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International Conference on Electrical Engineering and Photonics (EExPolytech)

Giant Cooperative Lamb Shift in a Waveguide

A. S. Kuraptsev, К. А. Баранцев, A. N. Litvinov, Г. В. Волошин, Hui Meng, Igor Sokolov

Published Oct 14, 2021• 0 citations
Publisher

Abstract

We have found out extremely large cooperative Lamb shift in a single-mode waveguide. Based on self-consistent quantum microscopic model treating atoms as coherent radiating dipoles, we have calculated the atomic transition spectrum. We demonstrate that the line shift induced by interatomic dipole-dipole interaction in a waveguide is much larger than its free space value.

DOI
10.1109/eexpolytech53083.2021.9614794

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We have found out extremely large cooperative Lamb shift in a single-mode waveguide. Based on self-consistent quantum microscopic model treating atoms as coherent radiating dipoles, we have calculated the atomic transition spectrum. We demonstrate that the line shift induced by interatomic dipole-dipole interaction in a waveguide is much larger than its free space value.
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According to quantum electrodynamics, the exchange of virtual photons in a system of identical quantum emitters causes a shift of its energy levels. Such shifts, known as cooperative Lamb shifts, have been studied mostly in the near-field regime. However, the resonant electromagnetic interaction persists also at large distances, providing coherent coupling between distant atoms. Here, we report a direct spectroscopic observation of the cooperative Lamb shift of an optical electric-dipole transition in an array of Sr(+) ions suspended in a Paul trap at inter-ion separations much larger than the resonance wavelength. By controlling the precise positions of the ions, we studied the far-field resonant coupling in chains of up to eight ions, extending to a length of 40 μm. This method provides a novel tool for experimental exploration of cooperative emission phenomena in extended mesoscopic atomic arrays.
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.
Superradiant decay is accompanied by two kinds of collective lineshifts, an induced shift and the spontaneous "collective Lamb shift." Both form as sum of dipole-dipole interaction-induced level shifts between atoms in the system. We have developed a procedure to obtain numerical results on this model that self-consistently incorporates the shifts. The induced shift displays large non-zero values early in the system evolution. In addition, its effect on the superradiant system is studied: there is only a very small dephasing effect on the decay rate. While the induced shift is largely absent in not-too strongly driven systems, this parameter region might provide a good experimental regime for measuring the collective Lamb shift. These results can have important consequences for highly sensitive systems, such as quantum information science or atomic clocks.
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.