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This work discusses the problem of optimal excitation of a three-level atom of ladder-configuration by light in the two-photon state and coherent light carrying an average of two photons. The applied atom-light interaction model is based on the Wigner-Weisskopf approximation. We characterize the properties of the optimal two-photon state that excites an atom perfectly, i.e. with probability equal to one: We find that the spectro-temporal shape of the optimal state of light is determined by the lifetimes of the atomic states, with the degree of photonic entanglement in the optimal state depends on the lifetime ratio. In consequence, two distinct interaction regimes can be identified in which the entanglement of the input state of light has qualitatively different impact. As the optimal states may be challenging to prepare in general, we compare the results with those obtained for photon pairs of selected experimentally-relevant pulse shapes. As these shapes are optimized for maximal atomic excitation probability, the results can be interpreted in terms of the overlap between the optimal and investigated pulse shapes., Comment: 16 pages, 14 figures

The dressed atom approach provides a tool to investigate the dynamics of an atom-laser system by fully retaining the quantum nature of the coherent mode. In its standard derivation, the internal atom-laser evolution is described within the rotating-wave approximation, which determines a doublet structure of the spectrum and the peculiar fluorescence triplet in the steady state. However, the rotating wave approximation may fail to apply to atomic systems subject to femtosecond light pulses, light-matter systems in the strong-coupling regime or sustaining permanent dipole moments. This work aims to demonstrate how the general features of the steady-state radiative cascade are affected by the interaction of the dressed atom with propagating radiation modes. Rather than focusing on a specific model, we analyze how these features depend on the parameters characterizing the dressed eigenstates in arbitrary atom-laser dynamics, given that a set of general hypotheses is satisfied. Our findings clarify the general conditions in which a description of the radiative cascade in terms of transition between dressed states is self-consistent. We provide a guideline to determine the properties of photon emission for any atom-laser interaction model, which can be particularly relevant when the model should be tailored to enhance a specific line. We apply the general results to the case in which a permanent dipole moment is a source of low-energy emission, whose frequency is of the order of the Rabi coupling., Comment: 13 pages, 4 figures

Two-photon absorption in molecules, of significance for high-resolution imaging applications, is typically characterised with low cross sections. To enhance the TPA signal, one effective approach exploits plasmonic enhancement. For this method to be efficient, it must meet several criteria, including broadband operational capability and a high fluorescence rate to ensure effective signal detection. In this context, we introduce a novel plus-shaped silver nanostructure designed to exploit the coupling of bright and dark plasmonic modes. This configuration considerably improves both the absorption and fluorescence of molecules across near-infrared and visible spectra. By fine-tuning the geometrical parameters of the nanostructure, we align the plasmonic resonances with the optical properties of specific TPA-active dyes, i.e., ATTO 700, Rhodamine 6G, and ATTO 610. The expected TPA signal enhancement is evaluated using classical estimations based on the assumption of independent enhancement of absorption and fluorescence. These results are then compared with outcomes obtained in a quantum-mechanical approach to evaluate the stationary photon emission rate. Our findings reveal the important role of molecular saturation determining the regimes where either absorption or fluorescence enhancement leads to an improved TPA signal intensity, considerably below the classical predictions. The proposed nanostructure design not only addresses these findings, but also might serve for their experimental verification, allowing for active polarization tuning of the plasmonic response targeting the absorption, fluorescence, or both. The insight into quantum-mechanical mechanisms of plasmonic signal enhancement provided in our work is a step forward in the more effective control of light-matter interactions at the nanoscale.

We investigate the dynamics of polar systems coupled to classical external beams in the ultrastrong coupling regime. The permanent dipole moments (PDMs) sustained by polar systems can couple to the electromagnetic field, giving rise to a variety of processes such as difference-frequency and harmonic generation, reflected in complicated dynamics of the atomic system. Here, we demonstrate that the dynamics can be described simply in a dynamic reference frame. We derive a Jaynes-Cummings-like framework with effective parameters describing frequency shift, coupling strength with the driving field, and a rescaled relaxation rate. The familiar linear scaling of the interaction strength with the field amplitude is replaced with a nonlinear dependence, suggesting potential applications for improving the coherence of quantum system ensembles with permanent dipoles.

