1. Introduction

Cavity QED has been an experimental paradigm for investigating and controlling fundamental optical interactions at the level of single photons and single atoms [1–3]. The success of atomic cavity QED as well as the potential applications of cavity QED systems in quantum information processing has stimulated strong interests in exploring cavity QED of artificial atoms, such as superconducting circuits, semiconductor quantum dots, as well as color centers and impurities in solids [4–6]. Negatively charged silicon-vacancy (SiV) centers in high purity single-crystal diamond have recently emerged as a promising system of artificial atoms for cavity QED. The SiV centers feature excellent optical properties [7–9]. The zero-phonon line of SiV centers contains about 70% of the total fluorescence, with nearly lifetime-limited optical linewidth. The inversion symmetry of SiV centers makes them robust against charge fluctuations in their surrounding environment. All optical control of SiV spins via a Λ-type three-level system has also been demonstrated [10–12].

Recent cavity QED studies with SiV centers have employed diamond photonic crystals and monolithic diamond microdisks [13–15]. The photonic-crystal-based studies have led to rapid experimental advances, including the realization of a quantum photonic switch operating at the single photon level, the use of cavity-enhanced Raman emission as a tunable single-photon source, the demonstration of cavity-mediated coherent interactions between two SiV emitters, the observation of quantum interference from superradiant emissions of two entangled SiV centers, and the demonstration of an integrated nanophotonic register coupling a SiV electron spin in a diamond photonic crystal to a nearby ¹³C nuclear spin [13,14,16–18]. Memory-enhanced quantum communication with a SiV center has also been demonstrated recently [19]. Diamond photonic crystals, however, feature a relatively broad optical cavity linewidth (> 20 GHz), limiting this platform to the bad cavity limit in cavity QED, for which the cavity linewidth is large compared with both the SiV optical linewidth and the single-photon dipole coupling rate.

In this paper, we report the development of an experimental platform, in which SiV centers in a thin diamond membrane couple to evanescent fields of optical whispery gallery modes (WGMs) in a silica microresonator (see Fig. 1). This composite system takes advantage of the exceptional optical and spin properties of SiV centers as well as the high finesse and small mode volume of WGMs in a silica microresonator [20–23]. Using a membrane as thin as 100 nm, we show that the composite cavity QED system can feature an overall cavity linewidth below 40 MHz and can in principle enable the achievement of the good cavity limit in cavity QED, for which the cavity linewidth is small compared with the single-photon dipole coupling rate as well as the SiV optical linewidth. In addition, efficient coupling of the photoluminescence from SiV centers into the WGMs has also been demonstrated.

 

Fig. 1. (a) Schematic of the composite cavity QED system consisting of a wedged diamond membrane in contact with a silica microsphere. A tapered optical fiber is used for the input and output coupling to WGMs confined near the equator of the sphere. We also use the fiber taper to collect optical emissions from SiV centers for PL and PLE experiments in the cavity QED setting. (b) An optical image of the wedged diamond membrane strips used in the cavity QED setup. Each set of fringes corresponds to a thickness variation of approximately 110 nm [25].

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2. Experimental design and setup

Our composite cavity QED system consists of a silica microsphere in contact with a thin diamond membrane, as illustrated schematically in Fig. 1(a). The silica microsphere serves as a WGM optical microresonator with ultrahigh optical Q-factors. SiV centers in the contact area of the thin diamond membrane couple to evanescent fields of WGMs near the equator of the microsphere. For our experimental studies, a silica microsphere is fabricated by reflowing the end of a tapered optical fiber with a CO₂ laser to form a sphere of the desired size. Subsequently, a second tapered fiber is also fused to the sphere along the same axis. The diameter of the microspheres typically ranges from 30 to 60 µm. The double-stemmed sphere allows for mechanical stretch-tuning of WGM resonances [24].

Diamond membranes as thin as 100 nm near the tip, as verified by additional measurements using an optical profilometer (Zygo NewView 7300), are fabricated with reactive ion etching from a high-purity single-crystal bulk diamond. SiV centers are created about 100 nm below the diamond surface via ion implantation with a straggle of 20 nm, followed by thermal annealing and additional surface treatment. Details of the membrane fabrication and the SiV creation as well as the characterization of the SiV centers in the membranes have been presented in an earlier study [26]. The diamond sample used in the cavity QED experiment contains multiple wedged membrane strips, as shown in Fig. 1(b). Each strip is 20 µm in width, with a length that varies from 80 µm to more than 100 µm. The thin membranes are attached to the 30 µm thick film. For experiments at low temperature, the sample is mounted on the cold finger of a closed cycle cryostat (Montana Instrument, Inc.).

