Demonstration of a simplified protocol for dissipative entanglement of two trapped-ion qubits

Quantum systems may be pumped into entangled states using dissipative dynamics. In this approach, dynamics are engineered that have a target entangled state as their sole attractor in the absence of experimental imperfections. Realization of these dynamics leads population to build up in the target state over time. The dissipative approach has lower sensitivity to certain errors when compared to unitary entanglement-generation protocols, and it can be used to prepare and stabilize entangled resource states in the presence of noise. We demonstrate a protocol for dissipative generation of an entangled state of two trapped ⁹Be⁺ ions. This protocol was proposed in Horn et al., NJP 20, 123010 (2018), and improves upon the one demonstrated in Lin et al., Nature 504, 415-418 (2013) by eliminating the need for sympathetic cooling. The protocol uses always-on couplings that include stimulated-Raman sideband transitions, repumping through an electronic excited state, and microwave carrier transitions to achieve steady-state entanglement. We discuss advantages of the protocol, including robustness against fluctuations in magnetic fields. We also discuss limiting errors, including heating of the ion crystal, spontaneous emission, and differential effects including magnetic field gradients and differential ac Stark shifts.