Numerical modeling of exciton–polariton Bose–Einstein condensate in a microcavity

Abstract

A novel, optimized numerical method of modeling of an exciton-polariton superfluid in a semiconductor microcavity was proposed. Exciton-polaritons are spin-carrying quasiparticles formed from photons strongly coupled to excitons. They possess unique properties, interesting from the point of view of fundamental research as well as numerous potential applications. However, their numerical modeling is challenging due to the structure of nonlinear differential equations describing their evolution. In this paper, we propose to solve the equations with a modified Runge-Kutta method of 4th order, further optimized for efficient computations. The algorithms were implemented in form of C++ programs fitted for parallel environments and utilizing vector instructions. The programs form the EPCGP suite which have been used for theoretical investigation of exciton-polaritons.Keywords: exciton-polariton superfluid; Bose-Einstein condensate; microcavity; Gross-Pitaevskii equation; Runge-Kutta method Nature of problem: An exciton-polariton superfluid is a novel, interesting physical system allowing investigation of high temperature Bose-Einstein condensation of exciton-polaritons-quasiparticles carrying spin. They have brought a lot of attention due to their unique properties and potential applications in polariton-based optoelectronic integrated circuits. This is an out-of-equilibrium quantum system confined within a semiconductor microcavity. It is described by a set of nonlinear differential equations similar in spirit to the Gross-Pitaevskii (GP) equation, but their unique properties do not allow standard GP solving frameworks to be utilized. Finding an accurate and efficient numerical algorithm as well as development of optimized numerical software is necessary for effective theoretical investigation of exciton-polaritons. Program summarySolution method: A Runge-Kutta method of 4th order was employed to solve the set of differential equations describing exciton-polariton superfluids. The method was fitted for the exciton-polariton equations and further optimized. The C++ programs utilize OpenMP extensions and vector operations in order to fully utilize the computer hardware.

Superluminal X-waves in a polariton quantum fluid

“…The device parameters were: m C = 4.27 × 10 −5 m e , γ C = 0.2 ps −1 , γ X = 0.2 ps −1 , g = 2 × 10 −3 meV • µm 2 , photon-exciton detuning ∆ = −0.55 meV, Ω R = 5.4 meV. The details of the numerical method are described in 47 . Numerical computations were performed with Zeus cluster of the ACK "Cyfronet" AGH computer center.…”

Exciton-polariton based WS₂ polarization modulator controlled by optical Stark beam

“…Here we demonstrate that through this shift, a continuous wave that can instantaneously cause a shift in the energy of excitons and create a potential (up to few meV to few tens of meV) of polaritons, the so-called OS effect. This OS effect causes the shift in the polariton quantum states and can be used to manipulate in various ways for optoelectronic applications 1,3,7,22,26 . Here, a polaritonic potential, i.e., OS shift, is created just like in ref.…”

“…The optical pumping will raise or lower the magnetic quantum number of excitons by one, and a circularly polarized Stark beam will prepare the spin-polarized excitons with blue-shifted excitonic energy 11,25,26,32 . As indicated in Fig.…”

“…It has been reported that a large OS shift of 21 meV is realizable in WS 2 excitons 11 , paving a way for various applications based on OS shift in TMDs in particular WS 2 microcavity. Various characteristics of the polaritons in WS 2 microcavity, has been studied and manipulated in different ways for design of optoelectronic devices 6,10,11,21,26 . For example, surface Plasmon polariton graphene Photodetectors have been reported in which they couple graphene with a plasmonic grating and exploit the resulting surface plasmon polaritons to deliver the collected photons to the junction region of a photodetector with 400% enhancement of responsivity and a 1000% increase in photoactive length 6 .…”

“…Currently, polariton based LED in monolayer of WS 2 is designed which is stable at room temperature and have quantum efficiency of 0.1% 23 . Recently we have proposed an all optical polariton based multimode interferometer, in which OS shift is used as a controlling parameter to control modal interference of polaritons without the consideration of polarization issue 26 . While exploiting spin characteriscs of polaritonic devices are still far from enough and deserves further study.…”