Optomechanical cavity consist of two fixed end mirror with "membrane at the middle set up". The membrane placed at node or antinode give rise to quadratic OPTM(optomechanical) coupling, which is compatible with a QND membranes energy H_m = ω_(m)* n_(m) , where n_(m) are the membrane phonon number. If number of phonons are less than one(Quantum effects can be observed like individual Quantum jump etc) and if greater than one( which is Present situation with membrane, and require substantial improvements in coupling strength and optical absorption).
People have improved coupling strength by avoided crossing of different modes and have achieved quantization of membrane.
1)what does it mean by avoided crossing of different modes and how can we achieve this?
2) Is it possible with numbers of membrane in cavity?
Thanks..
Avoided crossings occur whenever there is coupling between degenerate modes. if you consider two different modes with frequencies that vary under influence of some external parameter. At a certain value of the parameter the modes may become degenerate: they cross in a graph showing frequencies vs. the parameter. However if the modes are coupled, this will lift the degeneracy. At the former crossing point you will instead have two new frequencies. The corresponding eigenmodes are superpositions of the original uncoupled modes. The graph of frequencies vs. parameter now looks like two curves that avoid crossing. The stronger the mode coupling, the larger the minimum frequency splitting, i.e. the width of the avoided crossing.
Avoided crossings occur whenever there is coupling between degenerate modes. if you consider two different modes with frequencies that vary under influence of some external parameter. At a certain value of the parameter the modes may become degenerate: they cross in a graph showing frequencies vs. the parameter. However if the modes are coupled, this will lift the degeneracy. At the former crossing point you will instead have two new frequencies. The corresponding eigenmodes are superpositions of the original uncoupled modes. The graph of frequencies vs. parameter now looks like two curves that avoid crossing. The stronger the mode coupling, the larger the minimum frequency splitting, i.e. the width of the avoided crossing.
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