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International Journal of Numerical Modelling Electronic Networks Devices and Fields

The modeling techniques of the second‐order correlation function g(2)(τ) for a quantum emitter

Farooq Abdulghafoor Khaleel, Shelan Khasro Tawfeeq

Published Apr 18, 2022• 2 citations
Publisher

Abstract

Abstract The numerical techniques required to prove the single‐photon emission from any type of quantum emitter (QE) after being coupled to any nanostructure are presented in this paper. The Purcell effect modifies the emission characteristics of QEs, such as color centers in nanodiamonds, for example, nitrogen‐vacancy (NV) centers, silicon vacancy (SiV) centers, and so forth, or semiconductor quantum dots. Our numerical approach is based on the unique QEs' experimental photophysics parameters and numerical analysis software, which are MATLAB and Quantum Toolbox in Python (QuTiP). Our results show a comparable g(2) (τ) behavior between our proposed numerical model and the other two experimental results for the QE before and after coupling to a plasmonic waveguide with subwavelength dimensions. Our proposed method is essential to prove the single‐photon emission of modeled single‐photon source (SPS) in an on‐chip polarization‐dependent quantum key distribution system (QKD).

DOI
10.1002/jnm.3013

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Abstract The numerical techniques required to prove the single‐photon emission from any type of quantum emitter (QE) after being coupled to any nanostructure are presented in this paper. The Purcell effect modifies the emission characteristics of QEs, such as color centers in nanodiamonds, for example, nitrogen‐vacancy (NV) centers, silicon vacancy (SiV) centers, and so forth, or semiconductor quantum dots. Our numerical approach is based on the unique QEs' experimental photophysics parameters and numerical analysis software, which are MATLAB and Quantum Toolbox in Python (QuTiP). Our results show a comparable g(2) (τ) behavior between our proposed numerical model and the other two experimental results for the QE before and after coupling to a plasmonic waveguide with subwavelength dimensions. Our proposed method is essential to prove the single‐photon emission of modeled single‐photon source (SPS) in an on‐chip polarization‐dependent quantum key distribution system (QKD).
The development of integrated quantum technologies relies on efficient single-photon sources and deterministic quantum operations. Solid-state quantum emitters coupled to nanophotonic structures present a promising solution. This work investigates color centers in nanodiamonds,particularly Germanium Vacancy (GeV) [1], Silicon Vacancy (SiV), and Magnesium Vacancy (MgV) centers, a novel, understudied emitter [2], at both room and cryogenic temperatures. These nanodiamonds are chosen for their stability and superior coherence properties at cryogenic conditions. To collect their emission we have successfully deposited a single GeV- nanodiamond on tapered optical nanofibers by gently contacting a diluted droplet to the nanofiber [3], demonstrating an average coupling of 15% into a conventional optical fiber through the confined evanescent field of the nanofiber mode and single photon emission. Building on this achievement, we aim to study the system at cryogenic temperatures, which should enable the demonstration of efficient and indistinguishable single photons coupling to conventional optical fibers.Current collection efficiencies are intrinsically limited to 30% with the nanofiber[4], and improving light-matter coupling efficiency remains a key goal for high-performance single-photon sources and more advanced applications.To achieve this, we are investigating a newly developed technique [5]: the deterministic fabrication of dielectric and plasmonic nanostructures directly on the nanofiber surface using an “electron beam induced deposition” (EBID). The precision and versatility of this technique openthe way to different applications: Purcell enhancement of the quantum emitter emission using metallic nanoantennas and efficient light-matter coupling using dielectric structures. Our first calculation shown that optimizing the composition, geometry, and placement of these nanostructures a simple pattern of carbon pillars around the emitter should increase coupling efficiency up to 69% while maintaining high transmission in the nanofiber. We also demonstratethe fabrication of those nanostructures on top of the nanofiber.This work advances integrated nanophotonic devices for single-photon sources.[1] M. Nahra et al.,Single germanium vacancy centers in nanodia-monds with bulk-like spectral stability, AVS Quantum Science3(1), (2021).[2] E. Corte et al, Magnesium-Vacancy Optical Centers in Diamond, ACS Photonics, 10(1), p101-110, (2023)[3] Pierini et al. Highly Photostable Perovskite Nanocubes : TowardIntegrated Single Photon Sources Based on Tapered Nanofibers.ACS Photonics, 7(8), p.2265-2272, (2020).[4] Fujiwara et al., Highly efficient coupling of photons from na-noemitters into single-mode optical fibers, Nano Letters, 11(10),4362–4365, (2011).[5] A.Balena et al, Deterministic Bottom-Up Fabrication of Plasmonic Nanostructures on OpticalNanofibers via Blurred Electron Beam Deposition (soon to be published in Advance Material).
