Quantum Computing with Alkaline-Earth-Metal Atoms

We present a complete scheme for quantum information processing using the unique features of alkaline-earth-metal atoms. We show how two completely independent lattices can be formed for the ${}^{1}S_0$ and ${}^{3}P_0$ states, with one used as a storage lattice for qubits encoded on the nuclear spin, and the other as a transport lattice to move qubits and perform gate operations. We discuss how the ${}^{3}P_2$ level can be used for addressing of individual qubits, and how collisional losses from metastable states can be used to perform gates via a lossy blockade mechanism.

Figure 1

Quantum computing with independent lattices: (a) Qubits in long-lived states in a storage lattice are transferred to a completely independent transport lattice for gate operations between distant qubits, or addressed individually by coupling to a level that is shifted by a gradient field. (b) This can be accomplished by encoding qubits in nuclear spin states, producing independent lattices for the ${}^{1}S_0$ and ${}^{3}P_0$ levels, and using ${}^{3}P_2$ for individual addressing.

Figure 2

(a) Energy level diagram showing how independent optical lattices can be produced for the ${}^{1}S_0$ and ${}^{3}P_0$ levels by finding wavelengths where the polarizability of each of the levels is zero and the other nonzero. (b) ac polarizability of ${}^{1}S_0$ and ${}^{3}P_0$ levels near 627 nm. (c) ac polarizability of ${}^{1}S_0$ and ${}^{3}P_0$ levels near 689 nm. (d) ac polarizability of different $m_F$ sublevels of the ${}^{3}P_2$, $F=13/2$ hyperfine level for $\pi$-polarized light at 627 and 689.2 nm.

Figure 3

(a) Two-qubits levels in a lossy blockade gate, contrasting behavior for the initial state $|1,0⟩$, where the atoms are separated, and $|0,1⟩$, where the atoms undergo collisions in the excited state on the same site. Atoms are (i) excited from the state $|0⟩\to |0x⟩$, and then (ii) coupled from $|1⟩\to |1x⟩$. The second process is blocked for the initial state $|0,1⟩$ by elastic and inelastic collisional interactions. (b) Loss probability during step (ii) up to time $t$ with the initial state $|0x,1⟩$ for $\Gamma /\Omega =1$ (solid line), 10 (dashed), 100 (dash-dotted), and 1000 (dotted), with ${\Delta }_U=0$. (b) Loss probability up to the gate completion time $\Omega t=2\pi$ for $\Delta /\Omega =0$ (solid), 1 (dashed), 10 (dash-dotted), and 100 (dotted).