Coupling into and out of the WGMs in the sphere is achieved with a tapered optical fiber, as illustrated in Fig. 1(a). The fiber taper is orthogonal to the axis of the two fiber stems attached to the sphere. The fiber taper is suspended on an invar fork mounted on an x-z nano-positioner stack (ANP/x/51/LT and ANP/z/51/LT from Attocubes, Inc.) for the control of the taper-sphere separation as well as the latitudinal position of the taper along the stem axis such that equatorial WGMs can be preferentially excited. Note that equatorial and near equatorial WGMs confined near the surface of the sphere are used for the purpose of minimizing the effective mode volume and optimizing the overlap of the WGM evanescent field with the SiV centers near the sphere/membrane contact area.

We use the tapered fiber not only to excite the WGMs, but also to collect SiV optical emissions into the WGMs for photoluminescence (PL) and photoluminescence excitation (PLE) experiments in our cavity QED setting. For these experiments, we also focus excitation laser beams through a 20X objective (Mitutoyo, Inc.) and the silica microsphere onto the contact area between the membrane and the sphere, as illustrated schematically in Fig. 1(a).

Figure 2 shows the overall experimental setup, which we use for cavity transmission, PL, and PLE experiments. Transmission spectra of the composite cavity QED system are measured with an amplified photodiode (New Focus 2001-FC), as illustrated by Route 1 in Fig. 2. For PL and PLE experiments, optical emissions from the SiV centers into the WGMs are collected by the fiber taper and then directed into a spectrometer and an avalanche photodetector (APD), respectively, as illustrated by Route 2 in Fig. 2. Optical filters are also used to filter out the excitation laser beams near 532 nm (Laserglow DPSS Laser System) and near 737 nm (New Focus TLB-6711). Acousto-optical modulators (AOMs) are employed for the generation of the desired optical pulse sequences. In addition, the 20x objective discussed above is also used for the imaging and monitoring of the composite microsphere-membrane system.

 

Fig. 2. Schematic of the overall experimental setup, where b.s. stands for beam splitter. Route 1 is used for transmission experiments. Route 2 is used for PL and PLE experiments.

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3. Results and discussions

Experimental results presented in this section aim to demonstrate the feasibility of using the composite cavity QED system described in section 2 to reach the good cavity limit of cavity QED. In this regard, we have carried out transmission experiments to determine the cavity linewidth of the composite system as well as the Q-factor spoiling induced by the diamond membrane and have performed PL and PLE experiments in the cavity QED setting to show that SiV optical emissions couple efficiently into the WGMs. We have also estimated the single-photon dipole coupling rate, g, for the composite cavity QED system using known system parameters.

Figure 3(a) shows the transmission spectrum of an equatorial WGM in the composite cavity QED system, where the WGM resonance is detuned from the SiV centers and the diamond membrane is in contact with the silica microsphere with a diameter of approximately 50 µm. The WGM linewidth observed is 38 MHz [see Fig. 3(a)], demonstrating the high finesse of the composite cavity QED system. For comparison, the WGM linewidth decreases to 35 MHz [see Fig. 3(b)], when the membrane is moved away from the silica microsphere, indicating that the membrane-induced broadening is only 3 MHz. The observed bare cavity linewidth is primarily due to surface contaminations introduced in assembling the composite system. The linewidth can thus be considerably improved. Note that our earlier cavity optomechanics studies using silica microspheres with a dimeter near 30 µm have shown consistently that the bare cavity linewidth can be less than 20 MHz [27].

 

Fig. 3. (a) Transmission spectrum of an equatorial WGM of the composite cavity QED system, with a 110 nm thick diamond membrane in contact with a silica microsphere with a diameter of approximately 50 µm.

(b) Transmission spectrum obtained under the same condition as (a), except that the membrane is moved away from the silica microsphere. Solid redlines are least square fit to a Lorentzian, for which the transmission far away from the cavity resonance is set to 100%.

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Negatively charged SiV centers feature optical transitions with wavelengths near 737 nm. In the absence of an external magnetic field, both the ground and excited states are doublets due to spin-orbit interactions, as shown schematically in Fig. 4(a) [28]. The spin-orbit splitting for the ground and excited states is $\lambda _{so}^g$=47 GHz and $\lambda _{so}^u$=260 GHz, respectively. All transitions between the ground and excited states are dipole-allowed. Figure 4(b) shows the PL spectrum obtained at 5 K and with the SiV optical emissions collected from the fiber taper and with SiV centers in the membrane excited directly with a 532 nm laser, as illustrated in Fig. 1(a). The excited-state splitting (approximately 0.4 nm) can be clearly seen from the PL spectrum. The limited spectrometer resolution (0.2 nm for our experiments), however, prevents the observation of the ground state splitting. The characteristic SiV doublet nearly vanishes when the green excitation laser beam is moved 10 µm away from the contact area between the membrane and the silica microsphere, demonstrating that only SiV centers near the contact area can couple efficiently into the WGMs of the silica microsphere. Note that the inhomogeneous linewidth of SiV centers in our sample is approximately 0.04 nm and is much smaller than the free spectral range (FSR) of the WGMs, which is 2 nm for the silica microsphere used. As a result, periodic WGM spectral features, which were routinely observed in earlier cavity QED studies with silica microspheres [21], are not observed in the PL spectrum shown in Fig. 4(b).

