Precision of the acoustic control of single photon scattering with semiconductor quantum dots

Acoustic modulation of quantum dots allows one to control the scattering of photons. Here we theoretically characterize the degree of this acoustic control in the frequency domain. We formulate the theory of low-intensity resonance fluorescence in the presence of white noise and show that a high level of control is achievable with a two-tone acoustic field for appropriate settings of modulation amplitudes as long as the noise-induced phase diffusion coefficient remains one order of magnitude smaller than the acoustic frequency. In addition, using a quantitative model of optical signal collection, we determine that the acoustic phase must be stable over ${\mathbf{10}}^{\mathbf{4}}$ to ${\mathbf{10}}^{\mathbf{5}}$ acoustic periods for efficient control.