Symmetry-engineered collective dark state in an open quantum system

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 generate subradiant states that decouple from the dissipative waveguide environment.
In our experiment we strongly couple two pairs of transmon qubits to the fundamental TE₀₁ mode of a rectangular waveguide. We show that the decay of the four qubit entangled dark state is strongly suppressed, exceeding the waveguide-limited lifetimes of individual qubits by two orders of magnitude (1/Γ_DS = 200/Γ₁). Furthermore, we show coherent control of the dark state by measuring the coherence time in a Ramsey experiment. The collective dark state is read out by probing the superradiant state via the waveguide. This proof-of-principle experiment paves the way towards implementations of quantum many-body simulations in open quantum systems.