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Two-photon photoassociative spectroscopy of strontium-86

James Aman

Published Sep 6, 2019• 0 citations
OpenAlex

Abstract

This dissertation describes two-photon photoassociation to the least-bound vibrational level of the X$^1\Sigma_g^+$ electronic ground state of the $^{86}$Sr$_2$ dimer, which represents the first observation of this naturally occurring halo molecule. We measure the binding energy of this state to be $E_b=83.00(7)(20)$\,kHz. Using the precise determination of the halo state binding energy and the universal theory for a very weakly-bound state on a potential that asymptotes to a van der Waals form, we determine $s$-wave scattering lengths for all strontium isotopes. Our results are consistent with, but substantially more accurate than the previously determined values found from spectroscopic determination of long-range coefficients using other strontium isotopes. With a radial expectation value of $\langle r \rangle \approx 21$\,nm the halo state extends well into the classically forbidden region, which results in a large sensitivity of the dimer binding energy to light near-resonant with a bound-bound transition on the metastable $^1S_0-{^3P_1}$ potential. This suggests that $^{86}$Sr may be a promising candidate for manipulating atomic interactions via optical coupling of the molecular bound states and for probing naturally occurring Efimov states. Furthermore, we observe novel multi-photon spectral loss features due to strong coupling and small detuning of the photoassociation lasers. Numerical simulations of a simple three-level model undergoing a simultaneous two-frequency drive, shows that solutions of the time-dependent Schr\"{o}dinger equation accurately reproduce these additional loss features. A Floquet analysis of this model, yields analytic formulas for predicting the AC Stark shift of the halo molecule. Additionally, we report on the current state and recent modifications of our ultracold neutral strontium apparatus with a particular emphasis on the installation of a $532$\,nm optical lattice. Characterization of this laser system and applications are discussed for further investigation of the strontium-$86$ halo molecule and additional photoassociation experiments.

