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Not-so-normal mode decomposition

Michael M. Wolf

Phys. Rev. Lett. 100, 070505 **, (2008)

DOI: 10.1103/PhysRevLett.100.070505 Pfeil
*arXiv.org*: 0707.0604 Pfeil

Abstract: We provide a generalization of the normal mode decomposition for non-symmetric or locality constrained situations. This allows for instance to locally decouple a bipartitioned collection of arbitrarily correlated oscillators up to elementary pairs into which all correlations are condensed. Similarly, it enables us to decouple the interaction parts of multi-mode channels into single-mode and pair-interactions where the latter are shown to be a clear signature of squeezing between system and environment. In mathematical terms the result is a canonical matrix form with respect to real symplectic equivalence transformations.