Abstract
We examine coherent population trapping in a circuit-QED system consisting of an Al/${\mathrm{AlO}}_{x}$/Al transmon qubit embedded in an Al three-dimensional cavity. By engineering the dissipation rate of the cavity to be much larger than that of the qubit and continuously pumping a two-photon process to an excited state of the cavity-qubit system, we are able to invert the population into the qubit excited state with a fidelity of 94%. Applying a second continuous drive tone at the dressed cavity frequency forms an effective $\mathrm{\ensuremath{\Lambda}}$ system and enables us to coherently trap the system in a dark state formed from a superposition of the excited and ground states of the qubit. By performing quantum state tomography we demonstrate that the position of the dark state on the Bloch sphere can be controlled by changing the relative amplitudes and phases of the two drives.
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