Figure 1

(a) Energy diagram of singly and doubly occupied sites in an optical lattice. The doubly occupied site has on-site energy shifts $U_{gg}$ and $U_{ge}$ due to the interatomic interaction between two ground state atoms and between ground and excited state atoms, respectively. These energy shifts are revealed by a resonance shift of an excitation spectrum of the doubly occupied sites compared to that of the singly occupied sites. The interatomic potential between the atoms in the ${}^{1}S_0$ and ${}^{3}P_2$ states reflects the anisotropy interaction between them. (b) Relevant energy levels of a Yb atom for the spectroscopy.Reuse & Permissions

Figure 2

(a) Excitation spectra for ${}^{3}P_2(m_J=+2)$ state of ${}^{174}\mathrm{Yb}$ at various magnetic field strengths below 1 G. The insets show enlarged views of low frequency side of the corresponding spectra. The arrows indicate the resonances from the doubly occupied sites. The Zeeman shift in each spectrum is subtracted and the spectra are shifted vertically for clarity. The solid lines denote the fits with Gaussian functions for each of the resonances (see text). Plots of resonance peak positions (b) as a function of a magnetic field and (c) as a function of a scattering length $a_{ge}$ evaluated by using the analytic formula Eq. (2). Here $a_0$ is the Bohr radius. The rectangles denote the resonances for the singly occupied sites and excitations to the higher vibrational state, and the circles for the doubly occupied sites. The analytical curve based on Eq. (2) is indicated by the solid line, and zero and the trap frequency are indicated by the dashed lines. The error bars in (b) and (c) represent the standard error of the Gaussian fits. (d) Evaluated scattering length $a_{ge}$ as a function of a magnetic field. The solid line denotes a fit with a function $a_{ge}(B)=a_{bg}-(a_{bg}\Delta )/(B-B_0)$, with $a_{bg}=-3.4\pm 2.5\mathrm{nm}$, $\Delta =2.3\pm 1.6\mathrm{G}$, and $B_0=360\pm 10\mathrm{mG}$.Reuse & Permissions

Figure 3

(a) Resonance peak positions for ${}^{170}\mathrm{Yb}$ $[{}^{1}S_0\leftrightarrow {}^{3}P_2(m_J=-2)]$ as a function of a magnetic field. Circles and rectangles denote the resonances in the same manner as in Fig. 2b. (b) Evaluated scattering length $a_{ge}$ between ${}^{170}\mathrm{Yb}$ atoms in the ${}^{1}S_0$ and ${}^{3}P_2(m_J=-2)$ states. The solid line denotes a fit with the same form of the function $a_{ge}(B)$ as introduced in Fig. 2d with $a_{bg}=6.3\pm 0.8\mathrm{nm}$, $\Delta =2.1\pm 0.3\mathrm{G}$, and $B_0=1.12\pm 0.01\mathrm{G}$.Reuse & Permissions

Figure 4

Interatomic potential with an anisotropic electronic interaction including the Zeeman shift. The magnetic fields are (a) 1.1 G and (b) 360 mG, corresponding to the resonance values of ${}^{170}\mathrm{Yb}$ and ${}^{174}\mathrm{Yb}$. Dashed lines with zero energy indicate the energy of the entrance channel for each case. In this calculation, we take the values of the van der Waals coefficients of $C_6^{\Sigma }$ and $C_6^{\Pi }$ as 3500 and 2500 a.u., respectively, as typical ones [29].Reuse & Permissions