New double-pass type of the optical spring

In detuned optical cavities, the radiation pressure force acting on the mirrors depends on their displacements. This is equivalent to the rigidity (the optical spring), inserted between the mirrors. This effect can be used for optimization of the mechanical susceptibility of probe mirrors in high-precision force sensors. However, in some cases, the use of detuned cavities or even just any high-finesse cavities could be problematic due to technological constraints. We consider a new type of the optical spring that does not require the cavity (but can use a resonance tuned one to increase the optomechanical coupling). Instead, it uses the double interaction of the probing light with the mechanical object. An important advantage of this type of the optical spring is that it allows one to tune the optomechanical setup in a real time without affecting its core optics. We propose two possible implementation of this concept, suitable, respectively, for the atomic spin ensembles and for the laser gravitational-wave detectors.