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Journal of Physics Conference Series

Mass scaling in photoassociation of spin-singlet atoms

Mateusz Borkowski, Piotr Morzyński, R. Ciuryło, Piotr Szymon Żuchowski, Paul S. Julienne, Axel Görlitz, T. C. Killian, Yoshiro Takahashi

Published Sep 7, 2015• 0 citations
Publisher

Abstract

Photoassociation spectroscopy, based on forming of molecules from colliding atoms in the presence of light, is a priceless tool for the study of atomic interactions. It enables direct measurements of bound state energies, both in excited and ground state molecules. Applications include determinations of s -wave scattering lengths, as well as atomic state lifetimes. In this work we present the results of our research on the mass-scaling behaviour of molecular bound state energies and collisional properties in spin-singlet atoms. We will concentrate on two such species: strontium and ytterbium, both of which offer several stable isotopes, enabling mass tuning of the system's properties.

DOI
10.1088/1742-6596/635/9/092140

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Two-color photoassociation spectroscopy of ytterbium atoms and the precise determinations of s -wave scattering lengths

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By performing high-resolution two-color photoassociation spectroscopy, we have successfully determined the binding energies of several of the last bound states of the homonuclear dimers of six different isotopes of ytterbium. These spectroscopic data are in excellent agreement with theoretical calculations based on a simple model potential, which very precisely predicts the $s$-wave scattering lengths of all 28 pairs of the seven stable isotopes. The $s$-wave scattering lengths for collision of two atoms of the same isotopic species are 13.33(18) nm for $^{168}\text{Y}\text{b}$, 3.38(11) nm for $^{170}\text{Y}\text{b}$, $\ensuremath{-}0.15(19)\text{ }\text{nm}$ for $^{171}\text{Y}\text{b}$, $\ensuremath{-}31.7(3.4)\text{ }\text{nm}$ for $^{172}\text{Y}\text{b}$, 10.55(11) nm for $^{173}\text{Y}\text{b}$, 5.55(8) nm for $^{174}\text{Y}\text{b}$, and $\ensuremath{-}1.28(23)\text{ }\text{nm}$ for $^{176}\text{Y}\text{b}$. The coefficient of the lead term of the long-range van der Waals potential of the ${\text{Yb}}_{2}$ molecule is ${C}_{6}=1932(30)$ atomic units $({E}_{h}{a}_{0}^{6}\ensuremath{\approx}9.573\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}\text{ }\text{J}\text{ }{\text{nm}}^{6})$.

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We observe the formation of long-range Cs2 Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near 6s1/2(F=3,4)→np3/2 resonances (n=26-34). The spectra reveal two types of molecular states recently predicted by D. A. Anderson, S. A. Miller, and G. Raithel [Phys. Rev. A 90, 062518 (2014)]: states bound purely by triplet s-wave scattering with binding energies ranging from 400 MHz at n=26 to 80 MHz at n=34, and states bound by mixed singlet-triplet s-wave scattering with smaller and F-dependent binding energies. The experimental observations are accounted for by an effective Hamiltonian including s-wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom. The analysis enables the characterization of the role of singlet scattering in the formation of long-range Rydberg molecules and the determination of an effective singlet s-wave scattering length for low-energy-electron-Cs collisions.

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Narrow-line photoassociation spectroscopy and mass-scaling of bosonic strontium

Benjamin J. Reschovsky, Brandon Ruzic, Hirokazu Miyake +3 more

Using new experimental measurements of photoassociation resonances near the $^1\mathrm{S}_0 \rightarrow \phantom{ }^3\mathrm{P}_1$ intercombination transition in $^{84}$Sr and $^{86}$Sr, we present an updated study into the mass-scaling behavior of bosonic strontium dimers. A previous mass-scaling model [Borkowski et al., Phys. Rev. A 90, 032713 (2014)] was able to incorporate a large number of photoassociation resonances for $^{88}$Sr, but at the time only a handful of resonances close to the dissociation limit were known for $^{84}$Sr and $^{86}$Sr. In this work, we perform a more thorough measurement of $^{84}$Sr and $^{86}$Sr bound states, identifying multiple new resonances at deeper binding energies out to $E/h=-5$ GHz. We also identify several previously measured resonances that cannot be experimentally reproduced and provide alternative binding energies instead. With this improved spectrum, we develop a mass-scaled model that reproduces the observed binding energies of $^{86}$Sr and $^{88}$Sr to within 1 MHz. In order to accurately reproduce the deeper bound states, our model includes a second $1_u$ channel and more faithfully reproduces the depth of the potential. As determined by the previous mass-scaling study, $^{84}$Sr $0_u^+$ levels are strongly perturbed by the avoided crossing between the $^1\mathrm{S}_0 + \phantom{ }^3\mathrm{P}_1$ $0_u^+$ $(^3Π_u)$ and $^1\mathrm{S}_0 + \phantom{ }^1\mathrm{D}_2$ $0_u^+$ $(^1Σ_u^+)$ potential curves and therefore are not included in this mass-scaled model, but are accurately reproduced using an isotope-specific model with slightly different quantum defect parameters. In addition, the optical lengths of the $^{84}$Sr $0_u^+,\ ν=-2$ to $ν=-5$ states are measured and compared to numerical estimates to characterize their use as optical Feshbach resonances.

