Observation of spin-exchange dynamics between itinerant and localized ${}^{171}\mathrm{Yb}$ atoms

We report on the observation of the spin-exchange dynamics of ${}^{171}\mathrm{Yb}$ atoms in the ground state ${}^1{S}_0$ and in the metastable state ${}^3{P}_0$. We implement the mixed-dimensional two-orbital system using near-resonant and magic-wavelength optical lattices, where the ${}^1{S}_0$ and ${}^3{P}_0$ atoms are itinerant in a one-dimensional tube and localized in three dimensions, respectively. By exploiting an optical Stern-Gerlach method, we observe the spin depolarization of the ${}^1{S}_0$ atoms induced by the spin-exchange interaction with the ${}^3{P}_0$ atom. Our work could pave the way to the quantum simulation of the Kondo effect.

Figure 1

Schematic diagram of experiment. (a) Relevant energy diagram of a Yb atom. (b) Schematic illustration of beam configuration. The polarization of the clock excitation light is perpendicular to the quantization axis defined by the magnetic field, and it amounts to an equal mixture of ${\sigma }_{+}$ and ${\sigma }_{-}$ polarization. The circularly polarized OSG light propagates along the quantization axis. (c) Schematic illustration of the experimental procedure. (1) Initially, some fraction of the atoms in the $\left|g\downarrow \right.〉$ state (a green ball) are excited to the $\left|e\uparrow \right.〉$ state (a yellow ball) in a magnetic field of 30 G. The upper figure shows the schematic representation of the optical lattice potentials for the $\left|g\right.〉$ atom (a green curve) and the $\left|e\right.〉$ atom (a yellow curve). (2) After the excitation, a magnetic field is lowered to 0.5 G, and the spin-exchange dynamics is started. (3) After the hold time, the population of the atoms in $\left|g\uparrow \right.〉$ and in $\left|g\downarrow \right.〉$ is detected with an OSG technique. The upper figure shows the spin-dependent optical gradient potential to spatially separate the $\left|g\uparrow \right.〉$ atom and the $\left|g\downarrow \right.〉$ atom. The lower figure shows a typical example of the simultaneous observation of both spin states in the false color TOF image of the ${}^{171}\mathrm{Yb}$ gas in the $\left|g\right.〉$ state subjected to the OSG light.

Figure 2

Observation of spin-exchange dynamics. (a) Time evolution of the spin polarization of the $\left|g\right.〉$ atoms $\mathrm{\Delta }{N}_g/N_g$ with the different excitation rates to the $\left|e\right.〉$ state: $r=0.56$, 0.49, 0.41, and 0.31. Error bars show the standard deviations of the mean values obtained by averaging 10 measurements. Solid lines represent fits to the data with Eqs (3, 4, 5, 6). False color time-of-flight images of the $\left|g\right.〉$ atoms after the spin-exchange dynamics with $r=0.56$ are shown. The left and right figures correspond to the hold time of 3 and 68 ms, respectively. (b) Spin-exchange rate ${\mathrm{\Omega }}_{\mathrm{ex}}$ as a function of the excitation rate. Error bars are $1\sigma$ confidence intervals of the data fits. The solid line represents linear fits to the data.

Figure 3

Magnetic-field dependence of spin-exchange dynamics with the ${}^3{P}_0$ excitation rate $r=0.56$. Error bars show the standard deviations of the mean values obtained by averaging 10 measurements. In this experiment, the initial state of the exchange dynamics is prepared by the excitation $\left|g\uparrow \right.〉\to \left|e\uparrow \right.〉$ of the spin-balanced ${}^{171}\mathrm{Yb}$ atoms using $\pi$-polarized light since this scheme results in reduced uncertainty.