Phonon-Induced Dephasing in Quantum Dot-Cavity QED

We present a semi-analytic and asymptotically exact solution to the problem of phonon-induced decoherence in a quantum dot-microcavity system. Particular emphasis is placed on the linear polarization and optical absorption, but the approach presented herein may be straightforwardly adapted to address any elements of the exciton-cavity density matrix. At its core, the approach combines Trotter's decomposition theorem with the linked cluster expansion. The effects of the exciton-cavity and exciton-phonon couplings are taken into account on equal footing, thereby providing access to regimes of comparable polaron and polariton timescales. We show that the optical decoherence is realized by real phonon-assisted transitions between different polariton states of the quantum dot-cavity system, and that the polariton line broadening is well-described by Fermi's golden rule in the polariton frame. We also provide purely analytic approximations which accurately describe the system dynamics in the limit of longer polariton timescales

Resonant-state expansion for open optical systems: Generalization to magnetic, chiral, and bi-anisotropic materials

The resonant-state expansion, a recently developed powerful method in electrodynamics, is generalized here for open optical systems containing magnetic, chiral, or bi-anisotropic materials. It is shown that the key matrix eigenvalue equation of the method remains the same, but the matrix elements of the perturbation now contain variations of the permittivity, permeability, and bi-anisotropy tensors. A general normalization of resonant states in terms of the electric and magnetic fields is presented.Comment: 4 page

Exciton effective mass enhancement in coupled quantum wells in electric and magnetic fields

We present a calculation of exciton states in semiconductor coupled quantum wells (CQWs) in the presence of electric and magnetic fields applied perpendicular to the QW plane. The exciton Schr\"odinger equation is solved in real space in three dimensions to obtain the Landau levels of both direct and indirect excitons. Calculation of the exciton energy levels and oscillator strengths enables mapping of the electric and magnetic field dependence of the exciton absorption spectrum. For the ground state of the system, we evaluate the Bohr radius, optical lifetime, binding energy and dipole moment. The exciton mass renormalization due to the magnetic field is calculated using a perturbative approach. We predict a non-monotonous dependence of the exciton ground state effective mass on magnetic field. Such a trend is explained in a classical picture, in terms of the ground state tending from an indirect to a direct exciton with increasing magnetic field.Comment: 20 pages, 7 figure

Exact mode volume and Purcell factor of open optical systems

The Purcell factor quantifies the change of the radiative decay of a dipole in an electromagnetic environment relative to free space. Designing this factor is at the heart of photonics technology, striving to develop ever smaller or less lossy optical resonators. The Purcell factor can be expressed using the electromagnetic eigenmodes of the resonators, introducing the notion of a mode volume for each mode. This approach allows to use an analytic treatment, consisting only of sums over eigenmode resonances, a so-called spectral representation. We show in the present work that the expressions for the mode volumes known and used in literature are only approximately valid for modes of high quality factor, while in general they are incorrect. We rectify this issue, introducing the exact normalization of modes. We present an analytic theory of the Purcell effect based on the exact mode normalization and resulting effective mode volume. We use a homogeneous dielectric sphere in vacuum, which is analytically solvable, to exemplify these findings.Comment: Letter: 5 pages, 2 figures. Supplementary material: 16 pages, 10 figure

Controlled strong coupling and absence of dark polaritons in microcavities with double quantum wells

We demonstrate an efficient switching between strong and weak exciton-photon coupling regimes in microcavity-embedded asymmetric double quantum wells, controlled by an applied electric field. We show that a fine tuning of the electric field leads to drastic changes in the polariton properties, with the polariton ground state being red-shifted by a few meV and having acquired prominent features of a spatially indirect dipolar exciton. We study the properties of dipolar exciton polaritons, called dipolaritons, on a microscopic level and show that, unlike recent findings, they are not dark polaritons but, owing to the finite size of the excition, are mixed states with comparable contribution of the cavity photon, bright direct, and long-living indirect exciton modes.Comment: 5 pages, 5 figures, and supplementary materia

Resonant state expansion applied to planar open optical systems

The resonant state expansion (RSE), a novel perturbation theory of Brillouin-Wigner type developed in electrodynamics [Muljarov, Langbein, and Zimmermann, Europhys. Lett., 92, 50010(2010)], is applied to planar, effectively one-dimensional optical systems, such as layered dielectric slabs and Bragg reflector microcavities. It is demonstrated that the RSE converges with a power law in the basis size. Algorithms for error estimation and their reduction by extrapolation are presented and evaluated. Complex eigenfrequencies, electro-magnetic fields, and the Green's function of a selection of optical systems are calculated, as well as the observable transmission spectra. In particular we find that for a Bragg-mirror microcavity, which has sharp resonances in the spectrum, the transmission calculated using the resonant state expansion reproduces the result of the transfer/scattering matrix method

Resonant-state expansion of dispersive open optical systems: Creating gold from sand

A resonant-state expansion (RSE) for open optical systems with a general frequency dispersion of the permittivity is presented. The RSE of dispersive systems converts Maxwell's wave equation into a linear matrix eigenvalue problem in the basis of unperturbed resonant states, in this way numerically exactly determining all relevant eigenmodes of the optical system. The dispersive RSE is verified by application to the analytically solvable system of a sphere in vacuum, with a dispersion of the permittivity described by the Drude and Drude-Lorentz models. We calculate the optical modes converting the sphere material from gold to nondispersive sand and back to gold, and evaluate the accuracy using exact solutions