Ultrastrong coupling is a distinct regime of electromagnetic interaction that enables a rich variety of intriguing physical phenomena. Traditionally, this regime has been reached by coupling intersubband transitions of multiple quantum wells, superconducting artificial atoms, or two-dimensional electron gases to microcavity resonators. However, employing these platforms requires demanding experimental conditions such as cryogenic temperatures, strong magnetic fields, and high vacuum. Here, we use a plasmonic nanorod array positioned at the antinode of a resonant optical Fabry-Pérot microcavity to reach the ultrastrong coupling (USC) regime at ambient conditions and without the use of magnetic fields. From optical measurements we extract the value of the interaction strength over the transition energy as high as g/ω ~ 0.55, deep in the USC regime, while the nanorod array occupies only ∼4% of the cavity volume. Moreover, by comparing the resonant energies of the coupled and uncoupled systems, we indirectly observe up to ∼10% modification of the ground-state energy, which is a hallmark of USC. Our results suggest that plasmon-microcavity polaritons are a promising platform for room-temperature USC realizations in the optical and infrared ranges, and may lead to the long-sought direct visualization of the vacuum energy modification.

We propose a geometry-specific, mode-selective quantization scheme in coupled field-emitter systems which makes it easy to include material and geometrical properties, intrinsic losses as well as the positions of an arbitrary number of quantum emitters. The method is presented through the example of a spherically symmetric, non-magnetic, arbitrarily layered system. We follow it up by a framework to project the system on simpler, effective cavity QED models. Maintaining a well-defined connection to the original quantization, we derive the emerging effective quantities from the full, mode-selective model in a mathematically consistent way. We discuss the uses and limitations of these effective models.

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Käll, M. et al (2018) Quantum description and emergence of nonlinearities in strongly coupled single-emitter nanoantenna systems PHYSICAL REVIEW B, 98(4) http://dx.Realizing strong coupling between a single quantum emitter (QE) and an optical cavity is of crucial importance in the context of various quantum optical applications. Although Rabi splitting of single quantum emitters coupled to high-Q classical cavities has been reported in numerous configurations, attaining single emitter Rabi splitting with a plasmonic nanostructure remains a challenge. In particular, strong coupling at the single QE regime would open the path for the realization of single-photon nonlinearities. In this paper, we derive a plasmon quantization procedure for systems consisting of a single QE located in the gap of a nanoantenna. This procedure leads to the description of the quantum dynamics by a master equation for the state of the QE and the quantized plasmonic modes, which is crucial to demonstrate the emergence of single-photon nonlinearities. We investigate numerically the optical response and the resulting Rabi splitting in metallic nanoantennas and find the optimal geometries for the emergence of the strong-coupling regime with single QEs. Finally, we demonstrate the saturation of hybridized modes for a chosen configuration. Our results will be useful for implementation of realistic quantum plasmonic nanosystems involving single QEs at room temperature.

Ultrastrong coupling (USC) is a distinct regime of light-matter interaction in which the coupling strength is comparable to the resonance energy of the cavity or emitter. In the USC regime, common approximations to quantum optical Hamiltonians, such as the rotating wave approximation, break down as the ground state of the coupled system gains photonic character due to admixing of vacuum states with higher excited states, leading to ground-state energy changes. USC is usually achieved by collective coherent coupling of many quantum emitters to a single mode cavity, whereas USC with a single molecule remains challenging. Here, we show by time-dependent density functional theory (TDDFT) calculations that a single organic molecule can reach USC with a plasmonic dimer, consisting of a few hundred atoms. In this context, we discuss the capacity of TDDFT to represent strong coupling and its connection to the quantum optical Hamiltonian. We find that USC leads to appreciable ground-state energy modifications accounting for a non-negligible part of the total interaction energy, comparable to k B T at room temperature.

Hybrid molecular-plasmonic nanostructures have demonstrated their potential for surface enhanced spectroscopies, sensing or quantum control at the nanoscale. In this work, we investigate the strong coupling regime and explicitly describe the hybridization between the localized plasmons of a metal nanoparticle and the excited state of a quantum emitter, offering a simple and precise understanding of the energy exchange in full analogy with cavity quantum electrodynamics treatment and dressed atom picture. Both near field emission and far field radiation are discussed, revealing the richness of such optical nanosources.Optical microcavities can store light for a long time allowing efficient light-matter interaction with important applications in quantum technologies, low threshold laser [1], supercontinuum laser [2] or indistinguishable single photon source [3]. It relies on the extremely high quality factor of the cavity mode but at the price of diffraction limited sizes. That is why strong efforts have be done since a decade to transpose cavity quantum electrodynamics (cQED) concepts to nanophotonics and plasmonics [4][5][6][7][8]. Particular attention has been devoted to the strong coupling regime [9][10][11][12] since it offers the possibility of a control dynamics of the light emission, as e.g. photon blockade [13,14] or coherent control [15,16].In this letter, we build an effective Hamiltonian that fully transposes the cQED description to an hybrid plasmon-quantum emitter nanosource. We demonstrate it can be exactly described in full analogy with cQED representation. Specifically, the coupled plasmon-emitter system behaves like an emitter in a multimodal lossy cavity. We notably determine the structure of the emitter states dressed by the plasmon modes.We consider the hybrid system displayed in Fig. 1. A two level system (TLS) quantum emitter is located close to a metal nanoparticle (MNP). The optical transition is characterized by the frequency ω eg , the dipole moment d eg and the operatorσ † eg = |g e|. For the sake of clarity, we consider a TLS emitter coupled to spherical MNP since the localized surface plasmon (LSP) modes involved in the coupling process are well identified and the hybridization of the emitter and MNP modes will be unambiguously demonstrated. * gerard.colas-des-francs@u-bourgogne.fr The Hamiltonian of the coupled system writeŝThe first term refers to the TLS energy and we have phenomelogically introduced the decay rate of the excited state γ d in the second term.The third term describes the total energy of the electromagnetic field wheref † (f ) is the LSP polaritonic vector field operator associated to the creation (annihilation) of a quantum of electromagnetic mode in presence of the MNP. The last term describes the emitter-field interaction under the rotatingwave approximation.The electromagnetic field has to be quantized by taking into account the dispersing and absorbing nature of the metal [17][18][19]. The electromagnetic mode dispersion and absorption are governed by the real a...

We derive effective Hamiltonians for a single dipolar emitter coupled to a metal nanoparticle (MNP) with particular attention devoted to the role of losses. For small particles sizes, absorption dominates and a non hermitian effective Hamiltonian describes the dynamics of the hybrid emitter-MNP nanosource. We discuss the coupled system dynamics in the weak and strong coupling regimes offering a simple understanding of the energy exchange, including radiative and non radiative processes. We define the plasmon Purcell factors for each mode. For large particle sizes, radiative leakages can significantly perturbate the coupling process. We propose an effective Fano Hamiltonian including plasmon leakages and discuss the link with the quasinormal mode description. We also propose Lindblad equations for each situation and introduce a collective dissipator for describing the Fano behaviour.