Adsorbed atoms (adatoms) coupled to the matrix of solid state host materials as impurities can significantly modify their properties. Especially in low-dimensional materials, such as one-dimensional organic polymer chains or quasi-one-dimensional graphene nanoribbons, intriguing manipulation of the optical properties, such as the absorption cross section, is possible. The most widely used approach to couple quantum emitters to optical antennas is based on the Purcell effect. This formalism, however, does not comprise charge transfer from the emitter to the antenna, but only spontaneous emission of the quantum emitter into the tailored photonic environment, that is evoked by the antenna. To capture such effects, we present a tight-binding formalism to couple an adatom to a finite Su-Schrieffer-Heeger chain, where the former is treated as a two-level system and the latter acts as an optical antenna. We systematically analyze how the coupling strength and the position of the adatom influence the optical properties of the molecular chains in the model. We take into account charge transfer from the adatom to the antenna and vice versa via an inter-system hopping parameter, and also include Coulomb interaction within the antenna as well as between the adatom and the antenna. We show that coupling the adatom to one of the bulk atoms of the linear chain results in a substantial change in optical properties already for comparatively small coupling strengths. We also find that the position of the adatom crucially determines if and how the optical properties of the chains are altered. Therefore, we identify this adatom-chain hybrid system as a tunable platform for light-matter interaction at the nanoscale., Comment: 14 pages, 9 figures

The Rabi Hamiltonian, describing the interaction between a two-level atomic system and a single cavity mode of the electromagnetic field, is one of the fundamental models in quantum optics. The model becomes exactly solvable by considering an atom without permanent dipole moments, whose excitation energy is quasi-resonant with the cavity photon energy, and by neglecting the non resonant (counter-rotating) terms. In this case, after including the decay of either the atom or the cavity mode to a continuum, one is able to derive the well-known phenomenology of quasi-resonant transitions, including the fluorescence triplets. In this work we consider the most general Rabi model, incorporating the effects of permanent atomic electric dipole moments, and, based on a perturbative analysis, we compare the intensities of emission lines induced by rotating terms, counter-rotating terms and parity-symmetry-breaking terms. The analysis reveals that the emission strength related to the existence of permanent dipoles may surpass the one due to the counter-rotating interaction terms, but is usually much weaker than the emission due to the main, resonant coupling. This ratio can be modified in systems with a reduced dimensionality or by engineering the energy spectral density of the continuum., Comment: 11 pages, 7 figures

Plasmonic nanostructures attract tremendous attention as they confine electromagnetic fields well below the diffraction limit while simultaneously sustaining extreme local field enhancements. To fully exploit these properties, the identification and classification of resonances in such nanostructures is crucial. Recently, a novel figure of merit for resonance classification has been proposed 1 and its applicability was demonstrated mostly to toy model systems. This novel measure, the energy-based plasmonicity index (EPI), characterizes the nature of resonances in molecular nanostructures. The EPI distinguishes between either a single-particle-like or a plasmonic nature of resonances based on the energy space coherence dynamics of the excitation. To advance the further development of this newly established measure, we present here its exemplary application to characterize the resonances of graphene nanoantennas. In particular, we focus on resonances in a doped nanoantenna. The structure is of interest, as a consideration of the electron dynamics in real space might suggest a plasmonic nature of selected resonances in the low doping limit but our analysis reveals the opposite. We find that in the undoped and moderately doped nanoantenna, the EPI classifies all emerging resonances as predominantly single-particle-like and only after doping the structure heavily, the EPI observes plasmonic response., Comment: The following article has been submitted to the Journal of Applied Physics

We study a two-level quantum system embedded in a dispersive environment and coupled with the electromagnetic field. We expand the theory of light-matter interactions to include the spatial extension of the system, taken into account through its wavefunctions. This is a development beyond the point-dipole approximation. This ingredient enables us to overcome the divergence problem related to the Green tensor propagator. Hence, we can reformulate the expressions for the spontaneous emission rate and the Lamb shift. In particular, the inclusion of the spatial structure of the atomic system clarifies the role of the asymmetry of atomic states with respect to spatial inversion in these quantities., Comment: 22 pages, 8 figures

