Coherent control of a symmetry-engineered multi-qubit dark state in waveguide quantum electrodynamics

The coherence properties of an atom or superconducting qubit strongly depend on the electromagnetic environment. Typical circuit QED experiments protect the qubit mode from decay into dissipative modes by placing it into a cavity. Effectively, a reduction of the available mode density reduces the free-space spontaneous emission rate of the qubit. In waveguide QED the qubit is strongly coupled to a continuous mode spectrum, thus it decays rapidly. Collective effects between multiple qubits can be utilized to create subradiant states that decouple from the dissipative waveguide environment. In our experiment we strongly couple two pairs of transmon qubits to the fundamental propagating mode of a rectangular waveguide. We show that the decay of the four-qubit dark state is strongly suppressed, exceeding the waveguide-limited lifetimes of the individual qubits by two orders of magnitude [1]. This four-qubit dark-state can be coherently controlled by utilizing a novel driving scheme relying on the symmetries of the quantum states. The additionally appearing bright state can be used to read out the qubit encoded in the dark state. We characterize the dark state by measuring the coherence time in a Ramsey experiment and perform phase sensitive spectroscopy on the two-excitation manifold which can only be accurately modeled by considering the bosonic nature of the transmons [2]. In the future such a platform can be used to mediate entanglement between remote parts of a superconducting qubit quantum processor and implement quantum information protocols with collective states.