High fidelity macroscopic superposition states via shortcut to adiabaticity

TL;DR

This paper presents a shortcut to adiabaticity method using counterdiabatic driving to efficiently generate high-fidelity macroscopic superposition states in mechanical resonators, with robustness against noise and practical implementation proposals.

Contribution

It introduces a practical shortcut to adiabaticity scheme employing counterdiabatic drives for creating macroscopic superpositions in massive objects.

Findings

High-fidelity macroscopic superposition states can be prepared.

The scheme is robust against noise and imperfections.

Implementation in superconducting circuits is feasible.

Abstract

A shortcut to an adiabatic scheme is proposed for preparing a massive object in a macroscopic spatial superposition state. In this scheme we propose to employ counterdiabatic driving to maintain the system in the ground state of its instantaneous Hamiltonian while the trap potential is tuned from a parabola to a double well. This, in turn, is performed by properly ramping a control parameter. We show that a few counterdiabatic drives are enough for most practical cases. A hybrid electromechanical setup in superconducting circuits is proposed for the implementation. The efficiency of our scheme is benchmarked by numerically solving the system dynamics in the presence of noises and imperfections. The results show that a mechanical resonator with very-high-fidelity spatially distinguishable cat states can be prepared with our protocol. Furthermore, the protocol is robust against noises and imperfections. We also discuss a method for verifying the final state via spectroscopy of a coupled circuit electrodynamical cavity mode. Our work can serve as the ground work to feasibly realize and verify macroscopic superposition states in future experiments.