Scalable integration of long-lived quantum memories into a photonic circuit

We demonstrate a photonic circuit with integrated long-lived quantum memories. Pre-selected quantum nodes - diamond micro-waveguides containing single, stable, and negatively charged nitrogen vacancy centers - are deterministically integrated into low-loss silicon nitride waveguides. Each quantum memory node efficiently couples into the single-mode waveguide (>1 Mcps collected into the waveguide) and exhibits long spin coherence times of up to 120 {\mu}s. Our system facilitates the assembly of multiple quantum memories into a photonic integrated circuit with near unity yield, paving the way towards scalable quantum information processing.

PACS numbers: 42.50.Ex, 33.35.+r, 33.50.Dq Advanced quantum information systems, such as quantum computers [1] and quantum repeaters [2], require multiple entangled quantum memories that can be controlled individually [3]. Over the past decade, there has been rapid theoretical and experimental progress in developing such entangled networks using stationary quantum bits (qubits) connected via photons [4][5][6]. Photonic integrated circuits (PICs) could provide a compact, phase-stable, and scalable architecture for such quantum networks. However, the realization of this promise requires the high-yield integration of solid state quantum memories efficiently coupled to low-loss single-mode waveguides.
A promising solid-state quantum memory with secondscale spin coherence times is the negatively charged nitrogen vacancy (NV) center in diamond [7,8]. Its electronic spin state can be optically initialized, manipulated, measured [9], and mapped onto nearby auxiliary nuclear memories [10]. Quantum network protocols based on these unique qualities have been proposed [11], and entanglement generation and state teleportation between two spatially separated quantum nodes has been demonstrated [12,13]. Translating such entanglement techniques into on-chip architectures promises scalability, but can only succeed if quantum nodes are generated with high yield. So far, yield has been inherently low due to the stochastic process of NV creation, and waveguide patterning in diamond is challenging, preventing low-loss waveguides in the optical domain around 638 nm, the zero phonon line (ZPL) of the NV. Thus, while proof-of-principle network components have been demonstrated [14,15], the assembly of a quantum memory device into a PIC has not yet been shown. In contrast to diamond, silicon nitride (SiN)-based photonics relies * smouradi@mit.  on well-developed fabrication processes and is CMOScompatible [16]. Recently, ultra-low-loss channel waveguides (< 0.3 dB/cm) and high-fidelity nonlinear devices have been demonstrated [17]. Moreover, its large band gap (∼5 eV) and high index of refraction (n = 2.1) make it ideal for routing the visible emission of NVs in diamond.
Here, we address the challenges of high yield integration into low-loss photonic networks by integrating pre-selected, long-lived quantum memories based on NV centers into SiN PICs. In our approach, each quantum node consists of a diamond micro-waveguide (µWG) suspended over a coupling region in a SiN waveguide, as illustrated in Figure 1  (λ =600-780 nm) is guided into the diamond µWG with optimal, realistic NV dipole orientation (the projection of the emission dipole along the µWG propagation axis is minimized for <100> diamond µWG) and optimal NV position (the mode maximum of the diamond µWG), as seen in Figure 1b (dashed curve).
The SiN waveguide also supports single mode propagation over the NV emission spectrum with a cross section of 400×400 nm. Tapering of the overlapping SiN and diamond regions allows for an approximately adiabatic transition between the diamond and SiN waveguide modes. We performed FDTD simulations to optimize the tapered regions of the diamond and SiN waveguides to maximize the coupling between the diamond and SiN waveguides, as shown in Figure 1. Our simulations indicate that up to 95% of the NV fluorescence emitted into the diamond waveguide is transferred into the SiN waveguide with the optimized overlapping tapering regions shown in Figure  1c (see Appendix). Thus, as shown in Figure 1b (solid curve), we estimate that the total collection efficiency from the NV ZPL through the diamond µWG into the SiN WG is 82% for our optimized design (see Figure 1c).
We fabricated the diamond µWGs from a 200 nm-thick single crystal diamond membrane which was thinned from a 5 µm diamond slab produced by chemical vapor deposition. Natural NVs occurred at a concentration of approximately 0.25 NVs/µm 3 . A patterned silicon membrane is used as a hard etch mask [18] during an oxygen plasma etch of the diamond membrane [19] (see Appendix). We fabricated the SiN waveguides from a 400 nm thick SiN layer deposited on silicon dioxide [17]. The waveguides were cladded with a 3 µm layer of SiO 2 except for a 50 µm window over the coupling region for the integration of the diamond µWGs. Figure 2(b) shows a typical array of diamond µWGs. In this experiment, we used 12 µm-long, 200 nm wide µWGs with 4 µm-long tapers down to 100 nm on either side. This minimum taper size is larger than optimal, but fabrication yield was increased as the µWGs were connected at these ends. FDTD simulations indicated that this geometry should yield a 52.5% coupling efficiency from the NV ZPL to the SiN waveguide with optimal NV parameters (see Appendix).
