Phys. Rev. Applied 8, 024031 (2017) - Dynamics of Single-Photon Emission from Electrically Pumped Color Centers

Dynamics of Single-Photon Emission from Electrically Pumped Color Centers

Igor A. Khramtsov, Mario Agio, and Dmitry Yu. Fedyanin

Phys. Rev. Applied 8, 024031 – Published 31 August 2017

Abstract

Low-power, high-speed, and bright electrically driven true single-photon sources, which are able to operate at room temperature, are vital for the practical realization of quantum-communication networks and optical quantum computations. Color centers in semiconductors are currently the best candidates; however, in spite of their intensive study in the past decade, the behavior of color centers in electrically controlled systems is poorly understood. Here we present a physical model and establish a theoretical approach to address single-photon emission dynamics of electrically pumped color centers, which interprets experimental results. We support our analysis with self-consistent numerical simulations of a single-photon emitting diode based on a single nitrogen-vacancy center in diamond and predict the second-order autocorrelation function and other emission characteristics. Our theoretical findings demonstrate remarkable agreement with the experimental results and pave the way to the understanding of single-electron and single-photon processes in semiconductors.

Received 20 January 2017

DOI:https://doi.org/10.1103/PhysRevApplied.8.024031

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Color centers Electroluminescence Optical quantum information processing Optoelectronics Photonics Quantum communication Single photon sources

Nitrogen vacancy centers in diamond

Condensed Matter & Materials PhysicsGeneral PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Igor A. Khramtsov¹, Mario Agio^2,3, and Dmitry Yu. Fedyanin^1,*

¹Laboratory of Nanooptics and Plasmonics, Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russian Federation
²Laboratory of Nano-Optics, University of Siegen, 57072 Siegen, Germany
³National Institute of Optics (CNR-INO) and Center for Quantum Science and Technology in Arcetri (QSTAR), 50125 Florence, Italy

^*dmitry.fedyanin@phystech.edu

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Vol. 8, Iss. 2 — August 2017

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Figure 1
(a) Schematic illustration of the typical $g^{(2)}$ $g^{(2)}$ function of electrically pumped color center. (b)–(d) Diagram of the three-stage process of single-photon emission from the NV center in diamond under electrical pumping: (b) hole capture from the valence band, (c) photon emission, and (d) electron capture from the conduction band (or hole release to the conduction band). In panels (b) and (c), the excited level $E_{| e ⟩}^{0}$ $E_{| e ⟩}^{0}$ is shown below the ground level $E_{| g ⟩}^{0}$ $E_{| g ⟩}^{0}$ , since transitions in the $N V^{0}$ $N V^{0}$ center are related to the capture of a hole and its subsequent relaxation to the ground level. This energy level is physically responsible for the known $2 A_{1}$ ${}^{2}{A_{1}}$ excited state of the $N V^{0}$ $N V^{0}$ center.
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Figure 2
Characteristic times $τ_{1}$ $τ_{1}$ [panels (a) and (b)] and $τ_{2}$ $τ_{2}$ [panels (c) and (d)] of the $g^{(2)}$ $g^{(2)}$ function for the electrically pumped NV center in diamond at room temperature, $η = 30 %$ $η = 30 %$ [25]. At dashed lines, either $c_{p} p = 1 / τ_{0}$ $c_{p} p = 1 / τ_{0}$ or $c_{n} n = 1 / τ_{0}$ $c_{n} n = 1 / τ_{0}$ .
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Figure 3
(a) Schematic view of the single-photon emitting $p - i - n$ $p − i − n$ diamond diode (not to scale). The diameter of the diamond disk is equal to $220 μ m$ $220 μ m$ , the thickness of the $n$ $n$ -type layer is 500 nm, and the intrinsic region is $10 μ m$ $10 μ m$ thick. The NV center is at a depth of 300 nm and at a distance of about $30 μ m$ $30 μ m$ from the $n$ $n$ -type contact. (b)–(e) Background-corrected experimental $g^{(2)}$ $g^{(2)}$ curves extracted from Ref. [10] (shown in green) and numerically simulated $g^{(2)}$ $g^{(2)}$ functions (shown in orange) for four different pump currents. The experimentally measured current and corresponding local current density obtained in the simulations are shown in each panel. The quantum efficiency is extracted from the experiment and is equal to 78% in the simulations.
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Figure 4
(a) Characteristic times $τ_{1}$ $τ_{1}$ and $τ_{2}$ $τ_{2}$ of the $g^{(2)}$ $g^{(2)}$ function for the NV center in the $p - i - n$ $p − i − n$ diode versus the pump current density. Inset: Electron and hole densities in the vicinity of the color center as a function of the injection current. (b) Simulated evolution of the $g^{(2)}$ $g^{(2)}$ function with the increasing pump current.
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Figure 5
(a) Schematic illustration of the three-level model of the $N V^{0}$ $N V^{0}$ center, which should be used at the second stage [see Fig. 1] of the process of single-photon emission under electrical pumping [Figs. 1]. $τ_{NR}$ $τ_{NR}$ is the nonradiative lifetime of the excited state, and $τ_{s}$ $τ_{s}$ is the lifetime of the shelving state. (b) Half-rise time $τ_{1 / 2}$ $τ_{1 / 2}$ of the $g^{(2)}$ $g^{(2)}$ function versus the injection current in the diamond $p - i - n$ $p − i − n$ diode [see Fig. 3] retrieved from the experiment and obtained in the numerical simulations using either the two-level model or the three-level model, or the three-level mode with a 10 times longer lifetime of the shelving state.
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