An integrated nanophotonic quantum register based on silicon-vacancy spins in diamond

We realize an elementary quantum network node consisting of a silicon-vacancy (SiV) color center inside a diamond nanocavity coupled to a nearby nuclear spin with 100-ms-long coherence times. Specifically, we describe experimental techniques and discuss effects of strain, magnetic field, microwave driving, and spin bath on the properties of this two-qubit register. We then employ these techniques to generate Bell states between the SiV spin and an incident photon as well as between the SiV spin and a nearby nuclear spin. We also discuss control techniques and parameter regimes for utilizing the SiV-nanocavity system as an integrated quantum network node.

Figure 1

(a) Schematic of a quantum network. Nodes consisting of several qubits are coupled together via an optical interface. (b) A quantum network node based on the SiV. SiV centers and ancilla ${}^{13}\mathrm{C}$ are incorporated into a nanophotonic device and addressed with a coupled fiber and microwave coplanar waveguide.

Figure 2

(a) Schematic of the nanofabricataion process used to produce devices. (I) HSQ mask with a 10-nm titanium adhesion layer is patterned using EBL. (II) Pattern is transferred onto diamond using top down ${\mathrm{O}}_2$ RIE. (III) Angled IBE is used to separate structures from substrate. (IV) Devices are covered in PMMA and implantation apertures are formed using EBL. Device are then cleaned, implanted, and annealed. (V) PMMA is used in a liftoff procedure to pattern gold microwave striplines. (VI) Final devices are cleaned and prepared for experiment. (b) Scanning electron micrographs corresponding to steps II, III, and VI in the fabrication procedure.

Figure 3

(a) Experiment schematic. Devices $\mathrm{①}$ are mounted in the bore of a SC magnet $\mathrm{②}$ inside of a dilution refrigerator, and imaged with wide-field imaging $\mathrm{③}$ and piezo steppers $\mathrm{④}$. Devices are addressed with a tapered optical fiber $\mathrm{⑤}$ positioned using a second set of piezo steppers $\mathrm{⑥}$. Cavities are tuned using a nitrogen feed-through $\mathrm{⑦}$. (b) Fiber network used to probe devices. Excitation light is monitored $\mathrm{⑧}$ and sent to the device. Collected light is monitored $\mathrm{⑨}$ and filtered $\mathrm{⑩}$ then sent to one or several SPCMs $\mathrm{⑪}$. N.C. indicates no connection.

Figure 4

(a) SiV level diagram. Optical transitions $f_{{\uparrow \uparrow }^{\prime }},f_{{\downarrow \downarrow }^{\prime }}\sim 737$ nm are coupled to a nanophotonic cavity with mean detuning $\mathrm{\Delta }$. Microwaves at frequency $f_{\uparrow \downarrow }$ drive rotations in the lower branch (LB). (b) Qubit frequency $f_{\uparrow \downarrow }$ for differently strained emitters. Modeled splitting for ground-state g factors ${\mathrm{g}}_{\mathrm{gs}1}=1.99,{\mathrm{g}}_{\mathrm{gs}2}=1.89,\text{and}{\mathrm{g}}_{\mathrm{gs}3}=1.65$ (solid lines) based on independent measurements of ${\mathrm{\Delta }}_{\mathrm{gs}}$. (inset) Angle dependence of $f_{\uparrow \downarrow }$ at fixed field $B_{\mathrm{ext}}=0.19$ T. Solid lines are predictions using the same model parameters. (c) Optical splitting $f_{{\uparrow \uparrow }^{\prime }}-f_{{\downarrow \downarrow }^{\prime }}$. Fits extract excited-state g factors ${\mathrm{g}}_{\mathrm{es}1}=1.97,{\mathrm{g}}_{\mathrm{es}2}=1.83,\text{and}{\mathrm{g}}_{\mathrm{es}3}=1.62$ (solid lines). (inset) Angle dependence of $f_{{\uparrow \uparrow }^{\prime }}-f_{{\downarrow \downarrow }^{\prime }}$ at fixed field $B_{\mathrm{ext}}=0.1$ T. (d) Histogram of MW transition frequency for two different emitters. (e) Histogram of optical transition frequency for two different emitters. (f) Simultaneous measurement of $f_{\uparrow \downarrow }$ and $f_{{\uparrow \uparrow }^{\prime }}$ reveals correlations between optical and microwave spectral diffusion for emitter 2.

