Unraveling mirror properties in time-delayed quantum feedback scenarios |
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Authors: | Fabian M. Faulstich Manuel Kraft Alexander Carmele |
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Affiliation: | 1. Institut für Theoretische Physik, Technische Universit?t Berlin, Berlin, Germany.;2. Institut für Mathematik, Technische Universit?t Berlin, Berlin, Germany.faulstich@math.tu-berlin.de |
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Abstract: | AbstractWe derive in the Heisenberg picture a widely used phenomenological coupling element to treat feedback effects in quantum optical platforms. Our derivation is based on a microscopic Hamiltonian, which describes the mirror-emitter dynamics based on a dielectric, a mediating fully quantized electromagnetic field and a single two-level system in front of the dielectric. The dielectric is modelled as a system of identical two-state atoms. The Heisenberg equation yields a system of describing differential operator equations, which we solve in the Weisskopf–Wigner limit. Due to a finite round-trip time between emitter and dielectric, we yield delay differential operator equations. Our derivation motivates and justifies the typical phenomenologicalassumed coupling element and allows, furthermore, a generalization to a variety of mirrors, such as dissipative mirrors or mirrors with gain dynamics. |
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Keywords: | Quantum optics Fresnel reflection coefficient refraction index microscopic approach atom–plane dielectric interaction Weisskopf–Wigner narrow-band approximation |
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