After fabrication, we characterized the µWGs using a confocal microscope (NA = 0.9) with 532 nm excitation. Using photoluminescence (PL) raster scans, we identified µWGs with single NVs near the center as indicated in Figure 2c. A pre-selected diamond µWG was picked and transferred onto a SiN coupling region with a tungsten probe, where it adhered due to surface forces (see Appendix). Figure 2d and e show an SEM of the transferred structure and the corresponding PL scan, respectively. This bottom-up integration process ensures that every node contains exactly one NV memory. Such high yield is not possible without pre-selection even when nitrogen atoms are spatially implanted, as the number of NVs generated remains stochastic.
Single NVs in integrated devices were excited from the top with the confocal setup described above and PL was collected via the confocal setup into a single mode fiber (confocal collection) and through the SiN waveguide into a lensed single mode fiber (waveguide collection). In both cases, the collected fluorescence was filtered with a 550 nm long pass filter. We will focus on the optical analysis of the integrated system seen in Figure 2d,e. Figure  3a and b show PL raster scans of the NV under confocal excitation with confocal and waveguide collection, respectively.
Second order correlation measurements on photons collected via the confocal setup confirm that all NVs in tested µWGs show single emitter character, with antibunching as low as g (2) (0) = 0.07 (see Appendix), implying that the NVs are extremely well isolated from background sources of fluorescence. Figure 3c shows the normalized auto-correlation measurement of the NV in Figure 3a,b, with g (2) (0) = 0.17 at 100 µW of 532 nm excitation. We also performed cross-correlation measurements between photons collected via the confocal and waveguide setups. The normalized histogram in Figure  3d indicates clear anti-bunching at 60 µW of excitation. We attribute the increase in g (2) (0) from the confocal auto correlation measurement to PL from the SiN waveguide due to coupling of the 532 nm excitation laser into the WG. This PL is also observed in the spectrum collected through the waveguide (see Appendix). This background could be eliminated by fabricating a distributed Bragg reflector at the excitation laser wavelength into the SiN waveguide near the diamond coupling region [22,23]. This filter could block scattered laser light from traveling through the SiN WG and exciting background fluorescence. Figure 3e plots the spectrum of the fluorescence collected through the waveguide. An interference pattern is visible, which we attribute to an etalon effect at the diamond end facets. This etalon effect indicates an intensity reflection of r 2 = 0.17 and a waveguide group index of 1.7 for the 12 µm long diamond µWG, which matches our expectations (see Appendix).
To evaluate the enhancement in collection efficiency through the waveguide, we performed emitter saturation measurements with both confocal and waveguide collec-tion as seen in Figure 3f. In each case, the excitation polarization was tuned to maximize the signal-to-noise ratio. For confocal collection, this entailed maximizing the NV excitation rate, while under waveguide collection this entailed limiting the coupling of the 532 nm excitation into the waveguide to minimize background fluorescence. The optimized polarization for waveguide collection reduces the NV excitation rate, and as such increases the saturation intensity from 135 µW via confocal collection to 350 µW via waveguide collection. For confocal (waveguide) collection, 16 kcps (55 kcps) were detected at 60 µW of excitation, as used to measure the crosscorrelation seen in Figure 3d. Figure 3g shows the fits in Figure 3f without the linear background terms, and corrected for the measured collection efficiencies of each collection pathway. The waveguide (confocal) collection pathway has a measured efficiency of 25% (17%). Both are measured with an Si avalanche photodiode (APD) with quantum efficiency η = 0.65. Without these system inefficiencies, we estimate that 0.38×10 6 NV photons/second are collected into the objective at saturation, while 1.45×10 6 NV photons/second are collected into one direction of the single mode SiN waveguide. We integrated 4 such quantum memories into the SiN PIC, each of which contained a single NV center which emitted > 1×10 5 photons/second into the SiN waveguide at 125 µW of excitation (see Appendix).
In Figure 4 we present the electron spin properties of the NV center in a second integrated system in which 0.8 ×10 6 photons/second were collected into one direction of the waveguide at saturation. Figure 4a shows the transitions of the NV center with the magnetic sublevels m s = −1, 0, 1, obtained using optically detected magnetic resonance (ODMR) [24]. Figure 4b plots the ODMR fluorescence signal collected through the waveguide under continuous-wave laser excitation with no external magnetic field.
