Explicit effective Hamiltonians for general linear quantum-optical networks

@inproceedings{Leonhardt2009ExplicitEH,
  title={Explicit effective Hamiltonians for general linear quantum-optical networks},
  author={Ulf Leonhardt},
  year={2009}
}
Linear optical networks are devices that turn classical incident modes by a linear transformation into outgoing ones. In general, the quantum version of such transformations may mix annihilation and creation operators. We derive a simple formula for the effective Hamiltonian of a general linear quantum network, if such a Hamiltonian exists. Otherwise we show how the scattering matrix of the network is decomposed into a product of three matrices that can be generated by Hamiltonians. 

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