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Physical Review A

Spatially dependent Lamb shift in a waveguide and its influence on the optical polyatomic cooperative effects

A. S. Kuraptsev, Igor M. Sokolov

Published Apr 13, 2023• 3 citations
Publisher

Abstract

We show that the Lamb shift can significantly affect the nature of the interatomic dipole-dipole interaction in structured reservoirs. The effect is explained by the difference in the Lamb shift for atoms located at different positions due to the inhomogeneity of the spatial structure of the modes of the electromagnetic field. Based on the model system involving two atoms in a waveguide, we demonstrate that this difference can be the same order as the natural linewidth of the atomic transition.

DOI
10.1103/physreva.107.042808

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We show that the Lamb shift can significantly affect the nature of the interatomic dipole-dipole interaction in structured reservoirs. The effect is explained by the difference in the Lamb shift for atoms located at different positions due to the inhomogeneity of the spatial structure of the modes of the electromagnetic field. Based on the model system involving two atoms in a waveguide, we demonstrate that this difference can be the same order as the natural linewidth of the atomic transition.
Based on a consistent quantum microscopic approach, we investigate the peculiarities of collective polyatomic effects in atomic ensembles placed in a waveguide, caused by the presence of evanescent modes of electromagnetic field. We analyze the influence of these modes on the process of cooperative spontaneous decay, as well as on the nature of radiation transfer in the ensembles under consideration. We show that under certain conditions, their influence can be dominant compared to the role of radiation modes, and the mechanism for this influence is the modification of dipole-dipole interatomic interaction.
Atoms coupled to optical fields strongly confined in two spatial dimensions, as in solid-state microstructures, can experience large Lamb shifts due to a spectrally strongly asymmetric mode density. We use the generic example of a quasi–one-dimensional waveguide structure driven close to cutoff frequency of a new transverse branch of propagating modes. We analytically find strong shifts of the atomic resonance frequency due to the modified vacuum, which can be an order of magnitude larger than the atomic linewidth. At the same time one gets significantly enhanced scattering of the guided light by the atom, which could be used as a tool to investigate these effects or to build non-destructive single-atom detectors.
Collective couplings of atomic dipoles to a shared electromagnetic environment produce a wide range of many-body phenomena. We report on the direct observation of resonant electric dipole-dipole interactions in a cubic array of atoms in the many-excitation limit. The interactions produce spatially dependent cooperative Lamb shifts when spectroscopically interrogating the millihertz-wide optical clock transition in strontium-87. We show that the ensemble-averaged shifts can be suppressed below the level of evaluated systematic uncertainties for optical atomic clocks. Additionally, we demonstrate that excitation of the atomic dipoles near a Bragg angle can enhance these effects by nearly an order of magnitude compared with nonresonant geometries. Our work demonstrates a platform for precise studies of the quantum many-body physics of spins with long-range interactions mediated by propagating photons.
As the laser linewidth arises under the influence of spontaneous emission, it is of considerable interest to find effects that decrease it. In this paper it is considered the effect of cooperative atomic interactions on the linewidth of a single-mode laser. It can be shown by suitably generalizing the Scully-Lamb theory that the cooperative effects tend to decrease the natural linewidth of the laser at high intensities. Considering the interaction of two-two- level atoms with a single-mode quantized field and the effect of cooperative atomic interactions it was obtained an expression for the natural linewidth of the system. Based on the theoretical models we obtain the numerical results for the laser linewidth as a function of the cooperation parameter. We then present a set of graphs by suitably plotting these data and we discuss the results.
Finding a comprehensive and general description of the collective Lamb shift and cooperative broadening in a radiatively interacting system is a long-standing open question. Both energy levels and linewidth of individual atoms are modified by the exchange of real and virtual photons making up the dipole-dipole interaction. We introduce a method to theoretically study weakly-driven, low-excited ensembles of two-level atoms, and obtain an analytic description of the collective Lamb shift and linewidth via a self-consistent formalism including infinite order of correlations which stem from only two-body interactions. We predict the dependency of these quantities, as measurables, on system parameters: the number density of the ensemble, the detuning of an external probe field, and the geometry of the sample.