Generating Fock-state superposition from coherent state by quantum measurement

High-level Fock states and their superpositions are essentially exotic testbeds for nonclassical physics and valuable resources for quantum technologies. We provide a simple protocol on quantum measurement to generate an arbitrary Fock state and selected superposed Fock states from a coherent state of a target resonator, without any carefully tailored external driving. This conditional protocol can be efficiently constructed by a sequence of joint free-evolution of the resonator and an ancillary qubit, that are coupled via a Jaynes-Cummings interaction, and projective measurements on the qubit. By properly choosing the duration of each evolution-measurement cycle and the initial state of the resonator, we can generate a desired Fock state |n and a superposed Fock state (|0+|n)/√2, n~10, with a fidelity over $99%$ in less than $30$ measurements. Moreover, our protocol can be straightforwardly extended to the generation of a multi-excitation Bell state (|00+|nn)/√2 in a double-resonator system.