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URSI International Symposium on Electromagnetic Theory

Quantum emitter interacting with a dispersive dielectric object: a model based on the modified Langevin noise formalism

Giovanni Miano, Loris Maria Cangemi, Carlo Forestiere

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.46620/ursiemts25/pvwn7444

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In this paper, we model the interaction of a quantum emitter with a finite-size dispersive dielectric object in an unbounded space within the framework of macroscopic quantum electrodynamics, using the modified Langevin noise formalism, without any restrictions on the emitter level structure or dipole operator. The quantized electromagnetic field consists of two contributions: the medium-assisted field, which accounts for the electromagnetic field generated by the noise polarization currents of the dielectric, and the scattering-assisted field, which takes into account the electromagnetic field incoming from infinity and scattered by the dielectric. We show that the emitter couples to two distinct bosonic baths: a medium-assisted bath and a scattering-assisted bath, each characterized by its own spectral density. We identify the conditions under which the electromagnetic environment composed of these two baths can be effectively replaced by a single bosonic bath, so that the reduced dynamics of the quantum emitter remain unchanged. In particular, when the initial states of the medium- and scattering-assisted baths are thermal states with the same temperature, we find that a single bosonic bath with a spectral density equal to the sum of the medium-assisted and scattering-assisted spectral densities is equivalent to the original electromagnetic environment.

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In this paper, we model the interaction of a quantum emitter with a finite-size dispersive dielectric object in unbounded space within the framework of macroscopic quantum electrodynamics, using the modified Langevin noise formalism. The quantized electromagnetic field consists of two contributions: the medium-assisted field, which accounts for the electromagnetic field generated by the noise polarization currents of the dielectric, and the scattering-assisted field, which takes into account the electromagnetic field incoming from infinity and scattered by the dielectric. We show that the emitter couples to two distinct bosonic reservoirs: a medium-assisted reservoir and a scattering-assisted reservoir, each characterized by its own spectral density. We then use emitter-centered modes to reduce the degrees of freedom of both reservoirs. Eventually, we identify the conditions under which the electromagnetic environment composed of these two reservoirs can be effectively replaced by a single bosonic reservoir so that the reduced time evolution of the quantum emitter remains unchanged. In particular, when the initial states of the medium- and scattering-assisted reservoirs are thermal quantum states at the same temperature, we find that a single bosonic bath with a spectral density equal to the sum of the medium- and scattering-assisted spectral densities is equivalent to the original electromagnetic environment.

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Universal and rigorous asymptotic convergence of standard macroscopic quantum electrodynamics to the modified Langevin noise formalism

A. Ciattoni

The standard Langevin noise formalism (LNF) is a well-established approach for macroscopic quantum electrodynamics in unbounded lossy media, and accordingly, its application to finite objects requires endowing the surrounding vacuum with a fictitious absorption that is taken to asymptotically vanish. Existing justifications for such a singular limiting procedure have been mainly restricted to phenomena governed by vacuum fluctuations and medium-induced interactions (Casimir-Polder forces, thermal radiation, quantum emitter dynamics, etc.), thereby strictly excluding scenarios that involve the scattering of external quantum radiation. Conversely, the modified Langevin noise formalism (MLNF) has recently been established as the complete canonical quantum theory for arbitrary macroscopic systems and electromagnetic processes, entirely bypassing the need for limiting procedures, treating incident quantum radiation fields as independent degrees of freedom, and exactly reducing to the LNF for unbounded media. In this work, we demonstrate that the LNF limiting procedure is universally valid by showing that it recovers any physical prediction of the MLNF across all regimes, including arbitrary quantum scattering processes. Specifically, we introduce a suitable mapping associating any MLNF state and observable with a corresponding entity within the LNF augmented by fictitious vacuum absorption. We then rigorously prove that, as the fictitious absorption tends to zero, every LNF matrix element constructed via this mapping exactly converges to its MLNF original, so that the limiting procedure establishes the asymptotic convergence of the LNF to the MLNF.

quant-pharXiv:2610.05202•Oct 6, 2026
In this paper, we model the interaction of a quantum emitter with a finite-size dispersive dielectric object in an unbounded space within the framework of macroscopic quantum electrodynamics, using the modified Langevin noise formalism, without any restrictions on the emitter level structure or dipole operator. The quantized electromagnetic field consists of two contributions: the medium-assisted field, which accounts for the electromagnetic field generated by the noise polarization currents of the dielectric, and the scattering-assisted field, which takes into account the electromagnetic field incoming from infinity and scattered by the dielectric. We show that the emitter couples to two distinct bosonic baths: a medium-assisted bath and a scattering-assisted bath, each characterized by its own spectral density. We identify the conditions under which the electromagnetic environment composed of these two baths can be effectively replaced by a single bosonic bath, so that the reduced dynamics of the quantum emitter remain unchanged. In particular, when the initial states of the medium- and scattering-assisted baths are thermal states with the same temperature, we find that a single bosonic bath with a spectral density equal to the sum of the medium-assisted and scattering-assisted spectral densities is equivalent to the original electromagnetic environment.
In this paper, we model the interaction of a quantum emitter with a finite-size dispersive dielectric object in unbounded space within the framework of macroscopic quantum electrodynamics, using the modified Langevin noise formalism. The quantized electromagnetic field consists of two contributions: the medium-assisted field, which accounts for the electromagnetic field generated by the noise polarization currents of the dielectric, and the scattering-assisted field, which takes into account the electromagnetic field incoming from infinity and scattered by the dielectric. We show that the emitter couples to two distinct bosonic reservoirs: a medium-assisted reservoir and a scattering-assisted reservoir, each characterized by its own spectral density. We then use emitter-centered modes to reduce the degrees of freedom of both reservoirs. Eventually, we identify the conditions under which the electromagnetic environment composed of these two reservoirs can be effectively replaced by a single bosonic reservoir so that the reduced time evolution of the quantum emitter remains unchanged. In particular, when the initial states of the medium- and scattering-assisted reservoirs are thermal quantum states at the same temperature, we find that a single bosonic bath with a spectral density equal to the sum of the medium- and scattering-assisted spectral densities is equivalent to the original electromagnetic environment.
The standard Langevin noise formalism (LNF) is a well-established approach for macroscopic quantum electrodynamics in unbounded lossy media, and accordingly, its application to finite objects requires endowing the surrounding vacuum with a fictitious absorption that is taken to asymptotically vanish. Existing justifications for such a singular limiting procedure have been mainly restricted to phenomena governed by vacuum fluctuations and medium-induced interactions (Casimir-Polder forces, thermal radiation, quantum emitter dynamics, etc.), thereby strictly excluding scenarios that involve the scattering of external quantum radiation. Conversely, the modified Langevin noise formalism (MLNF) has recently been established as the complete canonical quantum theory for arbitrary macroscopic systems and electromagnetic processes, entirely bypassing the need for limiting procedures, treating incident quantum radiation fields as independent degrees of freedom, and exactly reducing to the LNF for unbounded media. In this work, we demonstrate that the LNF limiting procedure is universally valid by showing that it recovers any physical prediction of the MLNF across all regimes, including arbitrary quantum scattering processes. Specifically, we introduce a suitable mapping associating any MLNF state and observable with a corresponding entity within the LNF augmented by fictitious vacuum absorption. We then rigorously prove that, as the fictitious absorption tends to zero, every LNF matrix element constructed via this mapping exactly converges to its MLNF original, so that the limiting procedure establishes the asymptotic convergence of the LNF to the MLNF.