Coherent Addressing of Individual Neutral Atoms in a 3D Optical Lattice

We demonstrate arbitrary coherent addressing of individual neutral atoms in a $5\times 5\times 5$ array formed by an optical lattice. Addressing is accomplished using rapidly reconfigurable crossed laser beams to selectively ac Stark shift target atoms, so that only target atoms are resonant with state-changing microwaves. The effect of these targeted single qubit gates on the quantum information stored in nontargeted atoms is smaller than $3\times {10}^{-3}$ in state fidelity. This is an important step along the path of converting the scalability promise of neutral atoms into reality.

Figure 1

(a) Diagram of addressing a $5\times 5\times 5$ array of neutral atoms. Each addressing beam can be parallel translated within $5\mu \mathrm{s}$ to any line of atoms, so that any site can be put at their intersection. The addressing beams are circularly polarized, and the 140 mG magnetic field is in the same plane. (b) The relevant part of the ground state energy level structure for addressing (not to scale). A target atom experiences twice the ac Stark shift of any other atom (its shift is illustrated by the orange dashed lines), so that, starting in the storage basis, $|3,0⟩$ and $|4,0⟩$, it alone is resonant with ${\omega }_1$. After it is transferred to the computation basis, $|3,1⟩$ and $|4,1⟩$, it alone is resonant with ${\omega }_2$.

Figure 2

(a) Probability that an atom makes a transition from $|4,0⟩$ to $|3,-1⟩$ as a function of the detuning of ${\omega }_1$ from the unshifted resonance. The orange points correspond to the four target sites in two planes addressed in this sequence, the blue points correspond to nontarget atoms traversed by addressing beams, and the green points correspond to all the other atoms. The solid lines are fits to Gaussians. The error bars are from counting noise. (b) Summed images of the raw signals from three planes using the value of ${\omega }_1$ that yields the orange peak in (a). Two sites in each of planes 1 and 3 are addressed in each implementation [labeled by (1, 1, 1), (3, 3, 1), (1, 3, 3), and (3, 1, 3)]. The signal in plane 2 is the out-of-focus light from the adjacent planes; out-of-focus atom images have nearly double the radius, the probability of them giving a false positive in our occupancy maps is below ${10}^{-6}$.

Figure 3

Fringe contrast for a spin-echo sequence on all the atoms. The fit exponential time constant is 7.4 s. Since the contrast is lost due to spontaneous emission, the rate of which depends on an atom’s vibrational state, the true function is more complicated. The insets are the unnormalized fringes at the indicated times, where the phase of the final $\pi /2$ pulse in $\pi /2\text{−}\pi \text{−}\pi /2$ is varied.

Figure 4

Arbitrary single qubit gates. (a) The addressing pulse sequence. The top row shows the timing of the microwave pulses, which have Blackman temporal profiles. Black corresponds to ${\omega }_0$, red to ${\omega }_1$, and purple to ${\omega }_2$. The timing gaps are enhanced for clarity. The second row shows the addressing beam pulses versus time, and the third and fourth rows show the corresponding addressing beam locations. The atom color scheme is that of Fig. 1. The second and fourth sets of pulses are “dummy” gates—they have no target atom. Their purpose is to cancel out the phase shifts on nontarget atoms. (b) A Bloch sphere representation of qubit rotations due to the ${\omega }_2$ pulses. The solid black arrow is the initial quantum state, the blue and red arrows correspond to torque vectors, the red and blue arcs are the Bloch vector paths during the gates, and the dashed black arrows are the final states, labeled I, II, and III. (c) Interference fringe due to gate I of Fig. 4. The orange circles are due to the four target atoms, the blue triangles are for line atoms, the pink squares are for nearest neighbors, and the green diamonds are for other atoms. The gate target is a $\pi$-shifted fringe. (d) Interference fringe due gate II of Fig. 4. The gate target is a $\pi /2$-shifted fringe. (e) Interference fringe due to gate III of Fig. 4. The gate target is a horizontal line of half the peak of the unaffected fringe.