Spectroscopic determination of magnetic-field-dependent interactions in an ultracold Yb(${}^{3}P{}_2$)-Li mixture

We present experimental results on the inelastic and elastic interspecies interactions between ytterbium (Yb) in the metastable ${}^{3}P{}_2$ state loaded into a deep optical lattice and spin polarized lithium (Li) in its ground state. Focusing on the $m_J=0$ magnetic sublevel of $\mathrm{Yb}({}^{3}P{}_2$), bias magnetic fields between 20 and $800\mathrm{G}$ are investigated and significantly enhanced inelastic collision rates with high magnetic fields are found. In addition, by direct spectroscopy of the Yb Mott insulator immersed in the Li Fermi gas an upper boundary of the background scattering length of the $\mathrm{Yb}({}^{3}P{}_2,m_J=0)-\mathrm{Li}{(}^2{S}_{1/2},F=1/2,m_F=+1/2$) system is estimated, revealing the absence of useful Feshbach resonances. These observations are qualitatively consistent with the theoretical calculations.

Figure 1

(a) Quantum degenerate mixture of Yb and Li loaded into a 3D optical lattice. The effective lattice potential for Yb (solid line) is deep at $15E_R^{\mathrm{Yb}}$ and a Mott-insulator shell structure (blue and green dots) is formed. For clarity only lattice occupation numbers $n=1$ and 2 are shown. The effective Li potential (dashed line) is with only $0.7E_R^{\mathrm{Li}}$ shallow and Li unlocalized (red cloud). In the experiment the interactions between $\mathrm{Yb}({}^{3}P{}_2$) atoms (green dots) in $n=1$ sites and Li are investigated. (b) Yb level spectrum of importance to the experiment. The excitation laser (green) connects the ground to the metastable ${}^{3}P{}_2$ state. For imaging purposes (blue) two repumping lasers (red) are used to repopulate the ${}^{1}S_0$ state.

Figure 2

Experimental decay signal and lifetime determination. For the inelastic $\mathrm{Yb}({}^{3}P{}_2,m_J=0)-\mathrm{Li}(F=1/2,m_F=+1/2$) collisional process the decay of metastable Yb atoms is shown at magnetic bias field strength of 20 $\mathrm{G}$ (red circles) and 600 $\mathrm{G}$ (blue squares). Lines indicate exponential fits to the data where data points up to 5 and 2 $\mathrm{ms}$ (dashed lines), respectively, were evaluated. Lifetimes were found to be $10.7_{-0.8}^{+1.3}\mathrm{ms}$ and $1.4_{-0.1}^{+0.2}\mathrm{ms}$. The error bars indicate the standard deviation over typically five independent executions of the measurement.

Figure 3

Survey of inelastic collision rates for $\mathrm{Yb}({}^{3}P{}_2,m_J=0)-\mathrm{Li}{(}^2{S}_{1/2}$) collisions in magnetic bias field ranges between 20 and $800\mathrm{G}$. The Li sample is prepared in either the $F=1/2,m_F=\pm 1/2$ state (lower two panels) or the $F=3/2,m_F=\pm 3/2$ state (upper two panels). All panels are reproduced in the same scale and a smooth increase of the inelastic collision rates is observed in all four cases. No distinct resonance-like features are found that might indicate the presence of an underlying Feshbach resonance. See the main text for a discussion of the error bars. Also shown is the expected universal rate (green lines) and the shaded area (yellow) marks the parameter range in which additionally spectroscopic data on elastic properties was obtained; see Sec. 3b.

Figure 4

Direct spectroscopy of $\mathrm{Yb}({}^{3}P{}_2)-\mathrm{Li}(F=1/2,m_F=+1/2$) interspecies interaction. (a) Sketch of the measurement principle where a change in the interaction energy between Li (red) and Yb in either ${}^{1}S_0$ (blue) or ${}^{3}P{}_2$ (green) state leads to a shift of the transition energy (arrows). (b) Excitation spectra for singly occupied lattice sites at a lattice depth of $15E_R^{\mathrm{Yb}}$ and at $500\mathrm{G}$ magnetic bias field. With respect to the reference measurement without Li (red circles) a reduction of the peak height and a slight shift towards higher excitation frequencies in the case with Li (blue squares) is observed. The data are fitted by Gaussian functions (lines). Error bars denote the standard error from five measurements and the frequency detuning is set to zero when in resonance with the reference measurements. (c) Summary of the spectroscopic line shifts obtained in the range $50–800\mathrm{G}$. Data were taken in steps of $10\mathrm{G}$ and the frequency shifts with respect to a corresponding reference measurement without Li obtained by Gaussian fitting are reported here together with the fitting $1-\sigma$ error estimates. The dashed line is to mark vanishing frequency shifts. In the range $620–780\mathrm{G}$ a small positive frequency shift is observed (green line and shaded areas as $1-\sigma$ confidence interval).