Multi-plasmon absorption in graphene

We show that graphene possesses a strong nonlinear optical response in the form of multi-plasmon absorption, with exciting implications in classical and quantum nonlinear optics. Specifically, we predict that graphene nano-ribbons can be used as saturable absorbers with low saturation intensity in the far-infrared and terahertz spectrum. Moreover, we predict that two-plasmon absorption and extreme localization of plasmon fields in graphene nano-disks can lead to a plasmon blockade effect, in which a single quantized plasmon strongly suppresses the possibility of exciting a second plasmon

Theory of self-induced back-action optical trapping in nanophotonic systems

Optical trapping is an indispensable tool in physics and the life sciences. However, there is a clear trade off between the size of a particle to be trapped, its spatial confinement, and the intensities required. This is due to the decrease in optical response of smaller particles and the diffraction limit that governs the spatial variation of optical fields. It is thus highly desirable to find techniques that surpass these bounds. Recently, a number of experiments using nanophotonic cavities have observed a qualitatively different trapping mechanism described as "self-induced back-action trapping" (SIBA). In these systems, the particle motion couples to the resonance frequency of the cavity, which results in a strong interplay between the intra-cavity field intensity and the forces exerted. Here, we provide a theoretical description that for the first time captures the remarkable range of consequences. In particular, we show that SIBA can be exploited to yield dynamic reshaping of trap potentials, strongly sub-wavelength trap features, and significant reduction of intensities seen by the particle, which should have important implications for future trapping technologiesComment: 7 pages, 5 figure

Non-equilibrium diagrammatic approach to strongly interacting photons

We develop a non-equilibrium field-theoretical approach based on a systematic diagrammatic expansion for strongly interacting photons in optically dense atomic media. We consider the case where the characteristic photon-propagation range $L_P$ is much larger than the interatomic spacing $a$ and where the density of atomic excitations is low enough to neglect saturation effects. In the highly polarizable medium the photons experience nonlinearities through the interactions they inherit from the atoms. If the atom-atom interaction range $L_E$ is also large compared to $a$, we show that the subclass of diagrams describing scattering processes with momentum transfer between photons is suppressed by a factor $a/L_E$. We are then able to perform a self-consistent resummation of a specific (Hartree-like) diagram subclass and obtain quantitative results in the highly non-perturbative regime of large single-atom cooperativity. Here we find important, conceptually new collective phenomena emerging due to the dissipative nature of the interactions, which even give rise to novel phase transitions. The robustness of these is investigated by inclusion of the leading corrections in $a/L_E$. We consider specific applications to photons propagating under EIT conditions along waveguides near atomic arrays as well as within Rydberg ensembles.Comment: 72 pages, 36 figure

Optical properties of an atomic ensemble coupled to a band edge of a photonic crystal waveguide

We study the optical properties of an ensemble of two-level atoms coupled to a 1D photonic crystal waveguide (PCW), which mediates long-range coherent dipole-dipole interactions between the atoms. We show that the long-range interactions can dramatically alter the linear and nonlinear optical behavior, as compared to a typical atomic ensemble. In particular, in the linear regime, we find that the transmission spectrum reveals multiple transmission dips, whose properties we show how to characterize. In the many-photon regime the system response can be highly non-linear, and under certain circumstances the ensemble can behave like a single two-level system, which is only capable of absorbing and emitting a single excitation at a time. Our results are of direct relevance to atom-PCW experiments that should soon be realizable

Photon molecules in atomic gases trapped near photonic crystal waveguides

Realizing systems that support robust, controlled interactions between individual photons is an exciting frontier of nonlinear optics. To this end, one approach that has emerged recently is to leverage atomic interactions to create strong and spatially non-local interactions between photons. In particular, effective interactions have been successfully created via interactions between atoms excited to Rydberg levels. Here, we investigate an alternative approach, in which atomic interactions arise via their common coupling to photonic crystal waveguides. This technique takes advantage of the ability to separately tailor the strength and range of interactions via the dispersion engineering of the structure itself, which can lead to qualitatively new types of phenomena. As an example, we discuss the formation of correlated transparency windows, in which photonic states of a certain number and shape selectively propagate through the system. Through this technique, we show in particular that one can create molecular-like potentials that lead to molecular bound states of photon pairs

Multi-photon Scattering Theory and Generalized Master Equations

We develop a scattering theory to investigate the multi-photon transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not require the Markov approximation. We obtain the full time-evolution of the global system, including the emitters and the photonic field. Our theory allows us to compute the transition amplitude between arbitrary initial and final states, as well as the S-matrix of the asymptotic in- and out- states. For the case of few incident photons in the waveguide, we also re-derive a generalized master equation in the Markov limit. We compare the predictions of the developed scattering theory and that with the Markov approximation. We illustrate our methods with five examples of few-photon scattering: (i) by a two-level emitter, (ii) in the Jaynes-Cummings model; (iii) by an array of two-level emitters; (iv) by a two-level emitter in the half-end waveguide; (v) by an array of atoms coupled to Rydberg levels. In the first two, we show the application of the scattering theory in the photon scattering by a single emitter, and examine the correctness of our theory with the well-known results. In the third example, we analyze the condition of the Markov approximation for the photon scattering in the array of emitters. In the forth one, we show how a quantum emitter can generate entanglement of out-going photons. Finally, we highlight the interplay between the phenomenon of electromagnetic-induced transparency and the Rydberg interaction, and show how this results in a rich variety of possibilities in the quantum statistics of the scattering photons.Comment: 21 pages,10 figure