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

arXiv:cond-mat/0402334 · Physical Review A

Formation of molecules in an expanding Bose-Einstein condensate

Vladimir Yurovsky, A. Ben‐Reuven

Published Jul 27, 2004• 7 citations
arXivHTMLPDF

Abstract

A theoretical analysis of expanding hybrid atom-molecule Bose-Einstein condensates is presented with application to the recent experiments of the Rempe group on $^{87}\mathrm{Rb}$, in which the formation of ultracold molecules by Feshbach resonance was demonstrated. A mean-field approach is used to describe the molecular association process. The subsequent dissociation of the molecules is treated using a non-mean-field parametric approximation. The latter method is also used to derive optimal conditions for the formation of a molecular condensate.

DOI
10.1103/physreva.70.013613

Related papers

Formation of molecules and entangled atomic pairs from atomic BEC due to Feshbach resonance

Vladimir Yurovsky

Bose-Einstein condensate (BEC) is considered under conditions of Feshbach resonance in two-atom collisions due to a coupling of atomic pair and resonant molecular states. The association of condensate atoms can form a molecular BEC, and the molecules can dissociate to pairs of entangled atoms in two-mode squeezed states. Both entanglement and squeezing can be applied to quantum measurements and information processing. The processes in the atom-molecule quantum gas are analyzed using two theoretical approaches. The mean-field one takes into account deactivating collisions of resonant molecules with other atoms and molecules, neglecting quantum fluctuations. This method allows analysis of inhomogeneous systems, such as expanding BEC. The non-mean-field approach -- the parametric approximation -- takes into account both deactivation and quantum fluctuations. This method allows determination of optimal conditions for formation of molecular BEC and describes Bose-enhanced dissociation of molecular BEC, as well as entanglement and squeezing of the non-condensate atoms.

arXiv:cond-mat/0611054•Nov 2, 2006•2 citations

Formation of a molecular Bose-Einstein condensate and an entangled atomic gas by Feshbach resonance

Vladimir Yurovsky, A. Ben‐Reuven

Association in an atomic Bose-Einstein condensate, and dissociation of the resulting molecular condensate, due to a Feshbach resonance in a time-dependent magnetic field, are analyzed incorporating non-mean-field quantum corrections and inelastic collisions. Calculations for the Na atomic condensate demonstrate that there exist optimal conditions under which about 80% of the atomic population can be converted to a relatively long-lived molecular condensate (with lifetimes of 100 ms and more). Entangled atoms in two-mode squeezed states (with noise reduction of about 30 dB) may also be formed by molecular dissociation.

arXiv:cond-mat/0205267•Physical Review A•Apr 23, 2003•50 citations

Formation of molecules from a Cs Bose-Einstein condensate

Vladimir Yurovsky, A. Ben‐Reuven

Conversion of an expanding Bose-Einstein condensate of Cs atoms to a molecular one with an efficiency of more than 30% was observed recently in experiments by M. Mark et al. [Europhys. Lett. 69, 706 (2005)]. The theory presented here describes the experimental results. Values of resonance strength of 8 mG and rate coefficients for atom-molecule deactivation of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$ and molecule-molecule one of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$ are estimated by a fit of the theoretical results to the experimental data. Near the resonance, where the highest conversion efficiency was observed, the results demonstrate strong sensitivity to the magnetic field ripple and inhomogeneity. A conversion efficiency of about 60% is predicted by non-mean-field calculations for densities and sweep rates lower than the ones used in the experiments.

arXiv:cond-mat/0505180•Physical Review A•Nov 17, 2005•12 citations

Coherent Reaction between Molecular and Atomic Bose-Einstein Condensates: Integrable Model

Rajesh K. Malla, Vladimir Chernyak, Chen Sun +1 more

We solve a model that describes a stimulated conversion between ultracold bosonic atoms and molecules. The reaction is triggered by a linearly time-dependent transition throughout the Feshbach resonance. Our solution predicts a dependence, with a dynamic phase transition, of the reaction efficiency on the transition rate for both atoms-to-molecule pairing and molecular dissociation processes. We find that for the latter process with a linear energy dispersion of atomic modes, the emerging phase can have a thermalized energy distribution of noninteracting bosons with the temperature defined by the rate of the transition. This provides a simple interpretation of the phase transition in terms of the creation of equilibrium Bose-Einstein condensate.

arXiv:2112.12302•Physical Review Letters•Jul 11, 2022•14 citations

Association of ultracold double-species bosonic molecules

Claudia Weber, Giovanni Barontini, Jacopo Catani +3 more

We report on the creation of heterospecies bosonic molecules, associated from an ultracold Bose-Bose mixture of $^{41}\mathrm{K}$ and $^{87}\mathrm{Rb}$, by using a resonantly modulated magnetic field close to two Feshbach resonances. We measure the binding energy of the weakly bound molecular states versus the Feshbach field and compare our results to theoretical predictions. We observe the broadening and asymmetry of the association spectrum due to the thermal distribution of the atoms and a frequency shift occurring when the binding energy depends nonlinearly on the Feshbach field. A simple model is developed to quantitatively describe the association process. This work represents a required step toward Bose-Einstein condensates of dipolar molecules.

arXiv:0808.4077•Physical Review A•Dec 3, 2008•85 citations

Molecule formation in ultracold atomic gases

Hutson, J M, Soldan, P H

This review describes recent experimental and theoretical advances in forming molecules in ultracold gases of trapped alkali metal atoms, both by magnetic tuning through Feshbach resonances and by photoassociation. Molecular Bose-Einstein condensation of long-range states of both boson dimers and fermion dimers was achieved in 2002-3. Condensates of boson dimers were found to be short-lived, but long-lived condensates of fermion dimers have been produced. Signatures of triatomic and tetraatomic molecules have recently been observed. Both homonuclear and heteronuclear molecules have been formed by photoassociation, mostly in very high vibrational levels. Recent attempts to produce ultracold molecules in short-range states (low vibrational levels) are described. Experimental and theoretical work on collisions of ultracold molecules is discussed.

