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arXiv:1205.3938 · Physical Review Letters

Theory of Strong Coupling between Quantum Emitters and Propagating Surface Plasmons

Alejandro González-Tudela, Paloma A. Huidobro, Luis Martín-Moreno, C. Tejedor, Francisco José García-Vidal

Published Mar 19, 2013• 178 citations
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Abstract

Here we present the theoretical foundation of the strong coupling phenomenon between quantum emitters and propagating surface plasmons observed in two-dimensional metal surfaces. For that purpose, we develop a quantum framework that accounts for the coherent coupling between emitters and surface plasmons and incorporates the presence of dissipation and dephasing. Our formalism is able to reveal the key physical mechanisms that explain the reported phenomenology and also determine the physical parameters that optimize the strong coupling. A discussion regarding the classical or quantum nature of this phenomenon is also presented.

DOI
10.1103/physrevlett.110.126801

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Here we present the theoretical foundation of the strong coupling phenomenon between quantum emitters and propagating surface plasmons observed in two-dimensional metal surfaces. For that purpose, we develop a quantum framework that accounts for the coherent coupling between emitters and surface plasmons and incorporates the presence of dissipation and dephasing. Our formalism is able to reveal the key physical mechanisms that explain the reported phenomenology and also determine the physical parameters that optimize the strong coupling. A discussion regarding the classical or quantum nature of this phenomenon is also presented.
We investigate a system consisting of a single, as well as two emitters strongly coupled to surface plasmon modes of a nanowire using a Green's function approach. Explicit expressions are derived for the spontaneous decay rate into the plasmon modes and for the atom-plasmon coupling as well as a plasmon-mediated atom-atom coupling. Phenomena due to the presence of losses in the metal are discussed. In case of two atoms, we observe Dicke subradiance and superradiance resulting from their plasmon-mediated interaction. Based on this phenomenon, we propose a scheme for a deterministic two-qubit quantum gate. We also discuss a possible realization of interesting many-body Hamiltonians, such as the spin-boson model, using strong emitter-plasmon coupling.
Plasmons in nanostructured metals are widely utilized to trigger strong light-matter interactions with quantum light sources. While the nonclassical behavior of such quantum emitters (QEs) is well understood in this context, the role of quantum and surface effects in the plasmonic resonator is usually neglected. Here, we combine the Green's tensor approach with the Feibelman ddd-parameter formalism to theoretically explore the influence of quantum surface effects in metal-dielectric layered nanostructures on the relaxation dynamics of a proximal two-level QE. Having identified electron spill-out as the dominant source of quantum effects in jellium-like metals, we focus our study on sodium. Our results reveal a clear splitting in the emission spectrum, indicative of having reached the strong coupling regime, and, more importantly, non-Markovian relaxation dynamics of the emitter. Our findings establish that strong light-matter coupling is not suppressed by the emergence of nonclassical surface effects in the optical response of the metal.
We show that the interaction of surface plasmons with quantum emitters can be described by an effective model that has the same structure as a lossy multimode cavity quantum electromagnetic interaction. This allows the coherent manipulation of quantum emitters dressed by surface plasmons at the nanoscale. We show that strong coupling in quantum plasmonics can be used to mediate efficiently the interaction between emitters via a decoherence-free channel, immune to the strong plasmon dissipation. Efficient and robust population transfer, as well as the deterministic generation of entanglement between emitters are numerically shown. These results pave the way for an efficient use of the quantum plasmonic platform beyond its inherent losses.
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Surface plasmon polaritons are charge density waves of electrons in a metal, which are coupled to an electromagnetic field at a metal-dielectric interface. The electro- magnetic field associated with surface plasmons is confined, resulting in increased field intensities near the interface. Optical emitters placed near a metal film interact strongly with the surface plasmon modes present, not only modifying the radiation rates, but also the radiation profile. These emitters may be used to store and process information, and understanding their behaviour in the presence of a lossy metal film is important in determining the advantages and limitations of using surface plasmons. In this thesis, we wish to understand how we can optically control atoms by exploring two physical phenomena: first, the influence of surface plasmons on collective effects in an ensemble of emitters. Secondly, the single photon excitation of an emitter near a metal film. In the first case, we analyze the collective radiative behaviour of multiple classical emitters near a metal film that radiatively couple to the far-field through surface plasmon modes. We demonstrate that the contributions of dipolar image charges within the metal film significantly affect the cooperative emission of nearby sources, generating sub- and super-radiant emission that can be controlled with a suitably detuned external driving field. In the second case, we determine the excitation probability of an atom near a metal film by a single photon pulse that is time reversed. Using a quantum electro- dynamic description of absorbing dielectrics, we show that non-radiative decay will limit the excitation probability to about half of the maximum that could be achieved in the absence of losses.
The quantum control of emitters is a key issue for quantum information processing at the nanoscale. This generally necessitates the strong coupling of emitters to a high Q-cavity for efficient manipulation of the atoms and field dynamics (cavity quantum electrodynamics or cQED). Since almost a decade, strong efforts are put to transpose cQED concepts to plasmonics in order to profit of the strong mode confinement of surface plasmons polaritons. Despite the intrinsic presence of lossy channels leading to strong decoherence in plasmonics systems, it has been experimentally proven that it is possible to reach the strong coupling regim [1].