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The practical development of quantum plasmonic circuits incorporating non-classical interference [1] and sources of entangled states calls for a versatile quantum theoretical framework which can fully describe the generation and detection of entangled photons and plasmons. However, majority of the presently used theoretical approaches are typically limited to the toy models assuming loss-less and nondispersive elements or including just a few resonant modes. Here, we present a rigorous Green function approach describing entangled photon-plasmon state generation through spontaneous wave mixing in realistic metal-dielectric nanostructures.
Our approach is based on the local Huttner-Barnett quantization scheme [2], which enables problem formulation in terms of a Hermitian Hamiltonian where the losses and dispersion are fully encoded in the electromagnetic Green functions. Hence, the problem can be addressed by the standard quantum mechanical perturbation theory, overcoming mathematical difficulties associated with other quantization schemes. We derive explicit expressions with clear physical meaning for the spatially dependent two-photon detection probability, single-photon detection probability and single-photon density matrix. In the limiting case of low-loss nondispersive waveguides our approach reproduces the previous results [3,4]. Importantly, our technique is far more general and can quantitatively describe generation and detection of spatially-entangled photons in arbitrary metal-dielectric structures taking into account actual losses and dispersion. This is essential to perform the design and optimization of plasmonic structures for generation and control of quantum entangled states.
[1] J.S. Fakonas, H. Lee, Y.A. Kelaita and H.A. Atwater, Nature Photonics 8, 317(2014)
[2] W. Vogel and D.-G. Welsch, Quantum Optics, Wiley (2006).
[3] D.A. Antonosyan, A.S. Solntsev and A.A. Sukhorukov, Phys. Rev. A 90 043845 (2014)
[4] L.-G. Helt, J.E. Sipe and M.J. Steel, arXiv: 1407.4219
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