The quantum technologies series of articles started with the basics of quantum electromagnetics and then turned to deal with various promising applications. These range from the computation of the Casimir force to the analysis of interactions between electromagnetic waves and large molecules behaving as nanoantennas. Another article outlined the advantages of more futuristic higher level applications, such as quantum radars and lidars. Recent articles in the series covered device-level performance, including the quantum electrodynamics of plasmonic waveguides and construction of transmon qubits. Similarly, the present contribution, “Numerical Simulations of Laser Pulse Propagation in Quantum Active Media,” deals with the semiclassical analysis of field interaction with a collection of quantum dots, posing a heavy computational challenge. One typically sidesteps this by deriving a homogeneous behavior. But this leaves out interesting design opportunities. This article takes a different approach to the self-consistent analysis of a large ensemble of quantum dots. It combines analysis methods that are well known in the electromagnetics community together with predictor–corrector methods to solve for the evolution of the polarization of quantum dots. Interestingly, the approach correctly predicts experimentally observed behavior.
The quantum technologies series of articles started with the basics of quantum electromagnetics and then turned to deal with various promising applications. These range from the computation of the Casimir force to the analysis of interactions between electromagnetic waves and large molecules behaving as nanoantennas. Another article outlined the advantages of more futuristic higher level applications, such as quantum radars and lidars. Recent articles in the series covered device-level performance, including the quantum electrodynamics of plasmonic waveguides and construction of transmon qubits. Similarly, the present contribution, “Numerical Simulations of Laser Pulse Propagation in Quantum Active Media,” deals with the semiclassical analysis of field interaction with a collection of quantum dots, posing a heavy computational challenge. One typically sidesteps this by deriving a homogeneous behavior. But this leaves out interesting design opportunities. This article takes a different approach to the self-consistent analysis of a large ensemble of quantum dots. It combines analysis methods that are well known in the electromagnetics community together with predictor–corrector methods to solve for the evolution of the polarization of quantum dots. Interestingly, the approach correctly predicts experimentally observed behavior.
The nonlinear optical response of an ensemble of semiconductor quantum dots is analyzed by wave-mixing processes, where we focus on four-wave mixing with two incident pulses. Wave-mixing experiments are often described with semiclassical models, where the light is modeled classically and the material quantum mechanically. Here, however, we use a fully quantized model, where the light is given by a quantum state of light. Quantum light involves more degrees of freedom than classical light as e.g., its photon statistics and quantum correlations, which is a promising resource for quantum devices, such as quantum memories. The light-matter interaction is treated with a Jaynes-Cummings type model and the quantum field is given by a single mode since the quantum dots are embedded in a microcavity. We present numerical simulations of the four-wave-mixing response of a homogeneous system for pulse sequences and find a significant dependence of the result on the photon statistics of the incident pulses. The model constitutes a problem with a large state space which arises from the frequency distribution of the transition energies of the inhomogeneously broadened quantum dot ensemble that is coupled with a quantum light mode. Here we approximate the dynamics by summing over individual quantum dot-microcavity systems. Photon echoes arising from the excitation with different quantum states of light are simulated and compared.
Active media are materials that consist of quantum systems, such as atoms, impurities, or quantum dots, and are characterized by strong resonant absorption and re-emission of radiation. In this article, we present a general framework for the numerical simulation and analysis of time-dependent radiation-induced phenomena in active media. The formulation used is based on the solution of semiclassical Maxwell–Bloch equations describing the evolution of each quantum element under the effect of external and re-emitted radiation. Within these Maxwell–Bloch equations, the coupling of quantum systems to classical Maxwellian fields poses computational challenges due to the strong nonlinearities involved. In contrast to traditional mesh-based solvers, we adopt an electric field integral-operator approach that can reliably account for near-field effects—including self-radiation—and is scalable to large systems. We then focus on media based on large numbers of quantum dots and demonstrate various physical effects arising from the near-field coupling, including polarization modulations and superradiance.
