Analysis of light-induced frequency shifts in the photoassociation of ultracold metastable helium atoms

Abstract

We present an exhaustive analysis of the light-induced frequency shifts of the photoassociation lines of ultracold metastable 4 He * atoms in a magnetic trap. The measurements of the shifts of several vibrational levels bound in the purely longrange J = 1, 0 + u potential linked to the 2 3 S 1 − 2 3 P 0 asymptote were reported in a previous paper [1], and are analyzed here. The simplicity of this system makes it very appropriate for a detailed study. Indeed, the purely long-range character of the excited potential allows one to calculate exact excited molecular wavefunctions and to use asymptotic expansions at large internuclear distances of the ground state wavefunctions appearing in Franck-Condon type integrals. Moreover, the number of collisional channels to be considered is strongly reduced by the absence of hyperfine structure for 4 He * and the use of polarized ultracold atoms and polarized light. This allows us to derive semi-analytical expressions for the shifts showing explicitly their linear dependences on the s-wave scattering length a of spin polarized metastable 4 He * atoms. This explains how it is possible to derive the measurement of a from these shifts.

Cold and trapped metastable noble gases

“…Both these parameters depend on the scattering length a. A reliable determination of a resulted from the measurement of the shifts and of a theoretical analysis Whittingham, 2009, 2010;Portier et al, 2006). Uncertainties related to the laser intensity at the atom cloud were eliminated by comparing results for three different excited vibrational states in the 0 + u potential.…”

Control of laser-induced frequency shift in ultracold cesium molecules by an external magnetic field

“…LIFS has been experimentally studied by several groups dealing with ultracold helium molecules 4 He 2 [5,12], and ultracold alkali molecule samples such as 7 Li 2 [10,13], Na 2 [14], Rb 2 [15], and Cs 2 [16]. Several theoretical models have also been proposed for LIFS [8,10,15], among which a calculation based on the multichannel scattering theory is typically developed [17].…”

Laser-intensity dependence of photoassociation in ultracold metastable helium

“…Since the colliding atoms are so cold, the energy of the initial scattering state is well determined and the resonant laser energies corresponding to transitions to various bound states produce a very high resolution spectrum (< 1 MHz). At this level of precision, energy level shifts induced by the PA laser can be significant [3,4,5] and an understanding of the dependence of the energy level shifts upon the laser intensity, polarization and frequency is crucial.…”

“…Theoretical investigations of photoassociation in ultracold metastable helium are limited to the perturbative analysis of the light-induced energy level shifts of the excited J = 1, 0 + u rovibrational state [5] based upon the theories of [21,22]. In this model the shifts are linear in the laser intensity and in the s-wave scattering length a.…”