arXiv:1808.06507•Aug 20, 2018•4 citations
Photoassociation spectroscopy, based on forming of molecules from colliding atoms in the presence of light, is a priceless tool for the study of atomic interactions. It enables direct measurements of bound state energies, both in excited and ground state molecules. Applications include determinations of s -wave scattering lengths, as well as atomic state lifetimes. In this work we present the results of our research on the mass-scaling behaviour of molecular bound state energies and collisional properties in spin-singlet atoms. We will concentrate on two such species: strontium and ytterbium, both of which offer several stable isotopes, enabling mass tuning of the system's properties.
By performing high-resolution two-color photoassociation spectroscopy, we have successfully determined the binding energies of several of the last bound states of the homonuclear dimers of six different isotopes of ytterbium. These spectroscopic data are in excellent agreement with theoretical calculations based on a simple model potential, which very precisely predicts the sss-wave scattering lengths of all 28 pairs of the seven stable isotopes. The sss-wave scattering lengths for collision of two atoms of the same isotopic species are 13.33(18) nm for 168Yb^{168}\text{Y}\text{b}168Yb, 3.38(11) nm for 170Yb^{170}\text{Y}\text{b}170Yb, $\ensuremath{-}0.15(19)\text{ }\text{nm}$ for 171Yb^{171}\text{Y}\text{b}171Yb, $\ensuremath{-}31.7(3.4)\text{ }\text{nm}$ for 172Yb^{172}\text{Y}\text{b}172Yb, 10.55(11) nm for 173Yb^{173}\text{Y}\text{b}173Yb, 5.55(8) nm for 174Yb^{174}\text{Y}\text{b}174Yb, and $\ensuremath{-}1.28(23)\text{ }\text{nm}$ for 176Yb^{176}\text{Y}\text{b}176Yb. The coefficient of the lead term of the long-range van der Waals potential of the Yb2{\text{Yb}}_{2}Yb2​ molecule is C6=1932(30){C}_{6}=1932(30)C6​=1932(30) atomic units $({E}_{h}{a}_{0}^{6}\ensuremath{\approx}9.573\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}\text{ }\text{J}\text{ }{\text{nm}}^{6})$.
Advances in laser cooling of neutral atoms have made possible a new form of high-resolution laser spectroscopy: photoassociation of ultracold atoms. Colliding neutral atoms, confined in a laser trap, are photoassociated to bound excited states of the dimer molecule by absorbing a photon from a tunable laser. The technique can probe long range and “purely long range” molecular states that are difficult or impossible to detect by traditional means and, because of the extremely low energy of the colliding atoms (<1 mK), is capable of high resolution (<0.001 cm-1). The spectra are useful for atomic lifetime measurements, determination of atomic ground-state scattering information, and measurement of curve-crossing probabilities. Theoretical and experimental work in the field, including multiple resonance techniques and photo association line shapes, are reviewed.
Photoassociation is the process in which two colliding atoms absorb a photon to form an excited molecule. The development of laser-cooling techniques for producing gases at ultracold (<1mK)(<1\phantom{\rule{0.3em}{0ex}}\mathrm{mK})(<1mK) temperatures allows photoassociation spectroscopy to be performed with very high spectral resolution. Of particular interest is the investigation of molecular states whose properties can be related, with high precision, to the properties of their constituent atoms with the ``complications'' of chemical binding accounted for by a few parameters. These include bound long-range or purely long-range vibrational states in which two atoms spend most or all of their time at large internuclear separations. Low-energy atomic scattering states also share this characteristic. Photoassociation techniques have made important contributions to the study of all of these. This review describes what is special about photoassociation spectroscopy at ultracold temperatures, how it is performed, and a sampling of results including the determination of scattering lengths, their control via optical Feshbach resonances, precision determinations of atomic lifetimes from molecular spectra, limits on photoassociation rates in a Bose-Einstein condensate, and briefly, production of cold molecules. Discussions are illustrated with examples on alkali-metal atoms as well as other species. Progress in the field is already past the point where this review can be exhaustive, but an introduction is provided on the capabilities of photoassociation spectroscopy and the techniques presently in use.
