Aspects of cold bosonic atoms with a large scattering length

Motivated by recent experimental investigations of Cs-Cs-Li Efimov resonances, this work theoretically investigates the few-body properties of $N\ensuremath{-}1$ noninteracting identical heavy bosons, which interact with a light impurity through a large $s$ -wave scattering length. For Cs-Cs-Cs-Li, we predict the existence of universal four-body states with energies ${E}_{4}^{(n,1)}$ and ${E}_{4}^{(n,2)}$ , which are universally linked to the energy ${E}_{3}^{(n)}$ of the $n$ th Efimov trimer. For infinitely large $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{6}\mathrm{Li}$ and vanishing $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ scattering lengths, we find $({E}_{4}^{(1,1)}/{E}_{3}^{(1)}{)}^{1/2}\ensuremath{\approx}1.51$ and $({E}_{4}^{(1,2)}/{E}_{3}^{(1)}{)}^{1/2}\ensuremath{\approx}1.01$. The $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{6}\mathrm{Li}$ scattering lengths at which these states merge with the four-atom threshold, the dependence of these energy ratios on the mass ratio between the heavy and light atoms, and selected aspects of the generalized Efimov scenario for $N>4$ are also discussed. Possible implications of our results for ongoing cold atom experiments are presented.Motivated by recent experimental investigations of Cs-Cs-Li Efimov resonances, this work theoretically investigates the few-body properties of $N\ensuremath{-}1$ noninteracting identical heavy bosons, which interact with a light impurity through a large $s$-wave scattering length. For Cs-Cs-Cs-Li, we predict the existence of universal four-body states with energies ${E}_{4}^{(n,1)}$ and ${E}_{4}^{(n,2)}$, which are universally linked to the energy ${E}_{3}^{(n)}$ of the $n$th Efimov trimer. For infinitely large $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{6}\mathrm{Li}$ and vanishing $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ scattering lengths, we find $({E}_{4}^{(1,1)}/{E}_{3}^{(1)}{)}^{1/2}\ensuremath{\approx}1.51$ and $({E}_{4}^{(1,2)}/{E}_{3}^{(1)}{)}^{1/2}\ensuremath{\approx}1.01$. The $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{6}\mathrm{Li}$ scattering lengths at which these states merge with the four-atom threshold, the dependence of these energy ratios on the mass ratio between the heavy and light atoms, and selected aspects of the generalized Efimov scenario for $N>4$ are also discussed. Possible implications of our results for ongoing cold atom experiments are presented.

arXiv:1410.2314Physical Review LettersNov 18, 201444 citations

Ground State Properties of Cold Bosonic Atoms at Large Scattering Lengths

Jun Liang Song, Fei Zhou

In this Letter, we study bosonic atoms at large scattering lengths using a variational method where the condensate amplitude is a variational parameter. We further examine momentum distribution functions, chemical potentials, the speed of sound, and spatial density profiles of cold bosonic atoms in a trap in this limit. The latter two properties turn out to bear similarities to those of Fermi gases. The estimates obtained here are applicable near Feshbach resonances, particularly when the fraction of atoms forming three-body structures is small and can be tested in future cold atom experiments.In this Letter, we study bosonic atoms at large scattering lengths using a variational method where the condensate amplitude is a variational parameter. We further examine momentum distribution functions, chemical potentials, the speed of sound, and spatial density profiles of cold bosonic atoms in a trap in this limit. The latter two properties turn out to bear similarities to those of Fermi gases. The estimates obtained here are applicable near Feshbach resonances, particularly when the fraction of atoms forming three-body structures is small and can be tested in future cold atom experiments.

arXiv:0902.0366Physical Review LettersJul 8, 200947 citations

Studies of weak interactions with ultra-cold atoms

Renato Ejnisman, Paul Rudy, N. P. Bigelow +5 more

Brazilian Journal of PhysicsJun 1, 19970 citations

Efimov Physics in Cold Atoms

Eric Braaten, H.‐W. Hammer

Atoms with a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-atom sector, the universal properties are familiar and depend only on the scattering length. In the 3-atom sector for identical bosons, the universal properties include the existence of a sequence of shallow triatomic molecules called Efimov trimers and log-periodic dependence of scattering observables on the energy and the scattering length. In this review, we summarize the universal results that are currently known. We also summarize the experimental information that is currently available with an emphasis on 3-atom loss processes.Atoms with a large scattering length have universal low-energy properties that do not depend on the details of their structure or their interactions at short distances. In the 2-atom sector, the universal properties are familiar and depend only on the scattering length. In the 3-atom sector for identical bosons, the universal properties include the existence of a sequence of shallow triatomic molecules called Efimov trimers and log-periodic dependence of scattering observables on the energy and the scattering length. In this review, we summarize the universal results that are currently known. We also summarize the experimental information that is currently available with an emphasis on 3-atom loss processes.

Jan 1, 200674 citations

Cold atoms and the 2D Bose-Hubbard model

Ian B. Spielman

Bulletin of the American Physical SocietyJun 7, 20070 citations

s

-wave scattering length. For Cs-Cs-Cs-Li, we predict the existence of universal four-body states with energies

{E}_{4}^{(n,1)}

and

{E}_{4}^{(n,2)}

, which are universally linked to the energy

{E}_{3}^{(n)}

of the

n

th Efimov trimer. For infinitely large $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{6}\mathrm{Li}$ and vanishing $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ scattering lengths, we find $({E}_{4}^{(1,1)}/{E}_{3}^{(1)}{)}^{1/2}\ensuremath{\approx}1.51$ and $({E}_{4}^{(1,2)}/{E}_{3}^{(1)}{)}^{1/2}\ensuremath{\approx}1.01$. The $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{6}\mathrm{Li}$ scattering lengths at which these states merge with the four-atom threshold, the dependence of these energy ratios on the mass ratio between the heavy and light atoms, and selected aspects of the generalized Efimov scenario for

N>4

are also discussed. Possible implications of our results for ongoing cold atom experiments are presented.