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Europhysics Letters (EPL)

Photoassociation of metastable helium

A S Dickinson, Florent Xavier Gadéa, Thierry Leininger

Published Mar 24, 2005• 9 citations
Publisher

Abstract

A theoretical study is performed for the photoassociation of metastable helium. Combining short-range, high-level, ab initio calculations for 5 Σ g / u + and 5 Π g / u symmetries and long-range behaviour, better described in Hund's case (c), potential-energy curves for attractive, 5 Σ u + and 5 Π g , as well as repulsive, 5 Π u and 5 Σ g + , states of quintet metastable helium molecules dissociating to 2 3 S + 2 3 P are obtained. Taking into account the atomic spin-orbit couplings, vibrational levels are derived for near-dissociation levels at the 3 P 2 asymptote. Comparison with results from three recent photoassociation experiments obtained under different conditions (μK temperatures with spin alignment and mK temperatures without) allowed for an assignation of about three quarters of the observed levels. The robustness of the vibrational numbering is confirmed by testing a modification of the short-range potentials.

DOI
10.1209/epl/i2004-10491-y

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Daniel Cocks, Ian B. Whittingham

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A theoretical study is performed for the photoassociation of metastable helium. Combining short-range, high-level, ab initio calculations for 5 Σ g / u + and 5 Π g / u symmetries and long-range behaviour, better described in Hund's case (c), potential-energy curves for attractive, 5 Σ u + and 5 Π g , as well as repulsive, 5 Π u and 5 Σ g + , states of quintet metastable helium molecules dissociating to 2 3 S + 2 3 P are obtained. Taking into account the atomic spin-orbit couplings, vibrational levels are derived for near-dissociation levels at the 3 P 2 asymptote. Comparison with results from three recent photoassociation experiments obtained under different conditions (μK temperatures with spin alignment and mK temperatures without) allowed for an assignation of about three quarters of the observed levels. The robustness of the vibrational numbering is confirmed by testing a modification of the short-range potentials.
A new theoretical study for the photoassociation of metastable helium is presented, based on fully ab initio short-range potentials. Optimization of the exponents of the Gaussian orbitals of a smaller basis set than employed previously allowed the calculation of potentials dissociating to He(2 3 S)+He(2 3 P) at the multi-reference configuration interaction level down to internuclear separations of 3.5 a 0 . The good agreement with observed near-dissociation levels obtained previously using extrapolated short-range potentials is confirmed and almost all levels observed to the red of the He D 2 line, associated with the He 2 3 S + 2 3 P 2 dissociation limit, are assigned. The agreement is less satisfactory with the levels observed to the red of the He D 1 line, although vibrational levels have been found in the outer ultra-long-range well of a double-well potential with the He 2 3 P 1 dissociation limit. A semiclassical analysis is presented to explain the limited sensitivity of the near-dissociation binding energies to the short-range potential.
A theoretical analysis of photoassociation in ultracold metastable helium has been undertaken for the 2(^3)S1 + 2(^3)S1 to 2(^3)S1 + 2(^3)P transition. A full multichannel calculation is presented for two aspects of the system, a) the accurate calculation of energies for the bound vibrational levels of the dimer; and b) the non-perturbative calculation of the photoassociation line shapes allowing for abitrary laser intensity and detuning. A strong emphasis is placed on the accuracy of the calculations, and the elimination of approximations that have been used in previous investigations. The results indicate that full multichannel calculations are required rather than approximate single-channel calculations in some important situations, and are especially useful for making assignments between experiment and theory. Bound levels have been previously measured from the photoassociation of cold metastable thermal gases to energies close to the three asymptotes j = 0, 1, 2 of the 2(^3)S1 → 2(^3)Pj atomic transition. Previous analysis of these measurements was made using either approximate accumulated phase techniques based on long-range single-channel potentials, or using multichannel calculations and long-range potentials. Because accurate short-range electronic potentials have been calculated only recently, this thesis presents the first multichannel calculation for the levels near the j = 1, 2 asymptotes. The new short-range potentials had previously been used in an approximate single-channel calculation, but this type of calculation ignores the effects of non-adiabatic and Coriolis couplings. Presented here are the binding energies calculated from a fully multichannel technique which includes these