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Linear-and-quadratic reservoir engineering of non-Gaussian states in cavity optomechanics

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Reservoir engineering is a powerful tool that enables the robust preparation of pure quantum states in noisy environments. It has been successfully employed for the stabilization of squeezed and entangled states in trapped atoms and ions, circuit quantum electrodynamics and optomechanics. However, despite the success, bosonic reservoir engineering is currently limited by the linear character of the evolution, which restricts the set of target states to Gaussian ones. I will discuss a novel scheme for the unconditional preparation of pure non-Gaussian states of a target system. The target mode is nonlinearly coupled to an auxiliary damped mode, which acts as an engineered reservoir. For concreteness, I will discuss an optomechanical realization, where mechanical target states are stabilized in an optomechanical cavity that is parametrically coupled to both the mechanical displacement and the displacement squared. I will show how interesting families of non-Gaussian states, such as the cubic phase state or (squeezed and displaced) finite superpositions of Fock states, can be prepared following this recipe.

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