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arXiv:1804.02005 · Journal of the Optical Society of America B

Lamb shift multipolar analysis

Emmanuel Lassalle, Alexis Devilez, Nicolas Bonod, Thomas Durt, Brian Stout

Published Jun 2, 2017• 9 citations
arXivHTMLPDF

Abstract

It is now well established that radiative decay of quantum emitters can be strongly modified by their environment. In this paper, we present an exact—within the weak-coupling approximation—multipole expression to compute the Lamb (frequency) shift induced by an arbitrary set of resonant scatterers on a nearby quantum emitter, using multiscattering theory. We also adopt a quasi-normal mode description to account for the line shape of the Lamb shift spectrum in the near field of a plasmonic nanosphere. It is then shown that the Lamb shift resonance can be blueshifted as the size of the nanoparticle increases, suggesting that nanoparticles may be used to tune this resonant interaction. Finally, a realistic calculation of the Lamb shift is made for a dimer configuration.

DOI
10.1364/josab.34.001348

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It is now well established that radiative decay of quantum emitters can be strongly modified by their environment. In this paper, we present an exact—within the weak-coupling approximation—multipole expression to compute the Lamb (frequency) shift induced by an arbitrary set of resonant scatterers on a nearby quantum emitter, using multiscattering theory. We also adopt a quasi-normal mode description to account for the line shape of the Lamb shift spectrum in the near field of a plasmonic nanosphere. It is then shown that the Lamb shift resonance can be blueshifted as the size of the nanoparticle increases, suggesting that nanoparticles may be used to tune this resonant interaction. Finally, a realistic calculation of the Lamb shift is made for a dimer configuration.
Placing quantum emitters close to a metallic nanowire, an effective interaction can be achieved over distances large compared to the resonance wavelength due to the strong coupling between emitters and the surface plasmon modes of the wire. This leads to modified collective decay rates, as well as to Lamb and dipole-dipole shifts. In this paper, we present a general method for calculating these level shifts, which we subsequently apply to the case of a pair of atoms coupled to the guided modes of a nanowire.
Abstract It is demonstrated that the interaction of a two-level quantum emitter (atom, molecule, etc) with a plasmonic nanoparticle (prolate nanospheroid) in an external laser field features either an essential increase (up to a few orders of magnitude) or reduction (up to a few times) of the total decay rate of the emitter in specific areas around the nanoparticle in contrast to its decay rate in a vacuum. It is also shown that the resonance fluorescence spectrum of the emitter in close proximity to a plasmonic nanoparticle is very sensitive to both the location of the emitter around the nanoparticle and to polarization of the near-field, which depends in turn on the polarization of the incident laser field. This can be used in engineering potential quantum optics experiments with quantum emitters in the near-field, as well as for 3D nanoscopy of the near-field by registering the resonance fluorescence spectra of quantum emitters scattered in the vicinity of a plasmonic nanoparticle.
We investigate excitation dynamics in the system of a quantum dipole emitter (QDE) coupled to a located nearby metal nanoparticle (MNP), which exhibits a dipolar localized surface plasmon (LSP) resonance at the frequency of the QDE radiative transition, in the presence of a strong external resonant electromagnetic field. Considering the QDE-field interactions in the regime of strong QDE-field coupling, we show that the feedback provided by the MNP on the QDE (due to the LSP excitation with the field generated by the dipole moment of the QDE transition) influences significantly the coherent process of Rabi oscillations, resulting in the occurrence of additional satellite frequencies in the radiation spectrum scattered by the QDE-MNP configuration. The relative ratio of high harmonics depends strongly on the QDE-MNP separation, an important characteristic feature that can be used for observing this effect and can be exploited, for example, for controlling distances at the nanoscale.
Small particles respond to light through electric and magnetic patterns called multipoles. Their interference determines the direction of scattered light and affects the decay of nearby emitters. Larger nanoantenna arrays, metasurfaces, and other nanophotonic systems demand increasingly costly simulations to meet strict performance and reliability requirements. We show how to represent these responses with quantum bits (qubits) and use quantum circuits to calculate scattering and the Purcell effect, the change in an emitter's decay rate caused by its surroundings. The circuits can encode known multipoles or estimate unknown ones from Maxwell's equations at the particle surface. We test the method against classical theory using an ideal quantum simulator and real IBM and IonQ quantum computers. For a silicon nanoparticle of radius 78 nm illuminated at 679 nm, IonQ gives a forward directivity of 2.984, close to the ideal dipolar value 3, quantifying the concentration of scattered light in the forward direction. For an emitter 10 nm from a gold nanoparticle and emitting at 510 nm, IBM measurements yield a calculated total decay rate 20.48 times its vacuum value versus 20.47 from theory, with correction for errors in reading the qubit states. We also establish how the number of multipoles and the required accuracy set the demands on qubits and measurements. These results motivate quantum-assisted design studies of directional radiation and emitter decay in nanophotonic systems.
In this paper, we study the collective effects which appear as a pair of quantum emitters is positioned in close vicinity to a plasmonic nanoparticle. These effects include multipole-multipole interaction and collective decay, the strengths and rates of which are modified by the presence of the nanoparticle. As a result, entanglement is generated between the quantum emitters, which survives in the stationary state. To evaluate these effects, we exploit the Green's tensor-based quantization scheme in the Markovian limit, taking into account the corrections from light-matter coupling channels higher than the electric dipole. We find these higher-order channels to significantly influence the collective rates and degree of entanglement, and in particular, to qualitatively influence their spatial profiles. Our findings indicate that, apart from quantitatively modifying the results, the higher-order interaction channels may introduce asymmetry into the spatial distribution of the collective response.
We put forward a general approach for calculating the energy level shift of a quantum emitter (QE) in arbitrary-shaped nanostructure. It is expressed by the sum of the real part and a simple integral of the imaginary part of the scattered photon Green's function (GF) in a rather narrow real frequency range without a principal value. Compared with the method of direct evaluation of the principal value integral along the positive frequency axis or the method of transferring the principal value into an integration along the imaginary frequency axis, our method avoids the principal value integral and the evaluation of the scattered GF with imaginary frequency. It is numerically demonstrated for a QE located around a nanosphere and in a gap plasmonic nanocavity. The decay dynamics of an excited QE is calculated using the time-domain method through solving the Schr\"odinger equation in the form of a Volterra integral of the second kind, and using the frequency-domain method based on the Green's function expression for the evolution operator. It is found that the frequency domain method requires much narrower band information of the scattered GF. These findings are instructive in the field of coherent light-matter interactions.