This work is a proposal for an experimental platform to observe quantum fictitious anticentrifugal force. We present an analytical and numerical treatment of a rectangular toroidal dielectric waveguide. Solving the Helmholtz equation we obtain analytical solutions for transverse spatial modes and estimate their number as a function of system characteristics. On top of that, the analysis of the structure was extended onto a real material platform, a thin film lithium niobate on an insulator rib waveguide. The framework presented here can be directly applied to analyze the phenomenon of quantum anti-centrifugal force.

Coherent, optically dressed media composed of two-level molecular systems without inversion symmetry are considered as all-optically tunable sources of coherent radiation in the microwave domain. A theoretical model and a numerical toolbox are developed to confirm the main finding: the generation of a low-frequency radiation, and the buildup and propagation dynamics of such low-frequency signals in a medium of polar molecules in a gas phase. The physical mechanism of the signal generation relies on the permanent dipole moment characterizing systems without inversion symmetry. The molecules are polarized with a DC electric field yielding a permanent electric dipole moment in the laboratory frame; the direction and magnitude of the moment depend on the molecular state. As the system is resonantly driven, the dipole moment oscillates at the Rabi frequency and, hence, generates microwave radiation. We demonstrate the tuning capability of the output signal frequency with the drive amplitude and detuning. We find that even though decoherence mechanisms such as spontaneous emission may damp the output field, a scenario based on pulsed illumination yields a coherent, pulsed output of tunable temporal width. Finally, we discuss experimental scenarios exploiting rotational levels of gaseous ensembles of heteronuclear diatomic molecules., Comment: 12 pages, 6 figures

The photonic environment can significantly influence emission properties and interactions among atomic systems. In such scenarios, frequently the electric dipole approximation is assumed that is justified as long as the spatial extent of the atomic system is negligible compared to the spatial variations of the field. While this holds true for many canonical systems, it ceases to be applicable for more contemporary nanophotonic structures. To go beyond the electric dipole approximation, we propose and develop in this article an analytical framework to describe the impact of the photonic environment on emission and interaction properties of atomic systems beyond the electric dipole approximation. Particularly, we retain explicitly magnetic dipolar and electric quadrupolar contributions to the light-matter interactions. We exploit a field quantization scheme based on electromagnetic Green's tensors, suited for dispersive materials. We obtain expressions for spontaneous emission rate, Lamb shift, multipole-multipole shift and superradiance rate, all being modified with dispersive environment. The considered influence could be substantial for suitably tailored nanostructured photonic environments, as demonstrated exemplarily., Comment: 2 figures + supplementary material, 21 pages altogether

Spontaneous emission of quantum emitters can be modified by engineering their optical environment. This allows a resonant nanoantenna to significantly modify the radiative properties of a quantum emitter. In this article, we go beyond the common electric dipole approximation for the molecular electronic transition and take light-matter coupling through higher order multipoles into account. We investigate, by means of theory and numerical simulations, a strong enhancement of the magnetic dipole and electric quadrupole emission channels of a molecule adjacent to a plasmonic patch nanoantenna. While this on its own had been considered, the assumption in prior work usually has been that each molecular transition is dominated only by one of those multipolar emission channels. This leads naturally to the notion of discussing the modified emission in terms of a modified local density of states defined for each specific multipolar transition. In reality, this restricts the applicability of the approach, since specific molecular transitions occur via multiple multipolar pathways that have to be considered all at once. Here, we introduce a framework to study interference effects between higher order transitions in molecules by (a) a rigorous quantum-chemical calculation of their multipolar moments and (b) by a consecutive investigation of the transition rate upon coupling to an arbitrarily shaped nanoantenna. Based on that formalism we predict interference effects between these transition channels. This allows for a strong suppression of radiation by exploiting destructive interference. Our work suggests that placing a suitably chosen molecule at a well defined position and at a well defined orientation relative to a nanoantenna can fully suppress the transition probability., Comment: 30 pages, 8 figures

