Sublattice Addressing and Spin-Dependent Motion of Atoms in a Double-Well Lattice

We load atoms into every site of an optical lattice and selectively spin flip atoms in a sublattice consisting of every other site. These selected atoms are separated from their unselected neighbors by less than an optical wavelength. We also show spin-dependent transport, where atomic wave packets are coherently separated into adjacent sites according to their internal state. These tools should be useful for quantum information processing and quantum simulation of lattice models with neutral atoms.

Figure 1

(a) Schematic of the 2D horizontal lattice setup. (b) Example of a double-well optical lattice potential in the horizontal plane. Each copy of the unit cell (indicated by the rectangular box) is an isolated system, and atoms in the $L$ sublattice can be addressed by rf independently from atoms in the $R$ sublattice (and vice versa).

Figure 2

Calculated double-well potentials along $x$ for different configurations (a)–(d) of the laser light. Dashed lines represent the scalar potential $U_s$ seen by atoms in the $|m_F=0⟩$ state, solid lines show the state-dependent potential $U_s+U_v$ seen by atoms in the $|m_F=-1⟩$ state. (The large constant Zeeman shift has been subtracted.) The energy levels for the first two vibrational eigenstates of each spin are also shown as horizontal lines, with the position and the length of the lines representing the center-of-mass position and the rms full width of the corresponding wave functions. ($\delta x/\lambda =-0.5$ corresponds to the $\lambda$-lattice minima exactly half way between the $\lambda /2$-lattice minima.)

Figure 3

Measured population in $|-1⟩$ in the $L$ (circles) and $R$ (squares) sublattice after the rf pulse. The lines are fits to the expected line shape. The resonant frequency in the spin-dependent $R$ sublattice (34.178 MHz) is shifted by the vector light shift from the frequency in the spin-independent $L$ sublattice (34.146 MHz).

Figure 4

(a) Fraction of atoms in the $R$ sublattice at the end of the spin-dependent transport sequence (see text) for atoms in the $|-1⟩$ state (filled squares) and $|0⟩$ state (open squares) as a function of the relative position $\delta x/\lambda$ between the $\lambda$-lattice and the $\lambda /2$-lattice. The dashed vertical line indicates the best selective transfer: $\delta x=-0.42\lambda$, where atoms in $|0⟩$ are sorted into $R$ sites and atoms in $|-1⟩$ are sorted into $L$ sites, each with 92(2)% probability. (b) Using spin-dependent transport to measure spin populations after applying an rf pulse to atoms in the $\lambda$-lattice. Atoms in $|-1⟩$ are in the $L$ sublattice after transport. During the rf pulse, atoms oscillate between $|-1⟩$ and $|0⟩$. The solid line is a fit to a damped sine.

Figure 5

(a) Experimental sequence for demonstrating coherence in spin-dependent dynamics. Following the first $\pi$ pulse, wave functions are spin-dependently split into $L$ and $R$ sites. A $\pi$ pulse is applied to atoms in $L$ sites at the end of the transport so that all atoms end in the same final spin state. (b) The double-slit diffraction observed after the lattice is snapped off and after time-of-flight, indicating coherence after spin-dependent transport. (c) Integrated density profile of the double-slit diffraction pattern in (b).