Abstract
Non-Gaussian quantum states have been deterministically prepared and autonomously stabilized in single- and two-mode circuit quantum electrodynamics architectures via engineered dissipation. However, it is currently unknown how to scale up this technique to multi-mode non-Gaussian systems. Here, we upgrade dissipation engineering to collective (normal) modes of nonlinear resonator arrays and show how to stabilize multi-mode Schrodinger cat states. These states are multi-photon and multi-mode quantum superpositions of coherent states in a single normal mode 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. For both types of nonlinearity, we find the same exact closed-form solutions for the two-dimensional steady-state manifold spanned by superpositions of multi-mode Schrodinger cat states. We further show that, in the Zeno limit of strong dissipative coupling, the even parity multi-mode cat state can be deterministically prepared from the vacuum. 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, which sets in at longer times. 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.
Highlights
Schrödinger cat states—quantum superpositions of macroscopically distinct states—are a fundamental resource for quantum communication [1], quantum metrology [2,3,4], and quantum computation [5,6,7]
In the last section we showed that the steady states of Eq (3) belong to a decoherence-free subspace (DFS) spanned by multimode cat states
We showed that a two-dimensional manifold spanned by superpositions of multimode Schrödinger cat states can be stabilized in an array of resonators coupled via nonlocal dissipation
Summary
Schrödinger cat states—quantum superpositions of macroscopically distinct (or “classical”) states—are a fundamental resource for quantum communication [1], quantum metrology [2,3,4], and quantum computation [5,6,7]. The dissipative preparation of single-mode Schrödinger cat states using engineered twophoton loss and two-photon (parametric) drive was first envisioned in Ref. In both cases, the only source of coupling is provided by engineered nonlocal dissipation connecting neighboring pairs of modes. The only source of coupling is provided by engineered nonlocal dissipation connecting neighboring pairs of modes This kind of nonlocal dissipation has recently been considered in the proposal for the generation of two-mode Schrödinger cat states [33] and in several other contexts, e.g., to realize nonreciprocal photon transport in a pair of modes [31] or in cavity arrays [34,35]. The two-photon drive H G corresponds to the creation of a photon pair with a total quasimomentum θ
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