We present a quantization scheme for optical systems with absorptive losses, based on an expansion in the complete set of scattering solutions to Maxwell's equations. The natural emergence of both absorptive loss and fluctuations without introducing a thermal bath is demonstrated. Our model predicts mechanisms of absorption induced squeezing and dispersion mediated photon conversion., Comment: 27 pages, 1 figure

Unitary transformations are routinely modeled and implemented in the field of quantum optics. In contrast, nonunitary transformations that can involve loss and gain require a different approach. In this theory work, we present a universal method to deal with nonunitary networks. An input to the method is an arbitrary linear transformation matrix of optical modes that does not need to adhere to bosonic commutation relations. The method constructs a transformation that includes the network of interest and accounts for full quantum optical effects related to loss and gain. Furthermore, through a decomposition in terms of simple building blocks it provides a step-by-step implementation recipe, in a manner similar to the decomposition by Reck et al. [Reck et al., Phys. Rev. Lett. 73, 58 (1994)] but applicable to nonunitary transformations. Applications of the method include the implementation of positive-operator-valued measures and the design of probabilistic optical quantum information protocols., Comment: We also provide a MATLAB code for numerically implementing the full decomposition on GitHub, at https://github.com/NoraTischler/QuantOpt-linear-transformation-decomposition

We analytically examine propagation of surface plasmon polaritons (SPPs) at a thin metallic film between glass substrate and electromagnetically-induced-transparency (EIT) medium. High-precision and high-resolution in frequency domain provided by EIT paves the way towards plasmonic group velocities reduction even by $4$ orders of magnitude and corresponding lifetime enhancement of SPPs up to microseconds., Comment: 5 pages, 5 figures

We present, for the first time, the quantum mechanical description of light-matter interaction in the presence of optical cavities that are characterized by radiative losses. Unique to radiative losses is the unitary evolution and their full preservation of the coherence, in stark contrast to the usually considered dissipative losses. We elucidate the reduction of exact quantum electrodynamic equations to a form similar to the familiar Jaynes-Cummings model through the introduction and study of a new class of noise operators. The dynamics of this henceforth inherently dissipative model are then presented by formulating the resulting equations of motion. Furthermore, an input- output formalism is established, which provides a direct connection to the dynamics of output states accessible with detectors. The application-oriented cases of coherent and pulsed laser pumping are discussed as inputs. Finally the single-photon dynamics in an optical cavity with significant radiative loss - whose importance has to be contextualized in view of the prospects of light-matter interaction applications - are reviewed according to the proposed model. The formulation is kept as general as possible to emphasise the universal applicability to different implementations of quantum optical systems but from our own background we have an application in mind in the context of nanooptics., Comment: 14 pages, 6 figures

The spectral response of a plasmonic nanostructure may heavily depend on the refractive index of its surroundings. The key idea of this paper is to control this response by coherent optical means, i.e. with an optically controlled electromagnetically-induced-transparency medium. In such environment, an external laser provides a knob to shift the position of plasmonic resonances without the need to change the geometry of the nanostructure. Additionally, the setup can be exploited to excite narrow-band surface plasmon polaritons., Comment: 8 pages, 6 figures

We suggest a hybrid plasmonic device consisting of a bimodal metallic nanoantenna coupled to an incoherently pumped quantum emitter. This hybrid device emits light into the two modes entangled in the number of photons. The process is a prime example where losses are turned from a nuisance into something beneficial, since, even though counterintuitively, the entanglement is enabled by strong incoherent processes, i.e. dominant scattering and absorption rates of the nanoantenna. Both, the high emission rate and the degree of entanglement of the emitted light are insensitive with respect to imperfections in the nanoantenna geometry, rendering the scheme feasible for an implementation.