couplings, and some differences of up to 10% from the single-channel calculations are observed. The detailed knowledge of the bound wave functions is then exploited to determine a set of observability criteria that produce a near unique assignment of theoretical levels to experimental observations. From these unique assignments, a 1% correction to the short-range electronic potentials has been implemented that significantly improves the agreement between theory and experiment. Experimental measurements have previously been made of line shifts in the photoassociation spectra of vibrational levels in the 0+u long-range potential that asymptotes to 2(^3)S1 + 2(^3)P0 and their variation with laser intensity. These results were previously analysed by performing an approximate second-order perturbative calculation of the line shift that is valid only for low laser intensities. In this thesis a completely non-perturbative calculation of the spectra and line shapes for abitrary laser intensity is presented for photoassociation to the levels probed in experiment. The techniques of dressed state formalism and a modified radiative coupling are employed to properly treat the laser coupling for large interatomic separations. These calculations produce resonance profiles superimposed on a very significant background, a feature that is not seen in photoassociation calculations of other atomic species. From the calculated line shapes, the line shifts and line widths were determined for varying intensity and a small nonlinear intensity-dependence of up to 2.5% was found for the line shift. The effects of invoking the dipole approximation for the laser coupling for the long-range molecular system are analysed by solving the equations using the complete laser coupling that does not assume the dipole approximation. Important differences are obtained between the profiles with and without the dipole approximation, and the photoassociation resonances are found to be more discernible at larger intensities when the complete laser coupling is used.
The bound states of the fermionic (3)He(2 (3)S(1)) + (3)He(2 (3)P(j)) system, where j = 0, 1, 2, are investigated using the recently available ab initio short-range (1,3,5)Σ(+)(g,u) and (1,3,5)Π(g,u) potentials computed by Deguilhem et al. (J. Phys. B: At., Mol. Opt. Phys., 2009, 42, 015102). Single-channel and multichannel calculations have been undertaken in order to investigate the effects of Coriolis and non-adiabatic couplings. The possible experimental observability of the theoretical levels is assessed using criteria based upon the short-range character of each level and their coupling to metastable ground states. Purely long-range levels have been identified and 30 short-range levels near five asymptotes are suggested for experimental investigation.
The bound states of the fermionic ^3He(2 ^3S_1)+ ^3He(2 ^3P_j)system, where j=0,1,2, are investigated using the recently available ab initio short-range ^{1,3,5}\Sigma^{+}_{g,u} and ^{1,3,5}\Pi_{g,u} potentials computed by Deguilhem et al. (J. Phys. B: At. Mol. Opt. Phys., 2009, 42, 015102). Single-channel and multichannel calculations have been undertaken in order to investigate the effects of Coriolis and non-adiabatic couplings. The possible experimental observability of the theoretical levels is assessed using criteria based upon the short-range character of each level and their coupling to metastable ground states. Purely long-range levels have been identified and 30 short-range levels near five asymptotes are suggested for experimental investigation.
We observe light-induced frequency shifts in one-color photoassociative spectra of magnetically trapped 4 He* atoms in the metastable 2 3 S 1 state. A pair of ultracold spin-polarized 2 3 S 1 helium atoms is excited into a molecular bound state in the purely long-range 0 u + potential connected to the 2 3 S 1 -2 3 P 0 asymptote. The shift arises from the optical coupling of the molecular excited bound state with the scattering states and the bound states of two colliding 2 3 S 1 atoms. We measure the frequency-shifts for several ro-vibrational levels in the 0 u + potential and find a linear dependence on the photoassociation laser intensity. Comparison with a theoretical analysis provides a good indication for the s -wave scattering length a of the quintet ( 5 Σ g + ) potential, a = 7.2 ± 0.6 nm, which is significantly lower than most previous results obtained by non-spectroscopic methods.
Line shifts and line shapes for photoassociation of spin-polarised metastable helium to long-range vibrational states in the J = 1,0 + u potential dissociating to the 2 s 3 S 1 + 2 p 3 P 0 limit are studied using a nonperturbative multichannel calculation valid for arbitrary laser intensities. Asymptotically-free dressed states of the laser plus matter system are used to obtain the S-matrix elements required to generate the photoassociation profiles. Issues associated with the very shallow nature of the potentials that support the excited states are investigated.