Magnetoassociation of a Feshbach molecule and spin-orbit interaction between the ground and electronically excited states

By preparing a cold-atom ensemble of mixtures of the ground ${}^{1}S_0$ and metastable ${}^{3}P_2$ states of ytterbium atoms ${}^{171}\mathrm{Yb}$, we successfully associate a Feshbach molecule ${}^{171}\mathrm{Yb}_2$ with one ${}^{171}\mathrm{Yb}$ atom in its electronically excited state and another one in the ground state, by sweeping a magnetic field across a Feshbach resonance. The atom-molecule conversion efficiency reaches about 50%, confirmed by a separate image of atoms and molecules with a Stern-Gerlach effect and an atom loss measurement. In addition, we successfully implement a spin-orbit coupling with a one-photon process between the ${}^{3}P_2$ (pseudo-spin-up) and ground ${}^{1}S_0$ (pseudo-spin-down) states of a Yb atom. As a benchmark, we observe a spin-momentum locking behavior at a large Rabi frequency. The achieved successful production of Feshbach molecules, along with the implementation of spin-orbital coupling between the ${}^{1}S_0$ and ${}^{3}P_2$ states, provides an important step towards the study of a topological superfluid.

Figure 1

Magnetoassociation of Feshbach molecules and the detection with a Stern-Gerlach technique. (a) Scattering length as a function of a magnetic field calculated using the parameters taken from Ref. [9]. A narrow resonance at 6 G is omitted in this figure. (b) Binding energy of molecules as a function of a magnetic field. Note that the binding energy $E_b$ is calculated from the scattering length $a$ by the universal relation $E_b={\hslash }^2/\left(m{a}^2\right)$. A narrow resonance at 6 G is also omitted in this figure. Feshbach molecules are associated by an adiabatic sweep of a magnetic field from 7.0 G to 6.2 G. (c) Absorption imaging of $|A\rangle$ and $|B\rangle$ atoms before a magnetic field sweep. The TOF is 10 ms. (d) Absorption imaging of $|A\rangle$ atoms, $|B\rangle$ atoms, and molecules after a magnetic field sweep from 7 G to 6.2 G. (e) Absorption imaging of $|A\rangle$ atoms and ${}^{1}S_0$ component of molecules after a magnetic field sweep from 7 G to 6.2 G.

Figure 2

Time sequence for magnetoassociation of Feshbach molecules and the detection with a Stern-Gerlach technique. See text for details.

Figure 3

Time sequence for magnetoassociation of Feshbach molecules and the detection with a MOT. See text for details.

Figure 4

Atom number in the ${}^{1}S_0$ and ${}^{3}P_2$ states as a function of the holding time after the magnetic sweep from 7.466 G to final magnetic fields of (a) 7.5 G, (b) 6.6 G, (c) 6.2 G, and (d) 5.5 G. The fitting lines are also shown. Gray (yellow) shade shows the atom (molecular) component. The fitting parameters are shown in Table 1. See text for details. The insets show the long-time behaviors.

Figure 5

(a) Experimental setup and (b) time sequence for implementation of spin-orbital coupling with a one-photon process using ${}^{174}\mathrm{Yb}$. See text for details.

Figure 6

Quasimomentum distributions. (a)–(c) Integrated optical density for the ${}^{1}S_0$ state as a function of quasimomentum. (d)–(f) Atom images for the ${}^{1}S_0$ state in real momentum. (g)–(i) Atom images for the ${}^{3}P_2$ state in real momentum. (j)–(l) Integrated optical density for the ${}^{3}P_2$ state as a function of quasimomentum. (a), (d), (g), (j) $-8$ kHz detuning. (b), (e), (h), (k) 0 kHz detuning. (c), (f), (i), (l) +8 kHz detuning.

Figure 7

Quasimomentum distributions of integrated optical density, which are obtained by integrating the optical densities along the $z$ axis, as a function of laser detuning in the (a) ${}^{1}S_0$ and (b) ${}^{3}P_2$ states.

Figure 8

Time sequence for implementation of spin-orbital coupling with a one-photon process using ${}^{171}\mathrm{Yb}$. See text for details.

Figure 9

Spin-momentum locking. (a) Absorption images of the ${}^{1}S_0$ ($|C\rangle$) and ${}^{3}P_2$ ($|B\rangle$) states for various Rabi frequencies. (b) Schematic view of the experimental configuration. (c) Center-of-mass positions of an atom cloud of $|C\rangle$ (asterisk, blue) and $|B\rangle$ (open box, red), obtained by fitting using a Gaussian function. Solid lines with blue and red are the theoretically calculated center-of-mass position of an atom cloud for $|C\rangle$ and $|B\rangle$, respectively, under the assumptions of a Gaussian function for the atom distribution and 150 nK for the atom temperature. (d)–(g) Energy dispersions. See the text for details. The solid lines correspond to $E_{\pm }$ in the presence of SOC and dotted lines are those without SOC. The colors of red and blue indicate the compositions of $\left|B\right.〉$ and $\left|C\right.〉$ states, respectively.