dorsal/arxiv
View SchemaOscillator model for dissipative QED in an inhomogeneous dielectric
| Authors | A. J. van Wonderen, L. G. Suttorp |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0409161 |
| URL | https://arxiv.org/abs/quant-ph/0409161 |
| DOI | 10.1088/0305-4470/37/46/002 |
| Journal | Journal of Physics A 37(2004)11101 |
Abstract
The Ullersma model for the damped harmonic oscillator is coupled to the quantised electromagnetic field. All material parameters and interaction strengths are allowed to depend on position. The ensuing Hamiltonian is expressed in terms of canonical fields, and diagonalised by performing a normal-mode expansion. The commutation relations of the diagonalising operators are in agreement with the canonical commutation relations. For the proof we replace all sums of normal modes by complex integrals with the help of the residue theorem. The same technique helps us to explicitly calculate the quantum evolution of all canonical and electromagnetic fields. We identify the dielectric constant and the Green function of the wave equation for the electric field. Both functions are meromorphic in the complex frequency plane. The solution of the extended Ullersma model is in keeping with well-known phenomenological rules for setting up quantum electrodynamics in an absorptive and spatially inhomogeneous dielectric. To establish this fundamental justification, we subject the reservoir of independent harmonic oscillators to a continuum limit. The resonant frequencies of the reservoir are smeared out over the real axis. Consequently, the poles of both the dielectric constant and the Green function unite to form a branch cut. Performing an analytic continuation beyond this branch cut, we find that the long-time behaviour of the quantised electric field is completely determined by the sources of the reservoir. Through a Riemann-Lebesgue argument we demonstrate that the field itself tends to zero, whereas its quantum fluctuations stay alive. We argue that the last feature may have important consequences for application of entanglement and related processes in quantum devices.
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"abstract": "The Ullersma model for the damped harmonic oscillator is coupled to the\nquantised electromagnetic field. All material parameters and interaction\nstrengths are allowed to depend on position. The ensuing Hamiltonian is\nexpressed in terms of canonical fields, and diagonalised by performing a\nnormal-mode expansion. The commutation relations of the diagonalising operators\nare in agreement with the canonical commutation relations. For the proof we\nreplace all sums of normal modes by complex integrals with the help of the\nresidue theorem. The same technique helps us to explicitly calculate the\nquantum evolution of all canonical and electromagnetic fields. We identify the\ndielectric constant and the Green function of the wave equation for the\nelectric field. Both functions are meromorphic in the complex frequency plane.\nThe solution of the extended Ullersma model is in keeping with well-known\nphenomenological rules for setting up quantum electrodynamics in an absorptive\nand spatially inhomogeneous dielectric. To establish this fundamental\njustification, we subject the reservoir of independent harmonic oscillators to\na continuum limit. The resonant frequencies of the reservoir are smeared out\nover the real axis. Consequently, the poles of both the dielectric constant and\nthe Green function unite to form a branch cut. Performing an analytic\ncontinuation beyond this branch cut, we find that the long-time behaviour of\nthe quantised electric field is completely determined by the sources of the\nreservoir. Through a Riemann-Lebesgue argument we demonstrate that the field\nitself tends to zero, whereas its quantum fluctuations stay alive. We argue\nthat the last feature may have important consequences for application of\nentanglement and related processes in quantum devices.",
"arxiv_id": "quant-ph/0409161",
"authors": [
"A. J. van Wonderen",
"L. G. Suttorp"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/0305-4470/37/46/002",
"journal_ref": "Journal of Physics A 37(2004)11101",
"title": "Oscillator model for dissipative QED in an inhomogeneous dielectric",
"url": "https://arxiv.org/abs/quant-ph/0409161"
},
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