Spin-dependent optical superlattice

We propose and implement a lattice scheme for coherently manipulating atomic spins. Using a vector light shift and a superlattice structure, we demonstrate experimentally its capability on addressing spins in double wells and square plaquettes with subwavelength resolution. The quantum coherence of spin manipulations is verified through measuring atom tunneling and spin exchange dynamics. Our experiment presents a building block for engineering many-body quantum states in optical lattices for realizing quantum simulation and computation tasks.

Figure 1

Schematic of experimental setup and spin-dependent optical potentials. (a) The 1D superlattice is formed by overlapping two lattices on a dichromatic mirror (DM). The incident polarization of the short lattice is controlled by an electro-optical modulator (EOM) and a quarter-wave plate (QWP). The polarization of the reflected laser is in mirror symmetry with that of the incident beam with respect to the $x-z$ plane. (b) The DWs are formed by a combination of short- and long-lattice potentials. The polarized short lattice leads to a shift of the potential minimum in opposite directions for $\left|\uparrow \right.〉$ and $\left|\downarrow \right.〉$. The long lattice provides a period doubling potential and breaks the symmetry of the transition frequency in the DWs. Here, the optical lattices in the $y$ and $z$ directions are not shown.

Figure 2

One-dimensional spin addressing. (a) Band mapping of the spin states in DWs. Atoms in the left and right wells are mapped onto different Bloch bands. We then spatially separate the spin states by a Stern-Gerlach pulse. The left (right) picture is after spin flipping of the atoms in the left (right) sites. In the central picture, all the atoms are flipped by the MW pulse. (b) Spectroscopy of the microwave transitions. The red and blue curves are the transition ratios with and without the spin-dependent effect, respectively. The splitting of the resonance frequency between the DW sites is 18.7(1) kHz.

Figure 3

Two-dimensional spin addressing. (a) Lattice sites are marked as A–D in each square plaquette. The band mapping pattern shows the distribution of each site in momentum space. (b) The experimental sequence of 2D spin flipping. Before each MW pulse, the quantization axis is set and energy splitting is established. The first pulse flips sites C and D, the second pulse flips sites A and D, and the third and fourth pulses recover the initial state. (c) Band mapping pattern after 2D spin addressing. $\left|\uparrow \right.〉$ and $\left|\downarrow \right.〉$ states are spatially separated by a Stern-Gerlach pulse. The pattern after the second MW pulse shows both diagonal sites A and C transit to $\left|\uparrow \right.〉$.

Figure 4

Dynamics of (a) single-atom tunneling and (b) superexchange. (a) The quantum states in DWs are initialized to $\left|0,\downarrow \right.〉$ by removing the atoms in the left sites. We measure the tunneling dynamics by monitoring the occupancy probability of atoms in the left sites. The oscillation lasts for six cycles with a period of 1.32 ms. (b) Free evolution and suppressions of superexchange dynamics. The red curve is under the Hubbard parameters of tunneling $J/h=103\left(2\right)\mathrm{Hz}$, on-site interaction $U/h=1191\left(2\right)\mathrm{Hz}$, while the blue and the gray curves correspond to the dynamics with extra energy shifts of $\delta /h=60\mathrm{Hz}$ and $\delta /h=300\mathrm{Hz}$, respectively. The error bars represent a $\pm 1\sigma$ standard deviation.