Photocount statistics of chaotic lasers

We derive the photocount statistics of the radiation emitted from a chaotic laser resonator in the regime of single-mode lasing. Random spatial variations of the resonator eigenfunctions lead to strong mode-to-mode fluctuations of the laser emission. The distribution of the mean photocount over an ensemble of modes changes qualitatively at the lasing transition, and displays up to three peaks above the lasing threshold

Quantum theory of a two-mode open-cavity laser

We develop the quantum theory of an open-cavity laser assuming that only two modes compete for gain. We show that the modes interact to build up a collective mode that becomes the lasing mode when pumping exceeds a threshold. This collective mode exhibits all the features of a typical laser mode, whereas its precise behavior depends explicitly on the openness of the cavity. We approach the problem by using the density-matrix formalism and derive the master equation for the light field. Our results are of particular interest in the context random laser systems.Comment: 20 pages, 5 figure

Field quantization for chaotic resonators with overlapping modes

Feshbach's projector technique is employed to quantize the electromagnetic field in optical resonators with an arbitray number of escape channels. We find spectrally overlapping resonator modes coupled due to the damping and noise inflicted by the external radiation field. For wave chaotic resonators the mode dynamics is determined by a non--Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.Comment: 4 pages, 1 figur

Asymptotic Entanglement Dynamics and Geometry of Quantum States

A given dynamics for a composite quantum system can exhibit several distinct properties for the asymptotic entanglement behavior, like entanglement sudden death, asymptotic death of entanglement, sudden birth of entanglement, etc. A classification of the possible situations was given in [M. O. Terra Cunha, {\emph{New J. Phys}} {\bf{9}}, 237 (2007)] but for some classes there were no known examples. In this work we give a better classification for the possibile relaxing dynamics at the light of the geometry of their set of asymptotic states and give explicit examples for all the classes. Although the classification is completely general, in the search of examples it is sufficient to use two qubits with dynamics given by differential equations in Lindblad form (some of them non-autonomous). We also investigate, in each case, the probabilities to find each possible behavior for random initial states.Comment: 9 pages, 2 figures; revised version accepted for publication in J. Phys. A: Math. Theo

Fundamental and high-order anapoles in all-dielectric metamaterials via Fano-Feshbach modes competition

One of the most fascinating possibilities enabled by metamaterials is the strong reduction of the electromagnetic scattering from nanostructures. In dielectric nanoparticles, the formation of a minimal scattering state at specific wavelengths is associated with the excitation of photonic anapoles, which represent a peculiar type of radiationless state and whose existence has been demonstrated experimentally. In this work, we investigate the formation of anapole states in generic dielectric structures by applying a Fano–Feshbach projection scheme, a general technique widely used in the study of quantum mechanical open systems. By expressing the total scattering from the structure in terms of an orthogonal set of internal and external modes, defined in the interior and in the exterior of the dielectric structure, respectively, we show how anapole states are the result of a complex interaction among the resonances of the system and the surrounding environment. We apply our approach to a circular resonator, where we observe the formation of higher-order anapole states, which are originated by the superposition of several internal resonances of the system

Quantum statistics of overlapping modes in open resonators

We study the quantum dynamics of optical fields in weakly confining resonators with overlapping modes. Employing a recently developed quantization scheme involving a discrete set of resonator modes and continua of external modes we derive Langevin equations and a master equation for the resonator modes. Langevin dynamics and the master equation are proved to be equivalent in the Markovian limit. Our open-resonator dynamics may be used as a starting point for a quantum theory of random lasers.Comment: 6 pages, corrected typo

Field quantization for open optical cavities

We study the quantum properties of the electromagnetic field in optical cavities coupled to an arbitrary number of escape channels. We consider both inhomogeneous dielectric resonators with a scalar dielectric constant $\epsilon({\bf r})$ and cavities defined by mirrors of arbitrary shape. Using the Feshbach projector technique we quantize the field in terms of a set of resonator and bath modes. We rigorously show that the field Hamiltonian reduces to the system--and--bath Hamiltonian of quantum optics. The field dynamics is investigated using the input--output theory of Gardiner and Collet. In the case of strong coupling to the external radiation field we find spectrally overlapping resonator modes. The mode dynamics is coupled due to the damping and noise inflicted by the external field. For wave chaotic resonators the mode dynamics is determined by a non--Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.Comment: 16 pages, added references, corrected typo

Random Matrices close to Hermitian or unitary: overview of methods and results

The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical contexts, most importantly in random matrix description of quantum chaotic scattering as well as in the context of QCD-inspired random matrix models.Comment: Published version, with a few more misprints correcte