We observe the formation of long-range Cs2 Rydberg molecules consisting of a Rydberg and a ground-state atom by photoassociation spectroscopy in an ultracold Cs gas near 6s1/2(F=3,4)→np3/2 resonances (n=26-34). The spectra reveal two types of molecular states recently predicted by D. A. Anderson, S. A. Miller, and G. Raithel [Phys. Rev. A 90, 062518 (2014)]: states bound purely by triplet s-wave scattering with binding energies ranging from 400 MHz at n=26 to 80 MHz at n=34, and states bound by mixed singlet-triplet s-wave scattering with smaller and F-dependent binding energies. The experimental observations are accounted for by an effective Hamiltonian including s-wave scattering pseudopotentials, the hyperfine interaction of the ground-state atom, and the spin-orbit interaction of the Rydberg atom. The analysis enables the characterization of the role of singlet scattering in the formation of long-range Rydberg molecules and the determination of an effective singlet s-wave scattering length for low-energy-electron-Cs collisions.
The spectra of the high-lying vibrational levels of the Asp1Sigmasbspu+A\\sp1\\Sigma\\sbsp{u}{+}Asp1Sigmasbspu+ and 1sp3Sigmasbspg+1\\sp3\\Sigma\\sbsp{g}{+}1sp3Sigmasbspg+ singly excited states of both sp6rmLisb2\\sp6\\rm Li\\sb2sp6rmLisb2 and sp7rmLisb2\\sp7\\rm Li\\sb2sp7rmLisb2 are obtained via photoassociation of colliding ultracold atoms confined in a magneto-optical trap. The least bound state of the asp3Sigmasbspu+a\\sp3\\Sigma\\sbsp{u}{+}asp3Sigmasbspu+ ground state potential, obtained by two-photon photoassociative spectroscopy, is also presented for both sp7rmLisb2\\sp7\\rm Li\\sb2sp7rmLisb2 and sp6rmLisb2\\sp6\\rm Li\\sb2sp6rmLisb2. The vibrational levels have resolved hyperfine structure, whose relative energy splittings and transition strengths are accurately modeled. The photoassociative spectra are used to precisely determine both the singlet and triplet s-wave scattering lengths for both isotopes, which are important parameters in systems designed to observe quantum degenerate effects and Bose-Einstein condensation.
Using new experimental measurements of photoassociation resonances near the 1S0→3P1^1\mathrm{S}_0 \rightarrow \phantom{ }^3\mathrm{P}_11S0​→3P1​ intercombination transition in 84^{84}84Sr and 86^{86}86Sr, we present an updated study into the mass-scaling behavior of bosonic strontium dimers. A previous mass-scaling model [Borkowski et al., Phys. Rev. A 90, 032713 (2014)] was able to incorporate a large number of photoassociation resonances for 88^{88}88Sr, but at the time only a handful of resonances close to the dissociation limit were known for 84^{84}84Sr and 86^{86}86Sr. In this work, we perform a more thorough measurement of 84^{84}84Sr and 86^{86}86Sr bound states, identifying multiple new resonances at deeper binding energies out to E/h=−5E/h=-5E/h=−5 GHz. We also identify several previously measured resonances that cannot be experimentally reproduced and provide alternative binding energies instead. With this improved spectrum, we develop a mass-scaled model that reproduces the observed binding energies of 86^{86}86Sr and 88^{88}88Sr to within 1 MHz. In order to accurately reproduce the deeper bound states, our model includes a second 1u1_u1u​ channel and more faithfully reproduces the depth of the potential. As determined by the previous mass-scaling study, 84^{84}84Sr 0u+0_u^+0u+​ levels are strongly perturbed by the avoided crossing between the 1S0+3P1^1\mathrm{S}_0 + \phantom{ }^3\mathrm{P}_11S0​+3P1​ 0u+0_u^+0u+​ (3Πu)(^3Π_u)(3Πu​) and 1S0+1D2^1\mathrm{S}_0 + \phantom{ }^1\mathrm{D}_21S0​+1D2​ 0u+0_u^+0u+​ (1Σu+)(^1Σ_u^+)(1Σu+​) potential curves and therefore are not included in this mass-scaled model, but are accurately reproduced using an isotope-specific model with slightly different quantum defect parameters. In addition, the optical lengths of the 84^{84}84Sr 0u+, ν=−20_u^+,\ ν=-20u+​, ν=−2 to ν=−5ν=-5ν=−5 states are measured and compared to numerical estimates to characterize their use as optical Feshbach resonances.