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Physical Review A

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

Published Nov 9, 2007• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physreva.76.057802

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In two recent articles [D. Meiser and P. Meystre, Phys. Rev. A 73, 033417 (2006); 74, 065801 (2006)], Meiser and Meystre describe the coupled dynamics of a dense gas of atoms and an optical cavity pumped by a laser field. They make two important simplifying assumptions: (i) The gas of atoms forms a regular lattice and can be replaced by a fictitious mirror and (ii) the atoms strive to minimize the dipole potential. We show that the two assumptions are inconsistent: The configuration of atoms minimizing the dipole potential is not a perfect lattice. Assumption (ii) is erroneous, as in the strong coupling regime the dipole force does not arise from the dipole potential. The real steady state, where the dipole forces vanish, is indeed a regular lattice. Furthermore, the bistability predicted by Meiser and Meystre does not occur in this system.

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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.
In two recent articles [D. Meiser and P. Meystre, Phys. Rev. A 73, 033417 (2006); 74, 065801 (2006)], Meiser and Meystre describe the coupled dynamics of a dense gas of atoms and an optical cavity pumped by a laser field. They make two important simplifying assumptions: (i) The gas of atoms forms a regular lattice and can be replaced by a fictitious mirror and (ii) the atoms strive to minimize the dipole potential. We show that the two assumptions are inconsistent: The configuration of atoms minimizing the dipole potential is not a perfect lattice. Assumption (ii) is erroneous, as in the strong coupling regime the dipole force does not arise from the dipole potential. The real steady state, where the dipole forces vanish, is indeed a regular lattice. Furthermore, the bistability predicted by Meiser and Meystre does not occur in this system.
In two recent articles, Meiser and Meystre describe the coupled dynamics of a dense gas of atoms and an optical cavity pumped by a laser field. They make two important simplifying assumptions: (i) the gas of atoms forms a regular lattice and can be replaced by a fictitious mirror, and (ii) the atoms strive to minimize the dipole potential. We show that the two assumptions are inconsistent: the configuration of atoms minimizing the dipole potential is not a perfect lattice. Assumption (ii) is erroneous, as in the strong coupling regime the dipole force does not arise from the dipole potential. The real steady state, where the dipole forces vanish, is indeed a regular lattice. Furthermore, the bistability predicted by Meiser and Meystre does not occur in this system.
We describe a qualitatively different regime of cavity quantum electrodynamics, the superstrong coupling regime. This regime is characterized by atom-field coupling strengths of the order of the free spectral range of the cavity, resulting in a significant change in the spatial mode functions of the light field. It can be reached in practice for cold atoms trapped in an optical dipole potential inside the resonator. We present a nonperturbative scheme that allows us to calculate the frequencies and linewidths of the modified field modes, thereby providing a good starting point for a quantization of the theory.
We consider the motion of the end mirror of a cavity in whose standing-wave mode pattern atoms are trapped. The atoms and the light field strongly couple to each other because the atoms form a distributed Bragg mirror with a reflectivity that can be fairly high. We analyze how the dipole potential in which the atoms move is modified due to this back action of the atoms. We show that the position of the atoms can become bistable. These results are of a more general nature and can be applied to any situation where atoms are trapped in an optical lattice inside a cavity and where the back action of the atoms on the light field cannot be neglected. We analyze the dynamics of the coupled system in the adiabatic limit where the light field adjusts to the position of the atoms and the light field instantaneously and where the atoms move much faster than the mirror. We calculate the sideband spectrum of the light transmitted through the cavity and show that these spectra can be used to detect the coupled motion of the atoms and the mirror.
Recently, we introduced [C. Ufrecht and E. Giese, Phys. Rev. A 101, 053615 (2020)] a technique to calculate the phase of light-pulse atom interferometers caused by the presence of perturbation potentials and underlined its power by an illustrative example. In the preceding Comment [B. Dubetsky, Phys. Rev. A 102, 027301 (2020)], it was pointed out that other, less idealized situations could have been calculated as well. Our Reply emphasizes that our method is correct, the results from our example can be trivially generalized to other perturbations, and intricate effects of local environments can be even more prominent but also treated by our technique.
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.