Attempting to implement quantum information related applications utilizing atoms and photons, as they naturally form quantum systems supporting superposition states, hybrid quantum plasmonic systems emerged in the past as a platform to study and engineer light-matter interaction. This platform combines the unrivaled electromagnetic field localization of surface plasmon polaritons, boosting the light-matter coupling rate, with the tremendous integration potential of truly nanoscale structures, and both the significant emission rates of nanoantennas and photonic transmission velocities. In this work, a classical description of surface plasmon polaritons is combined with a light-matter interaction model based on a cavity quantum electrodynamical formalism. The resulting composite semi-classical method, introduced and described in this thesis, provides efficient and versatile means to simulate the dynamical behavior of radiative atomic transitions coupled to plasmonic cavity modes in the weak incoherent coupling regime. Both the emission into the far field and various dissipation mechanisms are included by expanding the model to an open quantum system. The variety of light-matter interaction applications that can be modeled with the outlined method is indicated by the four different exemplary scenarios detailed in the application chapter of this thesis. The classical description of localized surface plasmon polaritons is benchmarked by reproducing the experimental measurements of the molecular fluorescence manipulation through optical nanoantennas in a collaborative effort with experimental partners. Furthermore, in the weak light-matter coupling regime, the potential of achieving a higher nanoantenna functionality and simultaneously realizing more elaborate quantum dynamics is revealed by the three remaining applications. Each pivotally involving a bimodal nanoantenna and demonstrating different quantum optical phenomena, the implementation of cavity radiation mode conversion, non-classical cavity emission statistics, and non-classical cavity emission properties is shown and described in the application chapter.
Progress in the fabrication of high quality optical cavities operating with semiconductor-based active media has promoted the semiconductor quantum optics. The materials interaction with coherent electromagnetic field is a subject of quantum electrodynamics (QED), a well developed science after discovery of lasers. Many of the QED areas incorporate atomic physics, classical electrodynamics, and quantum field theory. The chapter reviews basics of the Cavity QED (CQED) and several results in the field mostly related to the quantum dots. In optical version of CQED one drives the cavity with a laser and monitors changes in the cavity transmission resulting from coupling to atoms falling through the cavity. The high degree of coherence which could be achieved in modern CQED experiments makes them a basis for quantum control and quantum computing. Quantum technology show great potential for revolutionizing the methods for collecting and distributing information.
Abstract Over the last few decades, the quantum aspects of light have been explored and major progress has been made in understanding the specific quantum aspects of the interaction between light and matter. Single photons are now routinely produced by single molecules on surfaces, vacancies in crystals, and quantum dots. The micrometre and nanometre scale is also the privileged range where fluctuations of electromagnetic fields manifest themselves through the Casimir force. The domain of classical optics has recently seen many exciting new developments, especially in the areas of nano-optics, nano-antennas, metamaterials, and optical cloaking. Approaches based on single-molecule detection and plasmonics have provided new avenues for exploring light–matter interaction at the nanometre scale. All these topics have in common a trend to consider and use smaller and smaller objects, down to the micrometre, nanometre, and even atomic range, a region where one gradually passes from classical physics to quantum physics. The summer school held in Les Houches in July 2013 treated all these subjects lying at the frontier between nanophotonics and quantum optics, in a series of lectures given by world experts in the domain and gathered together in the present volume.
Frontier quantum engineering tasks require reliable control over light-matter interaction dynamics, which could be obtained by introducing electromagnetic structuring. Initiated by the Purcell's discovery of spontaneous emission acceleration in a cavity, the concept of electromagnetic modes' design have gained a considerable amount of attention due to development of photonic crystals, micro-resonators, plasmonic nanostructures and metamaterials. Those approaches, however, offer qualitatively different strategies for tailoring light-matter interactions and are based on either high quality factor modes shaping, near field control, or both. Remarkably, rigorous quantum mechanical description might address those processes in a different fashion. While traditional cavity quantum electrodynamics tools are commonly based on mode decomposition approach, few challenges rise once dispersive and lossy nanostructures, such as noble metals (plasmonic) antennas or metamaterials, are involved. The primary objective of this review is to introduce key methods and techniques while aiming to obtain comprehensive quantum mechanical description of spontaneous, stimulated and higher order emission and interaction processes, tailored by nanostructured material environment. The main challenge and the complexity here are set by the level of rigorousity, up to which materials should be treated. While relatively big nanostructured features (10 nm and larger) could be addressed by applying fluctuation–dissipation theorem and corresponding Green functions' analysis, smaller objects will require individual approach. Effects of material granularity, spatial dispersion, tunneling over small gaps, material memory and others will be reviewed. Quantum phenomena, inspired and tailored by nanostructured environment, plays a key role in development of quantum information devices and related technologies. Rigorous analysis is required for both examination of experimental observations and prediction of new effects.