Experimental Realization and Characterization of Stabilized Pair Coherent States I: Motivation and Methods

The stabilization of Bosonic qubits in microwave cavities is a promising step towards implementing quantum error correction codes. The pair cat code, which utilizes a two mode entangled state, assures significant advantages over the previously implemented one-mode cat code for autonomous quantum error correction schemes. A pair coherent state (PCS) forms the basis of this pair cat code. This work is the first implementation of an engineered non-linear two-photon driven dissipation across two storage cavities that generates and stabilizes a PCS. This is part I of the talk and will be discussing the motivations along with the methods to create and characterize the PCS. To achieve this state we implement a cross-cavity pair-photon driven dissipation process, involving a four wave mixing (FWM) process converting a pair of the two storage photons into a reservoir photon and the reverse process. The cross-cavity aspect conserves the photon number difference allowing the state to stabilize to a specific complex amplitude. We introduce a technique of quantum subspace tomography, enabling direct measurements of individual coherence elements of a high-dimensional quantum state without global tomographic reconstruction, thus allowing characterization of the state.