A Viewpoint on : Indistinguishable Photons from Separated Silicon-Vacancy Centers in Diamond

When it comes to semiconductors, it is well known that one shouldn’t bet against silicon. Now it appears that silicon may also be the key to quantum technologies based on diamond. A team of scientists from Harvard University, Ulm University in Germany, and Tsukuba University and the National Institute for Materials Science, both in Japan, has demonstrated that two separated siliconvacancy (SiV) centers in diamond can emit photons that are indistinguishable [1], i.e., have identical properties (except for their position): same wavelength, same polarization, and when the photons are combined on a beam splitter, the same output directions. Such indistinguishability is one of the most important enablers of quantum information based on atom-photon interactions. It is, for instance, at the heart of measurement-based quantum information protocols, in which computation is carried out by measurements on prepared entangled states: Only if photons emitted from different sources are indistinguishable, can entanglement between them be generated [2]. The finding poses SiV as a potential element for a diamond-based quantum computer.

The realization of quantum networks, in which local quantum processing nodes are connected over long distances via optical photons, is an outstanding challenge in quantum information science [1]. Over the past few years, atomlike systems in the solid state have emerged as a promising platform for achieving this goal. Key building blocks have been demonstrated using nitrogen-vacancy (NV) centers in diamond, including long-lived qubit memory [2], spin-photon [3], and spin-spin entanglement [4], as well as teleportation between distant stationary qubits [5]. While NV centers can be used as excellent quantum registers, the current efforts to scale up these proof-of-concept experiments are limited by the small probability of coherent photon emission from NV centers and their spectral stability [6,7]. Here we demonstrate that silicon-vacancy (SiV) centers in diamond can be used to efficiently generate coherent optical photons with excellent spectral stability. We show that these features are due to the inversion symmetry associated with SiV centers and demonstrate generation of indistinguishable single photons from separate emitters in a Hong-Ou-Mandel (HOM) interference experiment [8].
The negatively charged SiV center in diamond consists of a silicon atom and a split vacancy, as shown in Fig. 1(a) [9,10]. The silicon atom is centered between two empty lattice sites, and this D 3d geometry forms an inversion symmetric potential for the electronic orbitals [9]. Recent measurements [10,11] and first principle calculations [12] have contributed to a detailed understanding of the electronic structure of the SiV center. As shown in Fig. 1(b), the ground and excited states each consist of a fourfold degenerate manifold where two degenerate orbitals are occupied by an S ¼ 1=2 particle [13]. At zero magnetic field, the degeneracy is partially lifted by the spin-orbit interaction. Each excited state has dipole transitions to the two ground states forming an optical Λ system, resulting in the emission spectrum shown in Fig. 1(c). These four transitions comprise the zero-phonon line (ZPL), which contains more than 70% of the total fluorescence. Remarkably, as discussed below, the inversion symmetry FIG. 1 (color online). Electronic structure and optical transitions of the SiV center. (a) The center is aligned along a h111i axis of the diamond host crystal, with the silicon atom (Si) located in the middle of two empty lattice sites. The system has D 3d symmetry which includes inversion symmetry. (b) The optical transition is between different parity states, 2 E u and 2 E g . Spin orbit interaction (λ SO u ∼ 250 GHz, λ SO g ∼ 50 GHz) partially lifts the degeneracy giving rise to doublets in the ground and excited states. Transitions A, B, C, D are all dipole allowed. (c) The emission spectrum measured using off-resonant excitation at 532 nm on a single SiV center at 4.5 K.
Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. results in weak coupling of the ZPL transitions to charge fluctuations in the SiV environment. This leads to the absence of spectral diffusion [14] and a narrow inhomogeneous distribution [15].
To demonstrate coherent emission of indistinguishable single photons from separate SiV centers, we use a HOM interference experiment. The interference of two identical single photons impinging on a beam splitter results in perfect photon bunching, with a vanishing probability of detecting coincident photons at the two different output ports. In our experiments, two separate SiV centers, cooled to cryogenic temperatures, were excited using a twochannel confocal optical microscope shown in Fig. 2(a). Dichroic mirrors were used to simultaneously collect the SiV fluorescence on both the ZPL (λ ∼ 737 nm) and phonon-side-band (PSB, λ ∼ 760-860 nm). In order to isolate a single two-level transition, the emission spectrum was filtered by solid etalons [ Fig. 2(b)] with a free spectral range of 20 GHz and a bandwidth of 1 GHz. The etalons were tuned by temperature to transition C, and the transmitted fluorescence spectrum is shown in Fig. 2(c), where only a single peak is visible as desired for indistinguishable photon generation.
