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arXiv:1505.00682 · New Journal of Physics

Mixing of ${0}^{+}$ and ${0}^{-}$ observed in the hyperfine and Zeeman structure of ultracold ${\mathrm{Rb}}_{2}$ molecules

Markus Deiß, Björn Drews, Johannes Hecker Denschlag, Eberhard Tiemann

Published Aug 18, 2015• 13 citations
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Abstract

We study the combination of the hyperfine and Zeeman structure in the spin–orbit coupled complex of . For this purpose, absorption spectroscopy at a magnetic field around G is carried out. We drive optical dipole transitions from the lowest rotational state of an ultracold Feshbach molecule to various vibrational levels with symmetry of the complex. In contrast to previous measurements with rotationally excited alkali-dimers, we do not observe equal spacings of the hyperfine levels. In addition, the spectra vary substantially for different vibrational quantum numbers, and exhibit large splittings of up to MHz, unexpected for states. The level structure is explained to be a result of the repulsion between the states and of , coupled via hyperfine and Zeeman interactions. In general, and have a spin–orbit induced energy spacing Δ , that is different for the individual vibrational states. From each measured spectrum we are able to extract Δ , which otherwise is not easily accessible in conventional spectroscopy schemes. We obtain values of Δ in the range of GHz which can be described by coupled channel calculations if a spin–orbit coupling is introduced that is different for and of .

DOI
10.1088/1367-2630/17/8/083032

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Mixing of 0+{0}^{+}0+ and 0−{0}^{-}0− observed in the hyperfine and Zeeman structure of ultracold Rb2{\mathrm{Rb}}_{2}Rb2​ molecules
We study the combination of the hyperfine and Zeeman structure in the spin–orbit coupled complex of . For this purpose, absorption spectroscopy at a magnetic field around G is carried out. We drive optical dipole transitions from the lowest rotational state of an ultracold Feshbach molecule to various vibrational levels with symmetry of the complex. In contrast to previous measurements with rotationally excited alkali-dimers, we do not observe equal spacings of the hyperfine levels. In addition, the spectra vary substantially for different vibrational quantum numbers, and exhibit large splittings of up to MHz, unexpected for states. The level structure is explained to be a result of the repulsion between the states and of , coupled via hyperfine and Zeeman interactions. In general, and have a spin–orbit induced energy spacing Δ , that is different for the individual vibrational states. From each measured spectrum we are able to extract Δ , which otherwise is not easily accessible in conventional spectroscopy schemes. We obtain values of Δ in the range of GHz which can be described by coupled channel calculations if a spin–orbit coupling is introduced that is different for and of .
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We spectroscopically investigate the hyperfine, rotational, and Zeeman structure of the vibrational levels ${v}^{\ensuremath{'}}=0,7,13$ within the electronically excited $c{\phantom{\rule{0.222222em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}$ state of 87Rb2^{87}\mathrm{Rb}_{2}87Rb2​ for magnetic fields of up to 1000G1000\phantom{\rule{0.28em}{0ex}}\text{G}1000G. As spectroscopic methods we use short-range photoassociation of ultracold Rb atoms as well as photoexcitation of ultracold molecules which have been previously prepared in several well-defined quantum states of the $a{\phantom{\rule{0.222222em}{0ex}}}^{3}\mathrm{\ensuremath{\Sigma}}{}_{u}^{+}$ potential. As a by-product, we present optical two-photon transfer of weakly bound Feshbach molecules into $a{\phantom{\rule{0.222222em}{0ex}}}^{3}\mathrm{\ensuremath{\Sigma}}{}_{u}^{+}$, v=0v=0v=0 levels featuring different nuclear spin quantum numbers. A simple model reproduces well the molecular level structures of the $c{\phantom{\rule{0.222222em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}$ vibrational states and provides a consistent assignment of the measured resonance lines. Furthermore, the model can be used to predict the relative transition strengths of the lines. From fits to the data we extract for each vibrational level the rotational constant, the effective spin-spin interaction constant, as well as the Fermi contact parameter and the anisotropic hyperfine constant. In an alternative approach, we perform coupled-channel calculations where we fit the relevant potential energy curves, spin-orbit interactions, and hyperfine functions. The calculations reproduce the measured hyperfine level term frequencies with an average uncertainty of $\ifmmode\pm\else\textpm\fi{}9\phantom{\rule{0.28em}{0ex}}\mathrm{MHz}$, similar as for the simple model. From these fits we obtain a section of the potential energy curve for the $c{\phantom{\rule{0.222222em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}_{g}{}^{+}$ state which can be used for predicting the level structure for the vibrational manifold ${v}^{\ensuremath{'}}=0$ to 13 of this electronic state.
Within the scope of this thesis, the production of ultracold molecules at a temperature of a few µK with various isotopes of rubidium (Rb) and ytterbium (Yb) was examined by means of photoassociation spectroscopy and magnetic Feshbach resonances in combined conservative traps. The long-term goal of this experiment is the production of ultracold RbYb molecules in the rovibronic ground state. It was possible to produce electronically excited ^{87}Rb ^{176}Yb molecules in a novel hybrid trap (HT) at a combined temperature of 1.7 µK by means of 1-photon photoassociation close to the Rb D1 line at 795 nm. This HT takes advantage of the different magnetic properties of Rb and Yb and allows for independent trapping and manipulation of the atomic species. It combines an Ioffe-Pritchard type magnetic trap for Rb and a near-resonant optical dipole trap for Yb. The excited molecular ^2 Pi_1/2 state could be characterized further extending previous works in a combined MOT and vibrational levels reaching binding energies up to E_b=-h x 2.2 THz could be assigned by trap-loss spectroscopy. Almost every detected vibrational state consists of two resonances that could be assigned to the molecular analogue of the hyperfine structure of ^{87}Rb. An important experimental observation is a decrease in hyperfine splitting with increasing binding energy of a vibrational level. For the deepest found vibrational state the hyperfine splitting amounts only 70 % of the atomic value (817 MHz) which emphasizes a gradual passage from weakly to tightly bound molecules. Furthermore, detailed attempts were undertaken to induce magnetic Feshbach resonances in ^{85}Rb and different Yb isotopes, especially ^{171}Yb in a crossed optical dipole trap at 1064 nm at temperatures of 10 µK. For this purpose, a homogeneous magnetic field was applied and scanned in small steps over the range of 495 G... 640 G. Unfortunately, our efforts were without success. Additionally, well known as well as not yet reported Rb_2 Feshbach resonances in ^{85}Rb and ^{87}Rb were detected. These resonances allowed for a detailed analysis of the typical behaviour of Feshbach resonances. The first experimental realization of photoassociation spectroscopy in a conservative is also a major step towards the ultimate project goal of producing ultracold RbYb molecules in the electronic ground state. A spatial confinement, which is in principle possible in the HT, is a prerequisite for transferring the molecules to the rovibronic ground state, e.g. with the help of a STIRAP process.
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