Numerical simulations of nanodiamond nitrogen-vacancy centers ...

Numerical simulations of nanodiamond nitrogen-vacancy centers coupled with tapered optical fibers as hybrid quantum nanophotonic devices Mohamed Almokhtar,1,2,3,4 Masazumi Fujiwara,1,2,4 ∗ Hideaki Takashima,1,2 and Shigeki Takeuchi1,2, 1 Research 2 The

Institute for Electronic Science, Hokkaido University, Sapporo 001-0021, Japan Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567-0047, Japan 3 Physics Department, Assiut University, Assiut 71516, Egypt 4 These authors contributed equally to this work. *[email protected]

Abstract: Tapered optical fibers are promising one-dimensional nanophotonic waveguides that can provide efficient coupling between their fundamental mode and quantum nanoemitters placed inside them. Here, we present numerical studies on the coupling of single nitrogen-vacancy (NV) centers (single point dipoles) in nanodiamonds with tapered fibers. Our results lead to two important conclusions: (1) A maximum coupling efficiency of 53.4% can be realized for the two fiber ends when the NV bare dipole is located at the center of the tapered fiber. (2) NV centers even in 100-nm-sized nanodiamonds where bulk-like optical properties were reported show a coupling efficiency of 22% at the taper surface, with the coupling efficiency monotonically decreasing as the nanodiamond size increases. These results will be helpful in guiding the development of hybrid quantum devices for applications in quantum information science. © 2014 Optical Society of America OCIS codes: (270.0270) Quantum optics; (280.4788) Optical sensing and sensors; (160.2220) Defect-center materials; (130.3990) Micro-optical devices.

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#212677 - $15.00 USD Received 23 May 2014; revised 16 Jul 2014; accepted 26 Jul 2014; published 12 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020045 | OPTICS EXPRESS 20045

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1. Introduction Nitrogen-vacancy (NV) color centers in diamond have recently emerged as promising solidstate atomic systems that can be used for various quantum engineering applications [1, 2]. NV centers exhibit narrow optical transitions with lifetime-limited linewidth [3,4], robust and stable photoemission [5], and paramagnetic electron spin resonance with a very long coherence time at room temperature [6]. These properties enable broad applications in quantum information and quantum sensing, e.g., single-photon sources [7,8], quantum memories [9], and highly sensitive nanoscale magnetometers [10–12], thus rendering NV centers distinct from other solid-state quantum nanoemitters. A promising approach for these applications is to use hybrid nanophotonic quantum devices, in which the high coupling of NV centers with photons (namely, guided modes or cavity modes) is obtained by assembling NV-embedding nanodiamonds with well-established nondiamond nanophotonic structures such as photonic crystals [13, 14], microcavities [15, 16], and tapered optical fibers [17–19]. For example, efficient coupling of single-NV centers in 20-nmsized nanodiamonds with ultrathin tapered fibers has been demonstrated recently [17–19], being proved to work as bright and efficient single-photon sources and sensitive magnetometers. Such efficient coupling of tapered fibers has also been known for other quantum emitters, such as atoms [20–23], colloidal quantum dots [24,25], and InAs quantum dots in GaAs waveguides [26]. In these systems, the electromagnetic environment surrounding the dipole is very different. For example, the dipole was considered to be in air for atoms and colloidal quantum dots (with a size very small compared to the optical wavelength). In contrast, the effect of the dipole of InAs quantum dots in GaAs waveguides must be considered in high-index semiconductor submicron structures. It is therefore important to properly take into account the dipolar environment to obtain efficient coupling with dipoles and tapered fibers. In previous research on NV centers in nanodimoands, the nanodiamonds have been regarded as point dipoles, i.e., the dipole in air when sitting on the surface of tapered fibers [17–19, 27]. However, for NV centers embedded in nanodiamonds, the effect of nanodiamond size and shape may be critically important. In real experiments, nanodiamond particle size exhibits a wide distribution, ranging from 5 to 500 nm [28–30], and size selection is decisively important for developing hybrid quantum nanophotonic devices. For example, smaller nanodiamonds are preferable in view of their coupling to nanophotonic structures or magnetic sensing. Such very small nanodiamonds (e.g., 5 nm), however, exhibit fluorescence intermittency [28, 29] or short T2 coherence time of the electron spins [10, 12, 31], and hence they cannot be used for many quantum applications. In contrast, larger size nanodiamonds exhibit bulk-like optical properties but relatively low coupling and optical scattering by themselves. For these reasons, investigating the effect of size and shape of nanodiamonds on the coupling efficiency of NV centers is critically important. In this paper, we numerically analyze the coupling of NV centers embedded in nanodiamonds #212677 - $15.00 USD Received 23 May 2014; revised 16 Jul 2014; accepted 26 Jul 2014; published 12 Aug 2014 (C) 2014 OSA 25 August 2014 | Vol. 22, No. 17 | DOI:10.1364/OE.22.020045 | OPTICS EXPRESS 20048

with tapered optical fibers. The results show that (1) a maximum coupling efficiency of 53.4% can be realized for the two fiber ends when a NV bare dipole is located at the center of the tapered fiber; and (2) NV centers even in 100-nm-sized nanodiamonds where bulk-like optical properties were reported show a coupling efficiency of 22% at the taper surface. These results will prove helpful in guiding the development of hybrid quantum devices for applications in quantum information science. 2. Methodology 2.1. Model structure The structure and geometry of our simulated model are shown in Fig. 1(a). The tapered fiber is a silica-glass cylinder (ns = 1.4469) with a diameter d. The dipole of the NV center is placed at the center of the tapered fiber (X = 0, Y = 0, Z = 0) or at the surface (X = d/2, Y = 0, Z = 0). Three dipolar orientations are considered: (1) radial orientation, where the dipole is directed perpendicular to the cylindrical surface (θ = 90◦ , ϕ = 0◦ ), (2) azimuthal orientation, where the dipole is tangent to the cylindrical surface (θ = 90◦ , ϕ = 90◦ ), and (3) axial orientation, where the dipole is parallel to the cylindrical axis (θ = 0◦ , ϕ = 0◦ ). Nanodiamonds (nd = 2.43) were directly attached to the surface of the tapered fiber [see Fig. 1(b)]. Note that a NV center does not have a linear dipole but has two dipole moments of equal size in the plane perpendicular to the NV axis [13, 32, 33]. However, we regard the NV center as a linear dipole because (1) this simplification makes the subsequent discussion simpler and more intuitive and (2) these two dipoles are incoherent with each other and any resultant fluorescence polarization can be described as a superposition of the three dipole orientations (radial, azimuthal, and axial), as will be discussed in Sec. 4.3. 2.2. Simulations Data were obtained computationally using the three-dimensional finite-difference time domain (FDTD) method (Lumerical, FDTD package). The computational region is a box of 6 × 6 × 30 µ m3 , as shown in Fig. 1(b). Both ends of the silica-glass cylinder (the tapered fiber) are placed outside of the simulation region. Absorbing perfectly matched layers (PMLs) are used as the end walls of this computational region. The reflectivity from the PMLs is set to