Figure 5

(a) SiV-cavity reflection spectrum at several detunings. The bare cavity spectrum (black) is modulated by the presence of the SiV. When the atom cavity detuning is small (blue, orange), high-contrast, broad features are the result of Purcell enhanced SiV transitions. Far from the cavity resonance (green), interaction results in narrow SiV-assisted transmission channels. (b) Spin-dependent reflection for large SiV-cavity detuning $\mathrm{\Delta }\approx -3\kappa , B_{\mathrm{ext}}=0.35$ T. In this regime, SiV spin states can be individually addressed. (c) Probing either transmission dip results in high-fidelity single-shot readout in an aligned field ($F=0.97$, threshold on detecting 13 photons). (d) Spin-dependent reflection near resonance $\mathrm{\Delta }\approx 0.5\kappa , B_{\mathrm{ext}}=0.19$ T. Dispersive line shapes allow for distinguishable reflection spectra from both SiV spin states. (e) A probe at the frequency of maximum contrast ($f_Q$) can determine the spin state in a single shot in a misaligned field ($F=0.92$, threshold on detecting $>1$ photon).

Figure 6

(a) Experimental schematic for microwave control. The amplitude and phase of a CW microwave source $\mathrm{①}$ are modulated via a microwave switch and IQ mixer controlled externally by an AWG $\mathrm{②}$. A CW radio frequency source $\mathrm{③}$ is controlled using a digital delay generator $\mathrm{④}$. Both signals are amplified by $30\mathrm{dB}$ amplifiers $\mathrm{⑤}$ before entering the DR. $0\mathrm{dB}$ cryoattenuators $\mathrm{⑥}$ thermalize coax cables at each DR stage, ultimately mounted to a PCB $\mathrm{⑦}$ on the sample stage and wire-bonded to the devices. (b) Schematic depicting microwave-induced heating of devices. (c) Modeled temperature at the SiV from a dynamical decoupling sequence. At long $\tau$, device cools down between each decoupling pulse, resulting in low temperatures. At short $\tau$, devices are insufficiently cooled, resulting in a higer max temperature ($T_{\max }$). (d) Effects of microwave heating on SiV coherence time. (Top) At high Rabi frequencies, SiV coherence is temporarily reduced for small $\tau$. (Bottom) The local temperature ($T_{\max }$) at the SiV calculated by taking the maximum value of the plots in figure (c). (e) Hahn echo for even lower Rabi frequencies, showing coherence times that scale with microwave power.

Figure 7

(a) $T_2$ scaling for two different SiVs. SiV 2 exhibits no scaling with number of pulses ($T_{2,\mathrm{SiV}2}=30 \mu \mathrm{s}$). (b) DEER ESR on SiV 2. Vertical red line is the expected frequency of a $\mathrm{g}=2$ spin based on our ability to determine the applied external field (Typically to within $10\%$). (c) DEER echo on SiV 2. $T_{2,\text{DEER}}=10 \mu \mathrm{s}$. (d) Dynamical-decoupling on SiV 1. Data points are $T_2$ measurements used in part [(a), blue curve], and solid lines are a noise model consisting of two Lorentzian noise baths.

Figure 8

(a) Experimental sequence for generating and verifying spin-photon entanglement. A time-bin encoded qubit is reflected by the cavity, and both the SiV and the photonic qubits are measured in the Z and X bases. (b) Spin-photon correlations measured in the Z-Z basis. Light (dark) bars are before (after) correcting for known readout error associated with single-shot readout of the SiV. (c) Spin-photon correlations measured in the X-X basis. Bell-state preparation fidelity of $F\ge 0.89\left(3\right)$ and a concurrence $\mathcal{C}\ge 0.72\left(7\right)$. (d) Preparation of second spin-photon Bell state. Changing the phase of the incoming photonic qubit prepares a Bell-state with inverted statistics in the X basis.

