  We present and analyze a proposal for a macroscopic quantum delayed-choice
experiment with massive mechanical resonators. In our approach, the electronic
spin of a single nitrogen-vacancy impurity is employed to control the coherent
coupling between the mechanical modes of two carbon nanotubes. We demonstrate
that a mechanical phonon can be in a coherent superposition of wave and
particle, thus exhibiting both behaviors at the same time. We also discuss the
mechanical noise tolerable in our proposal and predict a critical temperature
below which the morphing between wave and particle states can be effectively
observed in the presence of environment-induced fluctuations. Furthermore, we
describe how to amplify single-phonon excitations of the mechanical-resonator
superposition states to a macroscopic level, via squeezing the mechanical
modes. This approach corresponds to the phase-covariant cloning. Therefore, our
proposal can serve as a test of macroscopic quantum superpositions of massive
objects even with large excitations. This work, which describes a fundamental
test of the limits of quantum mechanics at the macroscopic scale, would have
implications for quantum metrology and quantum information processing.
