Phonon sensing in phosphorus-doped silicon with hyperfine modulation

Can modulation of hyperfine coupling in a phosphorus-doped silicon system be used to detect phonons? Weak electric fields and strain both introduce an isotropic shift to the hyperfine coupling. To modulate the hyperfine coupling isotropically, the electric field and the strain can be modulated. Two modulations with a phase difference populate the electron-nuclear correlation. A controlled modulation can be applied with an electric field or a resonant laser, while phonons introduce a strain modulation in the lattice. The phonon amplitude and phase can be characterized by measuring the electron-nuclear correlation. For an ensemble of $10^{16}$ donors in phosphorus doped silicon, it is calculated that the minimum detectable strain amplitude is $10^{-18}$ for linear strain.