Figure 9

(a) XY8-2 spin echo sequence reveals coupling to nuclear spins. (Left) Collapses $\langle S_x\rangle =0$ at short times indicate coupling to many nuclei. (Right) Collapses $\langle S_x\rangle \ne 0$ at long times indicate conditional gates on a single nuclear spin. (b) Trajectory of ${}^{13}\mathrm{C}$ on the Bloch sphere during a maximally entangling gate. Orange (purple) lines correspond to the SiV initially prepared in state $|\uparrow \rangle \left(|\downarrow \rangle \right)$; transitions from solid to dashed lines represent flips of the SiV electronic spin during the gate. (c) Maximally entangling gates of the form ${\mathcal{R}}_{\overrightarrow{n_{\uparrow }},\overrightarrow{n_{\downarrow }}}^{\varphi }$ are used to initialize and readout the two-qubit register. (d) Tuning up an initialization gate. Interpulse spacing $\tau$ for Init and Read gates are swept to maximize polarization. Solid line is the modeled pulse sequence using the hyperfine parameters extracted from (a). (e) Nuclear Ramsey measurement. Driving the ${}^{13}\mathrm{C}$ using composite gates on the SiV reveals $T_2^{*}=2.2$ ms. (Inset) Orange points are coherent oscillations of the Ramsey signal due to hyperfine coupling to the SiV. (f) Electron-nuclear correlations measured in the ZZ basis. Light (dark) bars are before (after) correcting for known errors associated with reading out the SiV and ${}^{13}\mathrm{C}$. (g) Electron-nuclear correlations measured in the XX basis. We estimate a Bell state preparation fidelity of $F\ge 0.59\left(4\right)$ and a concurrence $\mathcal{C}\ge 0.22\left(9\right)$.

Figure 10

(a) RF Rabi oscillations. Applying an RF tone directly drives nuclear rotations of a coupled ${}^{13}\mathrm{C}$. (b) SiV coherence in the presence of an RF drive. As the strength of the RF drive is increased, local heating from the CPW reduces the SiV $T_2$.

Figure 11

(a) Unit cell of a photonic crystal cavity (bounded by black lines). $H_x$ and $H_y$ define the size and aspect ratio of the hole, $a$ determines the lattice constant, and $w$ sets the waveguide width. (b) Electric field intensity profile of the TE mode inside the cavity, indicating strong confinement of the optical mode inside the waveguide. (c) Schematic of photonic crystal design. Blue shaded region is the bandgap generating structure, red shaded region represents the cavity structure. (d) Plot of $a, H_x$, and $H_y$ for the cavity shown in (c), showing cubic taper which defines the cavity region. All sizes are shown in fractions of $a_{\mathrm{nominal}}$, the unperturbed lattice constant.

Figure 12

Spectral diffusion of SiVs in nanostructures. (a) Spectral diffusion of SiV 2. We observe slow spectral wandering as well as spectral jumps. (b) Applying a short green repumping pulse before every measurement significantly speeds up the timescale for spectral diffusion. (c) Spectral diffusion of SiV 1. Line is stable to below 100 MHz over many minutes. Scale bar indicates normalized SiV reflection signal.

Figure 13

(a) Original initialization sequence from Ref. [65], note ${\mathcal{R}}_{z,\mathrm{C}}^{\pi /2}$ rotation. (b) Simplified initialization sequence used in this work. (c) Simulated performance of the initialization gate from (b) using 8 $\pi$ pulses per each nuclear gate, the initial state is $\left|\uparrow \uparrow \right.〉$ (blue) and $\left|\uparrow \downarrow \right.〉$ (orange). The resonances are narrow compared to (d) due to applying effectively twice more $\pi$ pulses (d) Simulated performance of ${\mathcal{R}}_{\pm x,\mathrm{SiV}-\mathrm{C}}^{\pi /2}$ gate for 8 $\pi$ pulses for SiV-${}^{13}\mathrm{C}$ register initialized in $\left|\uparrow \uparrow \right.〉$ (blue) and $\left|\downarrow \uparrow \right.〉$ (orange).