field dependence of the sss-wave scattering lengths of several mixtures of hyperfine states are determined, as are the decay rates due to exchange collisions. In one case, we find Feshbach resonances at B=0.08TB=0.08\mathrm{T}B=0.08T and B=1.98T.B=1.98\mathrm{T}.B=1.98T. We show that the exact coupled-channels calculation is well approximated over the entire range of magnetic fields by a simple analytical calculation.
This thesis has investigated the dynamics of ultracold atomic collisions in the presence of both static magnetic and oscillating radio-frequency (rf) fields. The bound state structure and scattering length of 39K+133Cs was examined in the presence of only a static magnetic field, where it was found that no Feshbach resonance of suitable width for magnetoassociation existed at a magnetic field where caesium can be cooled to degeneracy. We then showed that zero-energy Feshbach resonances may be engineered using an rf field in places where they did not previously exist. An rf field with frequency 79.9 MHz was chosen to induce a resonance near 21 G. The widths of such rf-induced Feshbach resonances increase quadratically with rf field strength. The resonances presented are lossless with circularly polarized rf, and the molecules created are long-lived even with plane-polarized RF. Collisional losses in rf-dressed magnetic traps were also investigated. An rf-induced loss mechanism that does not exist in the absence of rf radiation was identified. This mechanism is not suppressed by a centrifugal barrier in the outgoing channel, and can be much faster than spin relaxation, which is centrifugally suppressed. We explore the dependence of the rf-induced loss rate on singlet and triplet scattering lengths, hyperfine splittings and the strength of the rf field. The results were interpreted in terms of an adiabatic model of the collision dynamics, and calculate the corresponding nonadiabatic couplings. The loss rate can vary by 10 orders of magnitude as a function of singlet and triplet scattering lengths. 87Rb is a special case, where several factors combine to reduce rf-induced losses; as a result, they are slow compared to spin-relaxation losses. For most other alkali-metal pairs, rf-induced losses are expected to be much faster and may dominate. For heteronuclear mixtures an rf-modified spin-exchange mechanism was identified that results in loss rates orders of magnitude greater than the rf-induced loss rates in homonuclear cases. Fast loss is expected in mixtures where the Lande g-factors differ.