Preparation of Dicke States in an Ion Chain

TL;DR

This paper presents a method for preparing Dicke states in trapped ion chains by converting motional excitations into collective spin states, with theoretical fidelity analysis and experimental demonstration for two ions.

Contribution

The paper introduces a new protocol for Dicke state preparation in ion chains using global laser pulses and motional state manipulation, validated through experiment.

Findings

Fidelity limits are numerically calculated for the protocol.

Small deviations from ideal Dicke states are observed for m=1 and m=2.

Successful experimental preparation of the Dicke state |2,1> in two ions.

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 state $\D{2}{1}$ in two $^{25}$Mg$^+$ target ions trapped simultaneously with an $^{27}$Al$^+$ ancillary ion.