High-performance diamond-based single-photon sources for quantum communication

Chun-Hsu Su, Andrew D. Greentree, and Lloyd C. L. Hollenberg

Phys. Rev. A 80, 052308 – Published 9 November 2009

Abstract

Quantum communication places stringent requirements on single-photon sources. Here we report a theoretical study of the cavity Purcell enhancement of two diamond point defects, the nickel-nitrogen (NE8) and silicon-vacancy (SiV) centers, for high-performance, near on-demand single-photon generation. By coupling the centers strongly to high-finesse optical photonic-band-gap cavities with modest quality factor $Q = O (10^{4})$ and small mode volume $V = O (λ^{3})$ , these system can deliver picosecond single-photon pulses at their zero-phonon lines with probabilities of 0.954 (NE8) and 0.812 (SiV) under a realistic optical excitation scheme. The undesirable blinking effect due to transitions via metastable states can also be suppressed with $O (10^{- 4})$ blinking probability. We analyze the application of these enhanced centers, including the previously studied cavity-enhanced nitrogen-vacancy (NV) center, to long-distance Bennett-Brassard 1984 protocol quantum key distribution (QKD) in fiber-based, open-air terrestrial and satellite-ground setups. In this comparative study, we show that they can deliver performance comparable with decoy state implementation with weak coherent sources, and are most suitable for open-air communication.

Received 16 April 2009

DOI:https://doi.org/10.1103/PhysRevA.80.052308

Authors & Affiliations

Chun-Hsu Su¹, Andrew D. Greentree¹, and Lloyd C. L. Hollenberg²

¹School of Physics, University of Melbourne, Victoria 3010, Australia
²Centre of Quantum Computer Technology, School of Physics, University of Melbourne, Victoria 3010, Australia

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Vol. 80, Iss. 5 — November 2009

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Figure 1
(Color online) (a) Schematic of a cavity-center system for single-photon generation. The NE8 and SiV centers are modeled as a vibronic system that consists of a single excited state $| e ⟩$ and a ground state with two vibrational sublevels $| g_{i} ⟩$ . $| h ⟩$ is an additional metastable level. The center is pumped with an external classical field $r (t)$ acting as the trigger pulse. The $| e ⟩ - | g_{i} ⟩$ transition is coupled to a one-sided, single-moded cavity with coupling strength $Ω_{i}$ . Dashed arrows denote radiative decay and dotted arrows nonradiative relaxations. (b) Proposed design in diamond-based PBG lattice, missing holes constitute the cavities and waveguide. Solid circle (in box) denotes a center excited optically by a green laser. (c) NE8 complex in the carbon lattice, consisting of a Ni atom surrounded by four N atoms. (d) SiV structure consisting a substitutional Si atom and an adjacent vacancy.Reuse & Permissions
Figure 2
(Color online) (a) Cavity-enhanced photon emission at ZPL wavelengths from two diamond optical centers: NE8 $(λ_{c} = 794 nm)$ and SiV (738 nm). We take $V = {(λ_{c} / n)}^{3}$ and $Q = 3700$ (NE8), 1800 (SiV). The solid curves are calculated using top-hat excitation parameters $(T, r) = (0.16 ps, 20 THz)$ and (0.08 ps, 40 THz) for the respective centers. The dashed curves use shorter excitation pulses of $T = 40 fs$ (NE8) and 20 fs (SiV). Single-photon emission probability $P_{1}$ as a function of (b) $Q$ , and [(c) and (d)] the excitation parameters. Circles (squares) indicate the parameters that effect $P_{m} = O (10^{- 5})$ $[O (10^{- 7})]$ .Reuse & Permissions
Figure 3
Photon autocorrelation histogram of emissions from the cavity-center system implemented with an (a) NE8 and (b) a SiV center. Using quantum trajectory approach, HBT experiment is simulated using a pulsed excitation, corresponding to a top-hat pulse at respective repetition rates 10 and 20 GHz for over 5000 emission cycles.Reuse & Permissions
Figure 4
(Color online) Secure key rate over silica-fiber link as a function of total loss, for different single-photon sources. Dashed: BB84 with bare optical centers NV (black), NE8 (blue), and SiV (red). Solid: BB84 with cavity-enhanced centers distinguished by same color curves. Dotted: BB84 with 10 GHz WCSs at 650 nm (green) and $1.55 μ m$ (pink). Dashed dotted: decoy state with WCSs distinguished by same color curves. We use the parameters from Table , $η_{d} = 0.65$ (0.5), $R = 25 Hz$ (0.035 Hz) for visible (near-ir) wavelength transmission, $η_{o} = 0.6$ and $e_{0} = 0.02$ for all cases. To aid comparisons, solid circles are used to indicate the key rates over fiber length $l$ of 5 km.Reuse & Permissions
Figure 5
(Color online) Generic (a) open-air terrestrial and (b) LEO satellite-ground communications over a path length $l$ through atmospheric turbulence characterized by refractive-index structure parameter $C_{n}^{2}$ . (c) Transmitter using a typical Cassegrain telescope. Single photons generated at a repetition rate $ν$ are encoded using electro-optic modulator. (d) Receiving telescope with an angular field of view $θ_{fov}$ sees a broadened spot with radius $w_{eff}$ . Measurement basis is randomly chosen with a beam splitter (BS) and polarization states are distinguished with polarizing beam splitters (PBSs). ATP system, postprocessing, key management are not depicted here.Reuse & Permissions
Figure 6
(Color online) QKD performance of (a) open-air, terrestrial link at 3 km above sea level, (b) free-space uplink between a transmitter at an altitude $h_{0}$ and a LEO satellite at an altitude 2000 km, and (c) LEO satellite-ground downlink, on a standard-clear night with brightness $H_{b} = 1.5 \times 10^{- 3} {Wm}^{- 2} {Sr}^{- 1} μ m^{- 1}$ . In (a), $D_{T} = 0.15 m$ at Alice, $D_{R} = 1 m$ , $D_{d} = 0.5 mm$ , $a = 39$ , and $FOV = 12.5 μ rad$ at Bob. In (b), $D_{T} = 1 m$ on the ground (Alice), $D_{R} = 0.1 m$ , $D_{d} = 0.5 mm$ , $a = 50$ and $FOV = 100 μ rad$ on the satellite (Bob). In (c), $D_{T} = 0.1 m$ on the satellite, $D_{R} = 1 m$ , $D_{d} = 0.5 mm$ , $a = 5$ and $FOV = 100 μ rad$ on the ground. The values for $η_{d}$ , $R$ , $η_{o}$ , and $e_{0}$ follow Fig. 4, noise rates $N$ are tabulated in Table . Circles are used to indicate the estimated key rates for a particular transmission distance or altitude.Reuse & Permissions

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