Both dark and bright solitons are constructed exactly for a Bose–Einstein condensation with a time-dependent scattering length in an expulsive parabolic potential. It is shown analytically how the size of the cloud and the sharp peak of the condensate changes via the Feshbach resonance. It is also found that the atom loss due to three-body recombination can be controlled with the help of Feshbach resonance. The exact calculation is performed to compare the rate of the atom loss between the system with time-dependent scattering length in an expulsive parabolic potential and the system with constant scattering length.Both dark and bright solitons are constructed exactly for a Bose–Einstein condensation with a time-dependent scattering length in an expulsive parabolic potential. It is shown analytically how the size of the cloud and the sharp peak of the condensate changes via the Feshbach resonance. It is also found that the atom loss due to three-body recombination can be controlled with the help of Feshbach resonance. The exact calculation is performed to compare the rate of the atom loss between the system with time-dependent scattering length in an expulsive parabolic potential and the system with constant scattering length.

Physica ScriptaJan 12, 20073 citations

Dynamics of BECs with Two- and Three-Body Interactions

Wu-Ming Liu, Emmanuel Kengne

Springer eBooksJan 1, 20191 citation

Collisional relaxation of Feshbach molecules and three-body recombination in Rb87 Bose-Einstein condensates

G. Smirne, R. M. Godun, Donatella Cassettari +9 more

We predict the resonance-enhanced magnetic field dependence of atom-dimer relaxation and three-body recombination rates in a $^{87}\mathrm{Rb}$ Bose-Einstein condensate close to $1007\phantom{\rule{0.3em}{0ex}}\mathrm{G}$ . Our exact treatments of three-particle scattering explicitly include the dependence of the interactions on the atomic Zeeman levels. The Feshbach resonance distorts the entire diatomic energy spectrum, causing interferences in both loss phenomena. Our two independent experiments confirm the predicted recombination loss over a range of rate constants that spans four orders of magnitude.We predict the resonance-enhanced magnetic field dependence of atom-dimer relaxation and three-body recombination rates in a $^{87}\mathrm{Rb}$ Bose-Einstein condensate close to $1007\phantom{\rule{0.3em}{0ex}}\mathrm{G}$. Our exact treatments of three-particle scattering explicitly include the dependence of the interactions on the atomic Zeeman levels. The Feshbach resonance distorts the entire diatomic energy spectrum, causing interferences in both loss phenomena. Our two independent experiments confirm the predicted recombination loss over a range of rate constants that spans four orders of magnitude.

arXiv:cond-mat/0604183Physical Review AFeb 20, 200728 citations

Three particles in an external trap: Nature of the complete J=0 spectrum

D. Blume, Chris H. Greene

Three bosonic, spin-polarized atoms in a spherical oscillator potential constitutes the simplest nontrivial Bose-Einstein condensate (BEC). The present paper develops the tools needed to understand the nature of the complete $J=0$ energy spectrum for this prototype system, assuming a sum of two-body potentials. The resulting spectrum is calculated as a function of the two-body scattering length ${a}_{\mathrm{sc}},$ which documents the evolution of certain many-body levels that evolve from BEC-type to molecular-type as the scattering length is decreased. Implications for the behavior of the condensate excited-state spectrum and for condensate formation and decay are elucidated. The energy levels evolve smoothly, even through the regime where the number of two-body bound states ${N}_{b}$ increases by 1, and ${a}_{\mathrm{sc}}$ switches from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}.$ We point out the possibility of suppressing three-body recombination by tuning the two-body scattering length to values that are larger than the size of the condensate ground state. Comparisons with mean-field treatments are presented.Three bosonic, spin-polarized atoms in a spherical oscillator potential constitutes the simplest nontrivial Bose-Einstein condensate (BEC). The present paper develops the tools needed to understand the nature of the complete $J=0$ energy spectrum for this prototype system, assuming a sum of two-body potentials. The resulting spectrum is calculated as a function of the two-body scattering length ${a}_{\mathrm{sc}},$ which documents the evolution of certain many-body levels that evolve from BEC-type to molecular-type as the scattering length is decreased. Implications for the behavior of the condensate excited-state spectrum and for condensate formation and decay are elucidated. The energy levels evolve smoothly, even through the regime where the number of two-body bound states ${N}_{b}$ increases by 1, and ${a}_{\mathrm{sc}}$ switches from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}.$ We point out the possibility of suppressing three-body recombination by tuning the two-body scattering length to values that are larger than the size of the condensate ground state. Comparisons with mean-field treatments are presented.

arXiv:physics/0202060Physical Review AJul 11, 200226 citations

We predict the resonance-enhanced magnetic field dependence of atom-dimer relaxation and three-body recombination rates in a

^{87}\mathrm{Rb}

Bose-Einstein condensate close to

1007\phantom{\rule{0.3em}{0ex}}\mathrm{G}

. Our exact treatments of three-particle scattering explicitly include the dependence of the interactions on the atomic Zeeman levels. The Feshbach resonance distorts the entire diatomic energy spectrum, causing interferences in both loss phenomena. Our two independent experiments confirm the predicted recombination loss over a range of rate constants that spans four orders of magnitude.

J=0

energy spectrum for this prototype system, assuming a sum of two-body potentials. The resulting spectrum is calculated as a function of the two-body scattering length

{a}_{\mathrm{sc}},

which documents the evolution of certain many-body levels that evolve from BEC-type to molecular-type as the scattering length is decreased. Implications for the behavior of the condensate excited-state spectrum and for condensate formation and decay are elucidated. The energy levels evolve smoothly, even through the regime where the number of two-body bound states

{N}_{b}

increases by 1, and

{a}_{\mathrm{sc}}

switches from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}.$ We point out the possibility of suppressing three-body recombination by tuning the two-body scattering length to values that are larger than the size of the condensate ground state. Comparisons with mean-field treatments are presented.