Measurements of the photon second‐order correlation function, g (2) ( τ ), is a common tool for the characterization of single photon emitters, like nitrogen‐vacancy color centers in diamond. Such measurement requires background photoluminescence correction, which is easy when this background is homogeneous on a few wavelengths scale. However, if the sample contains emitting centers separated by a distance smaller than the optical diffraction limit, and having different and overlapping emission, these background correction techniques cannot be applied. We have recently shown that cathodoluminescence (CL) can be used to measure g (2) ( τ ) at the subwavelength scale. Here we propose a method, based on spatially and spectrally resolved CL, to subtract the background taking into account the nanometer spatial distribution of the emitted light. To this end, a nanometer‐resolved spectrum image is acquired on the same region where the g (2) ( τ ) is measured. As an example, we show the use of this method to the subtraction of the H3 background signal from a g (2) ( τ ) measurement done on NV 0 color centers.
We measured the second-order correlation function of the cathodoluminescence intensity and investigated the Purcell effect by comparing the lifetimes of quantum emitters with and without metal structure. The increase in the electromagnetic local density of state due to the coupling of a quantum emitter with a plasmonic structure causes a shortening of the emitter lifetime. Since the plasmon-enhanced electric field is confined well below the wavelength of light, the quantum emitter lifetime is changed in the nanoscale range. In this study, we combined cathodoluminescence in scanning (transmission) electron microscopy with Hanbury Brown--Twiss interferometry to measure the Purcell effect with nanometer and nanosecond resolutions. We used nitrogen-vacancy centers contained in nanodiamonds as the emitters and compared their lifetime in different environments: on a thin SiO2\mathrm{Si}{\mathrm{O}}_{2}SiO2​ membrane, on a thick flat silver film, and embedded in a silver film. The lifetime reductions of nitrogen-vacancy centers were observed in the samples with silver. We evaluated the lifetime by analytical calculation and numerical simulations and revealed the Purcell effects of emitters coupled to the propagating and localized surface plasmons.
The nitrogen vacancy center in diamond in its negative charge state is a promising candidate for quantum optic experiments that require single photon emitters. Important benefits of the NV center are its high brightness and photo-stability, even at room temperature. Engineering the emission properties of NV centers with optical resonators is a widely followed approach to meet the requirements for quantum technological applications, but the effect on non-radiative decay paths is yet to be understood. Here we report on modifying the internal quantum efficiency of a single NV center in a nanodiamond coupled to a 1D photonic crystal cavity. We assess the Purcell enhancement via three independent measurement techniques and perform autocorrelation measurements at elevated excitation powers in confocal microscopy. Employing a three-level model allows us to extract the setup efficiency, individual transition rates and thus the internal quantum efficiency of our system. Combining our results, we find that the enhancement of the radiative decay rate via the Purcell effect results in an internal quantum efficiency of 90 % for cavity-coupled NV centers. Our findings will facilitate the realization of nano-scale single photon sources with near-unity internal quantum efficiencies operating at high repetition rates.
Engineering the photo-emission characteristics of single-photon emitters is crucial for the growing field of quantum technologies. We show that the photoluminescence of a single nitrogen-vacancy color center in nanodiamond could be significantly enhanced when attached to a gold film of 50 nm with preserving photophysical properties as a single photon source. The nitrogen-vacancy center on the gold film showed a decreased excited-state lifetime and a modified saturation characteristic. The photoluminescence enhancement was due to the enhanced electric field by the surface plasmon and the energy transfer from the excited state of nitrogen-vacancy centers to the surface plasmon.
Abstract Integrated on‐demand single‐photon sources are critical for the implementation of photonic quantum information processing systems. To enable practical quantum photonic devices, the emission rates of solid‐state quantum emitters need to be substantially enhanced and the emitted signal must be directly coupled to an on‐chip circuitry. The photon emission rate speed‐up is best achieved via coupling to plasmonic antennas, while on‐chip integration can be realized by directly coupling emitters to photonic waveguides. The realization of practical devices requires that both the emission speed‐up and efficient out‐coupling are achieved in a single architecture. Here, a novel architecture is proposed that combines chip compatibility with high radiative emission rates—a quantum plasmonic launcher. The proposed launchers contain single nitrogen‐vacancy (NV) centers in nanodiamonds as quantum emitters that offer record‐high average fluorescence lifetime shortening factors of about 7000 times. Nanodiamonds with single NVs are sandwiched between two silver films that couple more than half of the emission into in‐plane propagating surface plasmon polaritons. This simple, compact, and scalable architecture represents a crucial step toward the practical realization of high‐speed on‐chip quantum networks.