Experimental Realization and Characterization of Stabilized Pair-Coherent States

The pair-coherent state (PCS) is a theoretical extension of the Glauber coherent state to two harmonic oscillators. It is an interesting class of non-Gaussian continuous-variable entangled state and it is also at the heart of a promising quantum error-correction code: the pair-cat code. Here, we report an experimental demonstration of the pair-coherent state of microwave photons in two superconducting cavities. We implement a cross-cavity pair-photon driven-dissipation process, which conserves the photon-number difference between cavities and stabilizes the state to a specific complex amplitude. We further introduce a technique of quantum subspace tomography, which enables direct measurements of individual coherence elements of a high-dimensional quantum state without global tomographic reconstruction. We characterize our two-mode quantum state with up to four photons in each cavity using this subspace tomography together with direct measurements of the photon-number difference and the joint Wigner function. We identify the spurious cross-Kerr interaction between the cavities and our dissipative reservoir mode as a prominent dephasing channel that limits the steady-state coherence in our current scheme. Our experiment provides a set of reservoir-engineering and state-characterization tools to study quantum optics and implement multimode bosonic codes in superconducting circuits.