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arXiv:1307.5615 · Physical Review A

Comment on “System-environment coupling derived by Maxwell's boundary conditions from the weak to the ultrastrong light-matter-coupling regime”

Simone De Liberato

Published Jan 6, 2014• 20 citations
arXivHTMLPDF

Abstract

In a recent paper, Bamba and Ogawa [Phys. Rev. A 88, 013814 (2013)] developed a microscopic model describing a photonic cavity coupled to an excitonlike resonance. One of the results they obtained studying such a model is that, in the ultrastrong coupling regime, dissipation rates calculated applying the rotating-wave approximation on the system-environment coupling qualitatively differ from the ones calculated using a microscopic theory based on the quantum electrodynamics for dielectric media. Here I show that this result is an artifact, caused by an inconsistent application of the rotating-wave approximation and by an unphysical parameter choice.

DOI
10.1103/physreva.89.017801

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As mentioned by De Liberato [Phys. Rev. A 89, 017801 (2014)], when we suppose the metallic thin mirror and perform the renormalization to the approach starting from the frequently used system-environment-coupling Hamiltonian, we can certainly resolve the discrepancy of its result from that obtained by the reliable approach in the main discussion of our paper [Phys. Rev. A 88, 013814 (2013)]. Although the suggested approach is currently applicable to the specific situation after checking its validity by our reliable but cumbersome approach, we instead propose to start from the system-environment-coupling Hamiltonian determined properly by the mechanism of the confinement and loss of the cavity fields. This approach is applicable to any cavity structure, in principle, and we do not face the renormalization problem appearing in the Comment.

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In a recent paper, Bamba and Ogawa [Phys. Rev. A 88, 013814 (2013)] developed a microscopic model describing a photonic cavity coupled to an excitonlike resonance. One of the results they obtained studying such a model is that, in the ultrastrong coupling regime, dissipation rates calculated applying the rotating-wave approximation on the system-environment coupling qualitatively differ from the ones calculated using a microscopic theory based on the quantum electrodynamics for dielectric media. Here I show that this result is an artifact, caused by an inconsistent application of the rotating-wave approximation and by an unphysical parameter choice.
As mentioned by De Liberato [Phys. Rev. A 89, 017801 (2014)], when we suppose the metallic thin mirror and perform the renormalization to the approach starting from the frequently used system-environment-coupling Hamiltonian, we can certainly resolve the discrepancy of its result from that obtained by the reliable approach in the main discussion of our paper [Phys. Rev. A 88, 013814 (2013)]. Although the suggested approach is currently applicable to the specific situation after checking its validity by our reliable but cumbersome approach, we instead propose to start from the system-environment-coupling Hamiltonian determined properly by the mechanism of the confinement and loss of the cavity fields. This approach is applicable to any cavity structure, in principle, and we do not face the renormalization problem appearing in the Comment.
In the standard theory of cavity quantum electrodynamics (QED), coupling between photons inside and outside a cavity (cavity system and environment) is given conserving the total number of photons. However, when the cavity photons (ultrastrongly) interact with atoms or excitations in matters, the system-environment coupling must be determined from a more fundamental viewpoint. Based on the Maxwell's boundary conditions in the QED theory for dielectric media, we derive the quantum Langevin equation and input-output relation, in which the total number of polaritons (not photons) inside the cavity and photons outside is conserved.
When the light interacts with matters in a lossy cavity, in the standard cavity quantum electrodynamics, the dissipation of cavity fields is characterized simply by the strengths of the two couplings: the light-matter interaction and the system-environment coupling through the cavity mirror. However, in the ultrastrong-light-matter-interaction regime, the dissipation depends also on whether the two couplings are mediated by the electric field or the magnetic one (capacitive or inductive in superconducting circuits). Even if we know correctly the microscopic mechanism (Lagrangian) of the system-environment coupling, the coupling Hamiltonian itself is in principle modified due to the ultrastrong interaction in the cavity. In this paper, we show a recipe for deriving a general expression of the Hamiltonian of the system-environment coupling, which is applicable even in the ultrastrong-light-matter-interaction regime in the good-cavity and independent-transition limits.
We have studied the thermal emission of a cavity quantum electrodynamic system in the ultrastrong-coupling regime, where the atom–cavity coupling rate becomes comparable with the cavity resonance frequency. In this regime, the standard descriptions of photodetection and dissipation fail. By following an approach that was recently put forward by Ridolfo et al (2012 Phys. Rev. Lett. 109 193602), we were able to calculate the emission of systems with arbitrary strength of light–matter interaction, by expressing the electric-field operator in the cavity–emitter dressed basis. In this paper, we present thermal photoluminescence spectra, calculated for given temperatures and for different couplings, in particular, for available circuit quantum electrodynamics parameters.
When the light interacts with matters in a lossy cavity, in the standard cavity quantum electrodynamics, the dissipation of cavity fields is characterized simply by the strengths of the two couplings: the light-matter interaction and the system-environment coupling through the cavity mirror. However, in the ultrastrong light-matter interaction regime, the dissipation depends also on whether the two couplings are mediated by the electric field or the magnetic one (capacitive or inductive in superconducting circuits). Even if we know correctly the microscopic mechanism (Lagrangian) of the system-environment coupling, the coupling Hamiltonian itself is in principle modified due to the ultrastrong interaction in the cavity. In this paper, we show a recipe for deriving a general expression of the Hamiltonian of the system-environment coupling, which is applicable even in the ultrastrong light-matter interaction regime in the good-cavity and independent-transition limit.
Phenomenological approaches to photon loss have long been the workhorse of cavity-QED, but prove inadequate in the presence of sufficiently broadband light-matter interactions. We present a rigorous and ab initio derivation of a quantum master equation for a quantized optical cavity mode coupled to a dipole, using a quasinormal mode (QNM) quantization procedure for plasmonic and dielectric open-system cavity-QED, which is valid in broadband light-matter interaction regimes, including ultrastrong coupling (USC). The theory supports general three-dimensional resonators with arbitrary dispersion and loss, and thus can be applied to a wide range of realistic open cavities. Our ab initio and gauge-invariant approach fully recovers a recent result for the spectral density of a quantized cavity with a single dipole and reveals important departures from previous heuristic assumptions about system-reservoir coupling. We identify a new criterion for what we term the "broadband dissipative" regime of cavity-QED, where phenomenological models require corrections in accordance with the intrinsic and spatially-dependent complex phase of the QNM, and also shed light on fundamental limits to single-mode models in extreme coupling regimes. Using experimentally motivated plasmonic and dielectric cavity examples, we show validity ranges of our QNM master equation and spectral USC calculations, and discuss prospects for near-term experimental observation of the broadband dissipative effects.