Collisionless Damping in Co-propagaging Light and Atomic Beams with Optomechanical and Electronic Feedback

The transverse stability of co-propagating light and matter beams is investigated in the collisionless regime, focusing on the interaction of optomechanical coupling and the electronic Kerr nonlinearity. The dynamic response of a classical monochromatic laser field and a mono-energetic beam of two-level atoms is studied through a Landau stability analysis of the Boltzmann and paraxial wave equations coupled by the gradient force and refractive index. The resulting dispersion relation captures both kinetic and saturation effects and shows that for blue detuning the homogeneous solution is unstable below a critical wavenumber which reduces to the Bespalov-Talanov instability in the limit of negligible optomechanical coupling. For red detuning, there exists a saturation threshold above which the kinetic instability stabilizes unconditionally. Even when saturation is negligible, an optomechanical analog of Landau damping stabilizes all wavenumbers above a critical wavenumber determined by the combined strength of the kinetic and refractive feedback. Numerical solution of the velocity-space perturbation reveals that the collisionless damping mechanism is related to the resonant interaction of atoms traveling along diagonals of the Talbot carpet.