Expression for the decoherence rate due to air-molecule scattering in spatial qubits

We provide an expression for the decoherence rate in spatial superpositions due to scattering or collision with air molecules which is independent of the wavelength of the air molecules. This result reproduces the short-and long-wavelength limits known in the literature. We compare the decoherence rate with several existing interpolations in the literature and evaluate the decoherence rate and experimental parameters when creating macroscopic quantum spatial superpositions (i.e., in micron-size spheres). The interpolation regime is relevant in, e.g., matter-wave interferometry, where one might switch between the wavelength limits during the experimental protocol. Finally, we consider the decoherence rate's time dependence while creating and closing the spatial superposition in an interferometer setup.