Stabilization of multi-mode Schrodinger cat states via normal-mode dissipation engineering

Non-Gaussian quantum states have been autonomously stabilized in single- and two-mode circuit QED architectures via engineered dissipation. Here, we upgrade dissipation engineering to collective modes of resonator arrays and show how to stabilize multi-mode Schrodinger cat states, delocalized over an arbitrary number of cavities. We consider tailored dissipative coupling between resonators that are parametrically driven and feature an on-site nonlinearity, which is either a Kerr-type nonlinearity or an engineered two-photon loss. We find exact closed-form solutions for the two-dimensional steady-state manifold spanned by multi-mode cat states. We further show that, in the Zeno limit of strong dissipative coupling, multi-mode cat states can be deterministically prepared. Remarkably, engineered two-photon loss gives rise to a fast relaxation towards the steady state, protecting the state preparation against decoherence due to intrinsic single-photon losses and imperfections in tailored dissipative coupling. The relaxation time is independent of system size making the state preparation scalable. Multi-mode cat states are naturally endowed with a noise bias that increases exponentially with system size and can thus be exploited for enhanced robust encoding of quantum information.