Sequential Generation of Entangled Multiqubit States

We consider the deterministic generation of entangled multiqubit states by the sequential coupling of an ancillary system to initially uncorrelated qubits. We characterize all achievable states in terms of classes of matrix-product states and give a recipe for the generation on demand of any multiqubit state. The proposed methods are suitable for any sequential generation scheme, though we focus on streams of single-photon time-bin qubits emitted by an atom coupled to an optical cavity. We show, in particular, how to generate familiar quantum information states such as $W$, Greenberger-Horne-Zeilinger, and cluster states within such a framework.

Figure 1

A trapped $D$-level atom is coupled to a cavity qubit, determined by the energy eigenstates $|0⟩$ and $|1⟩$. After arbitrary bipartite source-qubit operations, photonic time bins are sequentially and coherently emitted at the cavity output, creating a desired entangled multiqubit stream.

Figure 2

(a) Atomic level structure: levels $|a⟩$, ($|b⟩$), and $|u⟩$ are coupled by a laser (cavity mode) off resonance. (b) After adiabatic elimination of the upper state $|u⟩$, we are left with an effective Jaynes-Cummings interaction, coupling states $|a,n⟩$ and $|b,n+1⟩$. The ac Stark shift introduced in the energy difference of these levels, $n{g}^2/\Delta$, and the Jaynes-Cummings coupling, $\sqrt{n+1}{\Omega }_{0}g/2\Delta$, depend on the photon number, $n$.