Converting signals between different electromagnetic modes is an asset for future information technologies. In general, slightly asymmetric optical nanoantennas enable the coupling between bright and dark modes sustained by an optical nanoantenna. However, the conversion efficiency might be very low. Here, we show that the additional incorporation of a quantum emitter allows to tremendously enhance this efficiency. The enhanced local density of states cycles the quantum emitter between its upper and lower level at an extremely hight rate; hence converting the energy very efficient. The process is robust with respect to possible experimental tolerances and adds a new ingredient to be exploited while studying and applying coupling phenomena in optical nanosystems., Comment: 5 pages, 3 figures

With the purpose to devise a novel lasing scheme, we consider a two level system with both a transversal and longitudinal coupling to the electromagnetic field. If the longitudinal coupling is sufficiently strong, multi-photon transitions become possible. We assume furthermore that the electromagnetic environment has a spectrum with a single sharp resonance, which serves as a lasing cavity. Additionally, the electromagnetic environment should have a very broad resonance around a frequency which differs form the sharp resonance. We use the polaron transformation and derive a rate equation to describe the dynamics of such system. We find that lasing at the frequency of the sharp mode is possible, if the energy difference of the atomic transition is similar to the sum of the frequencies of both peaks in the spectral function. This allows for the creation of lasing over a large frequency range and may in perspective enable THz lasing at room temperature., Comment: 7 pages

Highly integrated single photon sources are key components in future quantum-optical circuits. Whereas the probabilistic generation of single photons can routinely be done by now, their triggered generation is a much greater challenge. Here, we describe the triggered generation of single photons in a hybrid plasmonic device. It consists of a lambda-type quantum emitter coupled to a multimode optical nanoantenna. For moderate interaction strengths between the subsystems, the description of the quantum optical evolution can be simplified by an adiabatic elimination of the electromagnetic fields of the nanoantenna modes. This leads to an insightful analysis of the emitter's dynamics, entails the opportunity to understand the physics of the device, and to identify parameter regimes for a desired operation. Even though the approach presented in this work is general, we consider a simple exemplary design of a plasmonic nanoantenna, made of two silver nanorods, suitable for triggered generation of single photons., Comment: 13 pages, 7 figures

A novel scheme is proposed to generate a maximally entangled state between two qubits by means of a dissipation-driven process. To this end, we entangle the quantum states of qubits that are mutually coupled by a plasmonic nanoantenna. Upon enforcing a weak spectral asymmetry in the properties of the qubits, the steady-state probability to obtain a maximally entangled, subradiant state approaches unity. This occurs despite the high losses associated to the plasmonic nanoantenna that are usually considered as being detrimental. The entanglement scheme is shown to be quite robust against variations in the transition frequencies of the quantum dots and deviations in their prescribed position with respect to the nanoantenna. Our work paves the way for novel applications in the field of quantum computation in highly integrated optical circuits., Comment: 9 pages, 5 figures

We propose to use nanoantennas coupled to incoherently pumped quantum dots for ultra-bright single photon emission. Besides fully quantum calculations, we analyze an analytical expression for the emitted photon rate. From these analytical considerations it turns out that the Purcell factor and the pumping rate are the main quantities of interest. We also disclose a trade-off between the emitted photon rate and the nonclassical nature of the emitted light. This trade-off has to be considered while designing suitable nanoantennas, which we also discuss in depth.

An optical nanoantenna and adjacent atomic systems are strongly coupled when an excitation is repeatedly exchanged between these subsystems prior to its eventual dissipation into the environment. It remains challenging to reach the strong coupling regime but it is equally rewarding. Once being achieved, promising applications as signal processing at the nanoscale and at the single photon level would immediately come into reach. Here, we study such hybrid configuration from different perspectives. The configuration we consider consists of two identical atomic systems, described in a two-level approximation, which are strongly coupled to an optical nanoantenna. First, we investigate when this hybrid system requires a fully quantum description and provide a simple analytical criterion. Second, a design for a nanoantenna is presented that enables the strong coupling regime. Besides a vivid time evolution, the strong coupling is documented in experimentally accessible quantities, such as the extinction spectra. The latter are shown to be strongly modified if the hybrid system is weakly driven and operates in the quantum regime. We find that the extinction spectra depend sensitively on the number of atomic systems coupled to the nanoantenna., Comment: 14 pages, 7 figures