To probe the inhomogeneous distribution (see the Supplemental Material [16]) within the sample and select spectrally overlapping sites, the emitters were resonantly excited with a 737-nm probe laser using the ZPL. The laser was tuned to the center frequency (ν 0 ) of the inhomogeneous distribution for transition C while monitoring fluorescence intensity in the PSB. Figure 3(a) shows the diamond sample imaged by this technique in a region where the resonant site density was high, leading to a high background in any photon correlation experiments. In order to isolate single SiV centers and minimize background from other emitters [22], the laser was tuned to the edge of the inhomogeneous distribution (ν 1 ) in Fig. 3(b).  Figure 4 shows two measurements where the degree of indistinguishability of single photons is varied by changing the photon polarization. The two data sets show the second-order intensity correlation function, g 2 ðτÞ, measured for indistinguishable (pink) and distinguishable (green) photon states. For identically polarized indistinguishable photons, we find g 2 ∥ ð0Þ ¼ 0.26 AE 0.05 where the error bars denote shot noise estimates. After rotating the fluorescence polarization of SiV II by 90 degrees to make the photon sources distinguishable, g 2 ⊥ ð0Þ ¼ 0.66 AE 0.08 was observed. These results clearly demonstrate two-photon interference corresponding to a measured HOM visibility of  2 (color online). Schematic of the two-channel confocal microscope built for the HOM experiment. (a) Channels I and II were used to address different emitters separated by tens of micrometers in the same sample. A continuous-wave 532-nm laser was used for excitation, and fluorescence was collected in single-mode fibers on ZPL and PSB ports simultaneously. (b) Collected ZPL fluorescence from the two channels were directed onto a free-space 50∶50 nonpolarizing beam splitter. Linear polarizers were used to control the polarization of the single photons varying their distinguishability. Etalons were used to filter transition C before detection. (c) Emission spectrum before (brown) and after the etalons (blue). 113602-2 the emitters were spectrally stable throughout the 4-hour acquisition period. We find that the interference visibility, η, is limited by about equal contributions from detector timing response and background events.
We next turn to a discussion of the key properties of SiV centers which made the present observations possible. Despite uncertainty about the absolute quantum yield [14], the strong ZPL of SiV [23] means that photons are emitted at high rates into the optical transition of interest. Inhomogeneous broadening corresponded to only a few transition line widths (see the Supplemental Material [16]), and high spectral stability of the transitions has been observed in bulk diamond [14] and nanodiamonds [13]. Together with these observations, our work shows that the optical coherence properties of SiV centers can be superior to those of NV centers [7,24]. Some of this advantage can be understood to result from the inversion symmetry of SiV centers which reduces sensitivity to electric field. In addition, it is important to consider the effects of phonons (strain) resulting in homogenous (inhomogeneous) broadening mechanisms.
The electronic orbitals of the SiV center are parity eigenstates due to the inversion symmetry of the defect. The optical transitions take place between states of different parity, 2 E g and 2 E u , which differ in phase but have similar charge densities [12]. This small change in the electronic charge density results in the strong ZPL since optical excitations do not couple efficiently to local vibrations. The coherence of the optical transitions can also suffer from spectral diffusion, a time-dependent change in the optical transition frequencies that results in an increased line width. This effect is commonly observed for NV centers, where the dominant source of spectral diffusion has been shown to be from local electronic charge fluctuations [25]. These changes in the charge environment result in a fluctuating electric field at the emitter that reduces the coherence of the optical transitions via dc Stark shift [7,26]. The sensitivity of the optical transition frequencies to electric field fluctuations depends on the permanent electric dipole moments  of the orbital states of the emitter. Since the electronic states of the SiV center have vanishing permanent electric dipole moments due to their inversion symmetry, the optical transitions are relatively insensitive to external electric fields. This protects the optical coherence from charge dynamics in the crystal, preventing spectral diffusion and narrowing the inhomogeneous distribution of transition frequencies.
Additional homogeneous and inhomogeneous broadening mechanisms are provided by phonons and strain. Displacements of atoms in the host crystal can affect the optical transitions in two different ways. Static distortions, or strain, may reduce the symmetry of the defect and change the energy splittings [15] [shown in Fig. 1(b)]. A variation in local strain contributes to the inhomogeneous distribution of the resonance frequencies [16]. Displacements of the atoms can also give rise to dynamic effects during an optical excitation cycle. Acoustic phonons have been shown to cause orbital relaxation between E X and E Y states for the NV center in diamond [27]. For SiV centers, a similar process can happen between excited state orbitals by absorption (Γ ph ↑ ) or emission (Γ ph ↓ ) of an acoustic phonon, as shown in Fig. 1(b). Populations in the upper and lower excited state branches follow a Boltzmann distribution confirming thermalization of orbital states by phonons [14,15]. At low temperatures (k B T ≪ ℏλ SO u ∼ 250 GHz), spontaneous emission dominates over stimulated processes (Γ ph ↑ ≪ Γ ph ↓ ). To obtain an optical transition isolated from the phonon bath, our experiments were performed at 4.5-5 K (∼100 GHz) using the lower excited state branch. At these temperatures, we estimate a thermal broadening on transition C of about 12 MHz [14].
Our observations establish the SiV center as an excellent source of indistinguishable single photons. A strong ZPL transition, narrow inhomogeneous distribution, and spectral stability combine to make it a promising platform for applications in the fields of quantum networks and longdistance quantum communication. In particular, it should be possible to integrate SiV centers inside nanophotonic cavities [6,[28][29][30][31] while maintaining their spectral properties owing to their insensitivity to electric fields. This may allow the realization of GHz bandwidth deterministic single photon sources [32] and a broadband system for quantum nonlinear optics at the single-photon level [33]. The small inhomogeneous distribution also makes SiV centers promising candidates as sources of multiple indistinguishable photons for linear optics quantum computing [34]. Furthermore, the spin degree of freedom in the ground state [13] can potentially be utilized to store quantum information, allowing the use of SiV centers as quantum registers for quantum network applications [35]. Coupling to the 29 Si nuclear spin via hyperfine interactions [36] might allow realization of long-lived quantum memories [2]. Beyond these specific applications, the symmetry arguments presented above suggest that inversion symmetry might play an important role in the identification of new centers with suitable properties for quantum information science and technology [37].