Dissipative production of a maximally entangled steady state

We combine unitary processes with engineered dissipation into a zero-temperature bath to deterministically produce and stabilize an approximate Bell state of two trapped-ion qubits independent of their initial state [arXiv:1307.4443]. We implement the process on a $^9$Be$^+$-$^{24}$Mg$^+$-$^{24}$Mg$^+$-$^9$Be$^+$ four-ion chain in a linear radio-frequency Paul trap. The two $^9$Be$^+$\% ions serve as qubit ions while the two $^{24}$Mg$^+$ ions are used for sympathetic cooling as the zero-temperature bath. We simultaneously apply a combination of a unitary process consists of microwave and laser fields on $^9$Be$^+$ ions, and dissipative processes of optical pumping on $^9$Be$^+$\% ions and sympathetic cooling on $^{24}$Mg$^+$ ions. We realize maximally entangled steady states with a fidelity of F = 0.75(3). We also demonstrate that a sequential stepwise application of unitary and dissipative process can speed up the dynamics of the scheme and achieve a fidelity of F = 0.89(2) after approximately 30 repetitions. In both cases, the errors can be attributed to known experimental imperfections.