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This dissertation describes two-photon photoassociation to the least-bound vibrational level of the X1Σg+^1\Sigma_g^+1Σg+​ electronic ground state of the 86^{86}86Sr2_22​ dimer, which represents the first observation of this naturally occurring halo molecule. We measure the binding energy of this state to be Eb=83.00(7)(20)E_b=83.00(7)(20)Eb​=83.00(7)(20),kHz. Using the precise determination of the halo state binding energy and the universal theory for a very weakly-bound state on a potential that asymptotes to a van der Waals form, we determine sss-wave scattering lengths for all strontium isotopes. Our results are consistent with, but substantially more accurate than the previously determined values found from spectroscopic determination of long-range coefficients using other strontium isotopes. With a radial expectation value of ⟨r⟩≈21\langle r \rangle \approx 21⟨r⟩≈21,nm the halo state extends well into the classically forbidden region, which results in a large sensitivity of the dimer binding energy to light near-resonant with a bound-bound transition on the metastable 1S0−3P1^1S_0-{^3P_1}1S0​−3P1​ potential. This suggests that 86^{86}86Sr may be a promising candidate for manipulating atomic interactions via optical coupling of the molecular bound states and for probing naturally occurring Efimov states. Furthermore, we observe novel multi-photon spectral loss features due to strong coupling and small detuning of the photoassociation lasers. Numerical simulations of a simple three-level model undergoing a simultaneous two-frequency drive, shows that solutions of the time-dependent Schr"{o}dinger equation accurately reproduce these additional loss features. A Floquet analysis of this model, yields analytic formulas for predicting the AC Stark shift of the halo molecule. Additionally, we report on the current state and recent modifications of our ultracold neutral strontium apparatus with a particular emphasis on the installation of a 532532532,nm optical lattice. Characterization of this laser system and applications are discussed for further investigation of the strontium-868686 halo molecule and additional photoassociation experiments.
We investigate two-frequency photoassociation of a weakly bound molecular state, focusing on a regime where the AC Stark shift is comparable to the halo-state energy. In this ``high-intensity'' regime, we observe features absent in low-intensity two-frequency photoassociation. We experimentally measure the spectra of 86Sr^{86}\mathrm{Sr}86Sr atoms coupled to the least bound state of the 86Sr2^{86}\mathrm{Sr}_{2}86Sr2​ ground electronic channel through an intermediate electronically excited molecular state. We compare the spectra to a simple three-level model that includes a two-frequency drive on each leg of the transition. With numerical solution of the time-dependent Schr\"odinger equation, we show that this model accurately captures (1) the existence of experimentally observed satellite peaks that arise from nonlinear processes, (2) the locations of the two-photon peak in the spectrum, including AC Stark shifts, and (3) in some cases, spectral line shapes. To better understand these numerical results, we develop an approximate treatment of this model, based on Floquet and perturbation theory, that gives simple formulas that accurately capture the halo-state energies. We expect these expressions to be valuable tools to analyze and guide future two-frequency photoassociation experiments.
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.
Creation and precise spectroscopy of 86^{86}86Sr2_22​ halo molecules
We report on the creation of 86^{86}86Sr2_22​ molecules in the halo state and neighboring weakly bound states. Efficient molecule production via one-photon photoassociation relies on sufficient wavefunction overlap between the target vibrational states in the electronic excited- and ground-state potentials. Using Autler-Townes spectroscopy, transition strengths are measured to identify optimal pathways for production of weakly bound molecules. Vibrational splittings for the three least-bound vibrational states are measured, and dominant systematic uncertainties are evaluated with uncertainties below 100 Hz. From these splittings, absolute binding energies for these weakly bound vibrational states are determined. The results pave the way to a molecular isotope shift measurement with Sr2_22​.
We present results from two-photon photoassociative spectroscopy of the least-bound vibrational level of the $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ state of the 88Sr2^{88}\mathrm{Sr}_{2}88Sr2​ dimer. Measurement of the binding energy allows us to determine the sss-wave scattering length ${a}_{88}=\ensuremath{-}1.4(6){a}_{0}$. For the intermediate state, we use a bound level on the metastable $^{1}S_{0}\text{\ensuremath{-}}^{3}P_{1}$ potential, which provides large Franck-Condon transition factors and narrow one-photon photoassociative lines that are advantageous for observing quantum-optical effects such as Autler-Townes resonance splittings.
Halo 86{}^{86}86Sr2{}_{2}2​ molecules are photoassociated in their ground electronic state. The large sensitivity of the molecular binding energy to the near-resonant light suggests the possibility of probing naturally occurring Efimov states by optical means.
We report photoassociation spectroscopy of ultracold 86Sr^{86}\mathrm{Sr}86Sr atoms near the intercombination line and provide theoretical models to describe the obtained bound-state energies. We show that using only the molecular states correlating with the 1S0+3P1{}^{1}{S}_{0}+{}^{3}{P}_{1}1S0​+3P1​ asymptote is insufficient to provide a mass-scaled theoretical model that would reproduce the bound-state energies for all isotopes investigated to date: 84Sr,86Sr^{84}\mathrm{Sr},^{86}\mathrm{Sr}84Sr,86Sr, and 88Sr^{88}\mathrm{Sr}88Sr. We attribute that to the recently discovered avoided crossing between the 1S0+3P1{}^{1}{S}_{0}+{}^{3}{P}_{1}1S0​+3P1​ 0u+{0}_{u}^{+}0u+​ $({}^{3}{\ensuremath{\Pi}}_{u})$ and 1S0+1D2{}^{1}{S}_{0}+{}^{1}{D}_{2}1S0​+1D2​ 0u+{0}_{u}^{+}0u+​ $({}^{1}{\ensuremath{\Sigma}}_{u}^{+})$ potential curves at short range and we build a mass-scaled interaction model that quantitatively reproduces the available 0u+{0}_{u}^{+}0u+​ and 1u{1}_{u}1u​ bound-state energies for the three stable bosonic isotopes. We also provide isotope-specific two-channel models that incorporate the rotational (Coriolis) mixing between the 0u+{0}_{u}^{+}0u+​ and 1u{1}_{u}1u​ curves which, while not mass scaled, are capable of quantitatively describing the vibrational splittings observed in experiment. We find that the use of state-of-the-art ab initio potential curves significantly improves the quantitative description of the Coriolis mixing between the two $\ensuremath{-}8$-GHz bound states in 88Sr^{88}\mathrm{Sr}88Sr over the previously used model potentials. We show that one of the recently reported energy levels in 84Sr^{84}\mathrm{Sr}84Sr does not follow the long-range bound-state series and theorize on the possible causes. Finally, we give the Coriolis-mixing angles and linear Zeeman coefficients for all of the photoassociation lines. The long-range van der Waals coefficients C6(0u+)=3868(50){C}_{6}({0}_{u}^{+})=3868(50)C6​(0u+​)=3868(50) a.u. and C6(1u)=4085(50){C}_{6}({1}_{u})=4085(50)C6​(1u​)=4085(50) a.u. are reported.