•Jul 26, 2006•82 citations
A theoretical analysis of expanding hybrid atom-molecule Bose-Einstein condensates is presented with application to the recent experiments of the Rempe group on 87Rb^{87}\mathrm{Rb}87Rb, in which the formation of ultracold molecules by Feshbach resonance was demonstrated. A mean-field approach is used to describe the molecular association process. The subsequent dissociation of the molecules is treated using a non-mean-field parametric approximation. The latter method is also used to derive optimal conditions for the formation of a molecular condensate.
Bose-Einstein condensate (BEC) is considered under conditions of Feshbach resonance in two-atom collisions due to a coupling of atomic pair and resonant molecular states. The association of condensate atoms can form a molecular BEC, and the molecules can dissociate to pairs of entangled atoms in two-mode squeezed states. Both entanglement and squeezing can be applied to quantum measurements and information processing. The processes in the atom-molecule quantum gas are analyzed using two theoretical approaches. The mean-field one takes into account deactivating collisions of resonant molecules with other atoms and molecules, neglecting quantum fluctuations. This method allows analysis of inhomogeneous systems, such as expanding BEC. The non-mean-field approach -- the parametric approximation -- takes into account both deactivation and quantum fluctuations. This method allows determination of optimal conditions for formation of molecular BEC and describes Bose-enhanced dissociation of molecular BEC, as well as entanglement and squeezing of the non-condensate atoms.
Association in an atomic Bose-Einstein condensate, and dissociation of the resulting molecular condensate, due to a Feshbach resonance in a time-dependent magnetic field, are analyzed incorporating non-mean-field quantum corrections and inelastic collisions. Calculations for the Na atomic condensate demonstrate that there exist optimal conditions under which about 80% of the atomic population can be converted to a relatively long-lived molecular condensate (with lifetimes of 100 ms and more). Entangled atoms in two-mode squeezed states (with noise reduction of about 30 dB) may also be formed by molecular dissociation.
Conversion of an expanding Bose-Einstein condensate of Cs atoms to a molecular one with an efficiency of more than 30% was observed recently in experiments by M. Mark et al. [Europhys. Lett. 69, 706 (2005)]. The theory presented here describes the experimental results. Values of resonance strength of 8 mG and rate coefficients for atom-molecule deactivation of $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$ and molecule-molecule one of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}∕\mathrm{s}$ are estimated by a fit of the theoretical results to the experimental data. Near the resonance, where the highest conversion efficiency was observed, the results demonstrate strong sensitivity to the magnetic field ripple and inhomogeneity. A conversion efficiency of about 60% is predicted by non-mean-field calculations for densities and sweep rates lower than the ones used in the experiments.
We solve a model that describes a stimulated conversion between ultracold bosonic atoms and molecules. The reaction is triggered by a linearly time-dependent transition throughout the Feshbach resonance. Our solution predicts a dependence, with a dynamic phase transition, of the reaction efficiency on the transition rate for both atoms-to-molecule pairing and molecular dissociation processes. We find that for the latter process with a linear energy dispersion of atomic modes, the emerging phase can have a thermalized energy distribution of noninteracting bosons with the temperature defined by the rate of the transition. This provides a simple interpretation of the phase transition in terms of the creation of equilibrium Bose-Einstein condensate.
We report on the creation of heterospecies bosonic molecules, associated from an ultracold Bose-Bose mixture of 41K^{41}\mathrm{K}41K and 87Rb^{87}\mathrm{Rb}87Rb, by using a resonantly modulated magnetic field close to two Feshbach resonances. We measure the binding energy of the weakly bound molecular states versus the Feshbach field and compare our results to theoretical predictions. We observe the broadening and asymmetry of the association spectrum due to the thermal distribution of the atoms and a frequency shift occurring when the binding energy depends nonlinearly on the Feshbach field. A simple model is developed to quantitatively describe the association process. This work represents a required step toward Bose-Einstein condensates of dipolar molecules.
This review describes recent experimental and theoretical advances in forming molecules in ultracold gases of trapped alkali metal atoms, both by magnetic tuning through Feshbach resonances and by photoassociation. Molecular Bose-Einstein condensation of long-range states of both boson dimers and fermion dimers was achieved in 2002-3. Condensates of boson dimers were found to be short-lived, but long-lived condensates of fermion dimers have been produced. Signatures of triatomic and tetraatomic molecules have recently been observed. Both homonuclear and heteronuclear molecules have been formed by photoassociation, mostly in very high vibrational levels. Recent attempts to produce ultracold molecules in short-range states (low vibrational levels) are described. Experimental and theoretical work on collisions of ultracold molecules is discussed.