For state manipulation, the degeneracy of the m s = ±1 levels is lifted by the application of an magnetic field of ∼ 56 Gauss projected onto the NV axis. A Ramsey sequence, consisting of two π/2 pulses separated by a free evolution time τ , was used to probe the spin environment experienced by the NV. From this, we deduce an ensemble phase coherence time T * 2 2 µs. We also performed Hahn-echo measurements [25], which indicate a spin coherence time of T 2 120 µs, see Figure 4d. This long spin coherence time is similar to values observed in the parent diamond crystal [26]. We anticipate that using isotropically purified 12 C diamond, together with dynamical decoupling, should enable spin coherence times in excess of tens of milliseconds [27].
In conclusion, we have realized the integration of multiple quantum nodes into a photonic network. Each integrated node contains a single high quality solid-state qubit. The design of the diamond-SiN interface allows for efficient coupling of photons emitted by the NV center into the single mode SiN waveguide, which itself exhibits The ms = 0 to 1 transition is driven off resonance and 3 Ramsey frequencies are observed due to coupling between the NV electronic spin and the host N 14 nuclear spin, with a decay due to the surrounding spin bath (T * 2 = 2 µs) . (d) The π and π/2 times of an on-resonance driving field are used to construct a Hahn-Echo sequence to decouple the NV from the surrounding spin bath and measure T2 > 120 µs from the exponential decay of the coherent revivals.
low propagation loss (∼ 0.3 dB/cm) and enables high coupling to single mode fiber (∼ 3 dB loss). This high collection efficiency into a single spatial mode indicates the promise of this system as an efficient source of single photons in a single spatial mode. Moreover, our experimental results show that each integrated node contained one long-lived quantum memories. Finally, this method can be generalized to other systems (e.g. photonic crystal cavities containing single emitters) to integrate prescreened functional nodes into high quality PICs with essentially unity yield, paving the way towards scalable on-chip quantum networks. Research also carried out in part at the Cornell NanoScale Facility, a member of the National Nanotechnology Infrastructure Network, which is supported by the National Science Foundation (Grant ECCS-0335765). MLM and DJT was supported by the DARPA Quiness program. We thank Matt Trusheim for valuable discussions.

APPENDIX Appendix A: Simulations
To predict and optimize the coupling efficiency from an NV center to a SiN WG, we simulate our systems using FDTD computations. The NV center is represented as an electric dipole placed in the center of the of a 200 nm x 200 nm diamond µWG (n = 2.4), oriented perpendicular to the propagation axis of the µWG and 35 • off-horizontal. This is consistent with a diamond slab oriented in the <100> direction, as we use in our experiment. We placed Poynting flux monitors (i) to either side of the NV, overlapping the diamond µWG before the SiN WG begins, (ii) at each end of the SiN WG, and (iii) surrounding the entire structure. These are used to monitor where electro magnetic power is lost; the ratio of (i) to (iii) gives the NV coupling efficiency to the diamond µWG, and the ratio of (ii) to (iii) yields the total coupling efficiency of the device.
The optimized device geometry was determined by evaluating the coupling efficiency from the fundamental TE mode of the diamond µWG to the SiN WG while sweeping the diamond µWG and SiN WG taper lengths. The tapers are aligned such that the taper regions in SiN and diamond do not overlap, minimizing the photon loss. Based on these results, we chose a µWG taper length of 6 µum and a SiN WG taper length of 5 µm. Finally, we use a 2 µm gap in the WG to maintain high coupling from the NV into the diamond µWG. This results in a µWG which is 24 µm long, and yields an overall dipole-to-WG coupling efficiency of 83% (41.5% on each side), as seen in Figure 5. We also simulated the structure used in the experiments reported here, which was shorter, and had blunt tips (tapered down to 100 nm instead of 0 nm), increasing losses. This gives a coupling efficiency from the diamond µWG to the SiN WG of 52.5%, as seen in Figure  5.

Appendix B: Fabrication
We begin fabrication with a 5 µm ultra-pure diamond slab produced by chemical vapor deposition. The diamond slab is polished with Ar and Cl 2 down to a final thickness of 200 nm. This membrane is patterned with oxygen plasma, using a transferrable patterned silicon membrane as an etch mask, a technique that is introduced and explained in previous publications [18] The PL collected through the waveguide consists of PL originating from the diamond µWG and PL caused by laser propagation through the SiN waveguide. The PL originating from the diamond µWG experiences an etalon effect due to the diamond µWG ends. The de-