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arXiv:1311.1564 · Physical Review A

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

Motoaki Bamba, Tetsuo Ogawa

Published Jan 6, 2014• 4 citations
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Abstract

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.

DOI
10.1103/physreva.89.017802

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Reply to “Comment on ‘Coupled dynamics of atoms and radiation-pressure-driven interferometers’ and ‘Superstrong coupling regime of cavity quantum electrodynamics’ ”

D. Meiser, Pierre Meystre

In their Comment, Asb\'oth and Domokos question the consistency of two approximations introduced in two recent articles [D. Meiser and P. Meystre, Phys. Rev. A 73, 033417 (2006); 74, 065801 (2006)]. They show that the minimization of the atomic dipole potential does not in general give rise to a regular lattice of ultracold atoms and that the steady-state positions of atoms in a cavity are not normally characterized by a minimum of the dipole potential. Instead, the steady-state positions correspond to a vanishing force on each individual atom, the relevant force being proportional to the derivative of the optical field mode function. We agree with Asb\'oth and Domokos that the atomic lattice should be irregular. Using a microscopic model we show however that in the regime considered in our works and also in the preceding Comment the concept of force is generally not well defined, and a semiclassical theory may be inadequate for the description of the atomic motion.

Physical Review A•Nov 9, 2007•1 citation
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 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.
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.
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.
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.
From the Hamiltonian connecting the inside and outside of a Fabry-P\'erot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to the connecting Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in the framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultrastrong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical electrodynamics.
In their Comment, Asb\'oth and Domokos question the consistency of two approximations introduced in two recent articles [D. Meiser and P. Meystre, Phys. Rev. A 73, 033417 (2006); 74, 065801 (2006)]. They show that the minimization of the atomic dipole potential does not in general give rise to a regular lattice of ultracold atoms and that the steady-state positions of atoms in a cavity are not normally characterized by a minimum of the dipole potential. Instead, the steady-state positions correspond to a vanishing force on each individual atom, the relevant force being proportional to the derivative of the optical field mode function. We agree with Asb\'oth and Domokos that the atomic lattice should be irregular. Using a microscopic model we show however that in the regime considered in our works and also in the preceding Comment the concept of force is generally not well defined, and a semiclassical theory may be inadequate for the description of the atomic motion.