Generation Of The Superposition Of Mesoscopic States Of A Nanomechanical Resonator By A Single Two-Level System

We propose measurement-based conditional generation of the superposition of mesoscopic states of a nanomechanical resonator. We consider a two-level quantum mechanical system (qubit) coupled with a nanomechanical resonator through phonon exchange. An interaction, which produces shifts in the state of the nanomechanical resonator depending on the state of the qubit, is realized by driving the qubit through two resonant fields or a single field with controlled phase. The measurement of the state of the qubit produces superposition states of the nanomechanical resonator. We show that the quantum interference between the generated states in the superposition may lead to an arbitrary large displacement in the resonator. We also discuss decoherence of the generated states using the Wigner function.