Preparation of Dicke states in an ion chain

Abstract

We have investigated theoretically and experimentally a method for preparing Dicke states in trapped atomic ions. We consider a linear chain of $N$ ion qubits that is prepared in a particular Fock state of motion $|m⟩$. The $m$ phonons are removed by applying a laser pulse globally to the $N$ qubits and converting the motional excitation to $m$ flipped spins. The global nature of this pulse ensures that the $m$ flipped spins are shared by all the target ions in a state that is a close approximation to the Dicke state $|{D}_{N}^{(m)}⟩$. We calculate numerically the fidelity limits of the protocol and find small deviations from the ideal state for $m=1$ and $m=2$. We have demonstrated the basic features of this protocol by preparing the Bell state $|{D}_{2}^{(1)}⟩$ in two ${^{25}\text{M}\text{g}}^{+}$ target ions trapped simultaneously with an ${^{27}\text{A}\text{l}}^{+}$ ancillary ion.