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arXiv:0904.4751 · Physical Review A

Laser-intensity dependence of photoassociation in ultracold metastable helium

Daniel Cocks, Ian B. Whittingham

Published Aug 24, 2009• 6 citations
arXivHTMLPDF

Abstract

Photoassociation of spin-polarized metastable helium to the three lowest rovibrational levels of the $J=1$, ${0}_{u}^{+}$ state asymptoting to $2s\text{ }{^{3}S}_{1}+2p\text{ }{^{3}P}_{0}$ is studied using a second-order perturbative treatment of the line shifts valid for low laser intensities, and two variants of a nonperturbative close-coupled treatment, one based upon dressed states of the matter plus laser system, and the other on a modified radiative coupling which vanishes asymptotically, thus simulating experimental conditions. These nonperturbative treatments are valid for arbitrary laser intensities and yield the complete photoassociation resonance profile. Both variants give nearly identical results for the line shifts and widths of the resonances and show that their dependence upon laser intensity is very close to linear and quadratic, respectively, for the two lowest levels. The resonance profiles are superimposed upon a significant background loss, a feature for this metastable helium system not present in studies of photoassociation in other systems, which is due to the very shallow nature of the excited state ${0}_{u}^{+}$ potential. The results for the line shifts from the close-coupled and perturbative calculations agree very closely at low laser intensities.

DOI
10.1103/physreva.80.023417

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Photoassociation of spin-polarized metastable helium to the three lowest rovibrational levels of the J=1J=1J=1, 0u+{0}_{u}^{+}0u+​ state asymptoting to 2s 3S1+2p 3P02s\text{ }{^{3}S}_{1}+2p\text{ }{^{3}P}_{0}2s 3S1​+2p 3P0​ is studied using a second-order perturbative treatment of the line shifts valid for low laser intensities, and two variants of a nonperturbative close-coupled treatment, one based upon dressed states of the matter plus laser system, and the other on a modified radiative coupling which vanishes asymptotically, thus simulating experimental conditions. These nonperturbative treatments are valid for arbitrary laser intensities and yield the complete photoassociation resonance profile. Both variants give nearly identical results for the line shifts and widths of the resonances and show that their dependence upon laser intensity is very close to linear and quadratic, respectively, for the two lowest levels. The resonance profiles are superimposed upon a significant background loss, a feature for this metastable helium system not present in studies of photoassociation in other systems, which is due to the very shallow nature of the excited state 0u+{0}_{u}^{+}0u+​ potential. The results for the line shifts from the close-coupled and perturbative calculations agree very closely at low laser intensities.
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.
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.
Photoassociation (PA) of ultracold metastable helium to the 2s2p2s2p2s2p manifold is theoretically investigated using a nonperturbative close-coupled treatment in which the laser coupling is evaluated without assuming the dipole approximation. The results are compared with our previous study [D. G. Cocks and I. B. Whittingham, Phys. Rev. A 80, 023417 (2009)], which makes use of the dipole approximation. The approximation is found to strongly affect the PA spectra because the photoassociated levels are weakly bound, and a similar impact is predicted to occur in other systems of a weakly bound nature. The inclusion of the approximation does not affect the resonance positions or widths; however, significant differences are observed in the background of the spectra and the maximum laser intensity at which resonances are discernible. Couplings not satisfying the dipole selection rule $|J\ensuremath{-}1|\ensuremath{\leqslant}{J}^{\ensuremath{'}}\ensuremath{\leqslant}|J+1|$ do not lead to observable resonances.
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.
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 long-range J = 1, 0 u + potential linked to the 2 3 S 1 –2 3 P 0 asymptote were reported in a previous paper (Kim et al 2005 Europhys. Lett. 72 548), and are analysed 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.
We perform a theoretical analysis to interpret the spectra of purely long-range helium dimers produced by photoassociation (PA) in an ultracold gas of metastable helium atoms. The experimental spectrum obtained with the PA laser tuned closed to the $2\phantom{\rule{0.3em}{0ex}}^{3}S_{1}\ensuremath{\leftrightarrow}2\phantom{\rule{0.3em}{0ex}}^{3}P_{0}$ atomic line has been reported in a previous paper. Here, we first focus on the corrections to be applied to the measured resonance frequencies in order to infer the molecular binding energies. We then present a calculation of the vibrational spectra for the purely long-range molecular states, using adiabatic potentials obtained from perturbation theory. With retardation effects taken into account, the agreement between experimental and theoretical determinations of the spectrum for the 0u+{0}_{u}^{+}0u+​ purely long-range potential well is very good. The results yield a determination of the lifetime of the 23P2\phantom{\rule{0.3em}{0ex}}^{3}P23P atomic state.