 

Fig. 4. (a) Schematic of the energy level diagram and optical transitions in a negatively charged SiV center with no strain. (b) PL spectrum obtained at 5 K and with the SiV emissions collected by the fiber taper. The orange and blue curves show the data obtained when the green excitation laser beam is at and 10 µm away from the contact area between the microsphere and the diamond membrane, respectively.

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For the PLE experiment, the SiV centers are initialized with a 532 nm laser for a duration of 3 µs and are resonantly excited with a laser near 737 nm. The detection window follows shortly after the initialization and features a duration of 10 µs. This pulse sequence is shown schematically in Fig. 5(a). Figure 5(b) shows the PLE spectrum obtained at 5 K and with the SiV optical emissions collected from the fiber taper, as illustrated in Fig. 1(a). For convenience, the WGMs were over-coupled to the fiber taper with the taper in contact with the silica microsphere. The PLE spectrum features four SiV optical resonances with the expected ground- and excited-state splittings.

 

Fig. 5. (a) The pulse sequence used for the PLE experiment. (b) PLE spectrum obtained at 5 K and with the SiV emission collected by the fiber taper.

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Note that many noise-like spikes in Fig. 5(b) are due to resonant scattering of the red excitation laser beam into the WGMs. The contribution of the resonant scattering to the PLE experiment can be suppressed with a long-pass filter far away from the SiV transition frequencies. However, this will also greatly reduce contributions from the SiV emissions because of the relatively small phonon sideband of the SiV centers. In this regard, the characteristic doublet structure of the SiV excitation spectrum enables us to positively identify the SiV contributions in the cavity QED-based PLE experiment.

The contact area, in which SiV centers can effectively couple to evanescently fields of equatorial WGMs, is estimated to be 2πRd, where R is the sphere radius and d is the maximum distance between the membrane and the sphere surface, for which the evanescent coupling still remains significant. For R=25 µm and d=50 nm, the effective area is approximately 8 µm². Note that separate confocal PLE experiments with the membrane alone and with a 0.8 µm² laser spot size show on average 8 spectrally resolved individual SiV centers. For the diamond membrane sample used, a relatively large number of SiV centers are thus involved in the contact area. This, along with contributions from resonant scattering, makes it difficult to positively identify effects of individual SiV centers in the PLE spectrum. For further improvement and especially for the detection of effects of single SiV center in the cavity QED setting, we will need to significantly reduce the density of SiV centers in the membrane and will also need to tune the frequency of the WGMs for resonance matching between a WGM resonance and a SiV transition.

To calculate the single-photon dipole coupling rate for our composite cavity QED system, we estimated that the effective mode volume for an equatorial WGM near λ=737 nm in a sphere with R = 15 µm is approximately 110 µm³. The estimate was based on numerical calculations using MATLAB WGMode toolbox [29] and normalizing the electric field for the energy of a single cavity photon. For a SiV center, which is 25 nm away from the sphere surface, we estimated g/2π to be approximately 150 MHz. This estimate takes into account the polarization mismatch between the SiV electric dipole and the WGM electric field. Note that g can be further improved by bringing the SiV even closer to the diamond surface [30]. Using g/2π = 150 MHz, κ/2π = 40 MHz, and γ/2π = 200 MHz, where κ and γ are the cavity and SiV optical linewidth, respectively, we arrived at a cooperativity $C = 4{g^2}/\kappa \gamma \approx $11, a dimensionless parameter that characterizes the strength of the single-photon dipole coupling between a two-level system and a resonant cavity mode.

4. Summary

In summary, we have developed a composite cavity-QED system, which takes advantage of high-Q WGMs in a silica microresonator, for cavity QED of SiV centers in diamond. We have shown the feasibility of achieving the good cavity limit for cavity QED, which is otherwise difficult to achieve with monolithic photonic-crystal-based cavity QED systems. The composite system provides an alternative experimental platform and additional opportunities for exploring cavity QED based applications that do not require g > γ. A particular example is the exploration of dark states in a cavity QED setting [31], including the state transfer between optical and spin states via a dark state [32–34].