Physical Review A

Zero-energy bound or quasibound states and their implications for diatomic systems with an asymptotic van der Waals interaction

Bo Gao

Published Oct 18, 2000• 87 citations

Abstract

Using an l-insensitive quantum defect theory, we derive a set of universal properties, both spectral and scattering, that are shared by diatomic systems with an asymptotic van der Waals interaction and having a zero-energy bound or a quasibound state of angular momentum ${l}_{b}.$ The ${}^{133}\mathrm{Cs}$ dimer is studied as an example. Systems that are close to having a bound or a quasibound state at the threshold are also discussed.

DOI: 10.1103/physreva.62.050702

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Physical Review A

Zero-energy bound or quasibound states and their implications for diatomic systems with an asymptotic van der Waals interaction

Bo Gao

Published Oct 18, 2000• 87 citations

Publisher

Abstract

{l}_{b}.

The

{}^{133}\mathrm{Cs}

dimer is studied as an example. Systems that are close to having a bound or a quasibound state at the threshold are also discussed.

DOI: 10.1103/physreva.62.050702

Related papers

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Journal of Physics B Atomic Molecular and Optical PhysicsOct 27, 200446 citations

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{l}_{b}.

The

{}^{133}\mathrm{Cs}

dimer is studied as an example. Systems that are close to having a bound or a quasibound state at the threshold are also discussed.

At long distances, interactions between neutral ground-state atoms can be described by the van der Waals potential. In the ultracold regime, atom-atom scattering is dominated by

s

-waves phase shifts given by an effective range expansion in terms of the scattering length ${\ensuremath{\alpha}}_{0}$ and the effective range

{r}_{0}

. We show that while the scattering length cannot be predicted for these potentials, the effective range is given by the universal low-energy theorem ${r}_{0}=A+B/{\ensuremath{\alpha}}_{0}+C/{\ensuremath{\alpha}}_{0}^{2}$, where

A

B

, and

C

depend on the dispersion coefficients

{C}_{n}

and the reduced diatom mass. We confront this formula to about 100 determinations of

{r}_{0}

and ${\ensuremath{\alpha}}_{0}$ and show why the result is dominated by the leading dispersion coefficient

{C}_{6}

. Universality and scaling extend much beyond naive dimensional analysis estimates.

It is well-known that cold atoms near

s

-wave Feshbach resonances have universal properties that are insensitive to the short-range details of the interaction. What is less known is that atoms near higher partial-wave Feshbach resonances also have remarkable universal properties. We illustrate this with a single atom interacting resonantly with two fixed static centers. At a Feshbach resonance point with orbital angular momentum $L\ensuremath{\ge}1$, we find

2L+1

shallow bound states whose energies behave like

1/{R}^{2L+1}

when the distance

R

between the two centers is large. We then compute corrections to the binding energies due to other parameters in the effective range expansions. For completeness we also compute the binding energies near

s

-wave Feshbach resonances, taking into account the corrections. Afterwards we turn to the bound states at large but finite scattering volumes. For

p

-wave and higher partial-wave resonances we derive a simple formula for the energies in terms of a parameter called ``proximity parameter.'' These results are applicable to a free atom interacting resonantly with two atoms that are localized to two lattice sites of an optical lattice, and to one light atom interacting with two heavy ones in free space. Modifications of the low energy physics due to the long range van der Waals potential are also discussed.