Realization of dark state in a three-dimensional transmon superconducting qutrit

We realize the dark state in a three-dimensional transmon superconducting qutrit that consists of three cascading energy levels: |0⟩, |1⟩, and |2⟩. When the system is simultaneously driven with two tone microwaves on resonance with |0⟩, |1⟩ and |1⟩, |2⟩, respectively, it is found that the state of the system will generally evolve in time domain. However, the qutrit state is frozen-out if it is initialized in a dark state for corresponding drive amplitudes. We observe this freeze-out phenomenon by changing the amplitude of the microwaves while fixing the initial state or vice versa.