Arbitrary state preparation of a mechanical resonator via controlled pulse shaping and projective measurement in a qubit-resonator interaction

TL;DR

This paper presents a protocol for arbitrary state preparation of a mechanical resonator by shaping pulses and performing projective measurements on a coupled qubit-resonator system, enabling precise quantum control.

Contribution

It introduces a novel method to generate arbitrary measurement operators for mechanical resonators using pulse shaping and qubit measurements, advancing quantum state engineering.

Findings

Achieves near-unit fidelity in preparing desired mechanical states.

Demonstrates probabilistic generation of pure states with arbitrary wavefunctions.

Provides a practical protocol compatible with current experimental parameters.

Abstract

We introduce a protocol capable of generating a general measurement operator for a mechanical resonator. The technique requires a qubit-resonator interaction and uses a coherent pulse to drive qubit transitions. This is followed by projective measurement of the qubit's energy, constraining the resonator in a state that depends on the pulse shape. The freedom to choose a pulse shape for the coherent drive enables an arbitrary position-basis measurement operator. Using this measurement operator, we outline a two pulse protocol that probabilistically generates a pure mechanical state with a desired wavefunction, with near unit fidelity for realizable parameters.