Quantum network nodes based on diamond qubits with an efficient nanophotonic interface

TL;DR

This paper demonstrates a diamond nanocavity with silicon-vacancy centers and nuclear spins as a promising quantum network node, achieving high photon-spin coupling and long coherence times for quantum communication.

Contribution

It introduces an efficient diamond-based quantum node with integrated SiV centers and nuclear spins, enabling high-fidelity photon interfaces and long-lived quantum memories.

Findings

Achieved high cooperativity (C > 30) in SiV-cavity coupling.

Demonstrated heralded single-photon storage with coherence times over one millisecond.

Realized universal control of a two-qubit register with nearly second-long coherence.

Abstract

Quantum networks require functional nodes consisting of stationary registers with the capability of high-fidelity quantum processing and storage, which efficiently interface with photons propagating in an optical fiber. We report a significant step towards realization of such nodes using a diamond nanocavity with an embedded silicon-vacancy (SiV) color center and a proximal nuclear spin. Specifically, we show that efficient SiV-cavity coupling (with cooperativity $C >30$) provides a nearly-deterministic interface between photons and the electron spin memory, featuring coherence times exceeding one millisecond. Employing coherent microwave control, we demonstrate heralded single photon storage in the long-lived spin memory as well as a universal control over a cavity-coupled two-qubit register consisting of a SiV and a proximal $^{\mathrm{13}}$C nuclear spin with nearly second-long coherence time, laying the groundwork for implementing quantum repeaters.

Equations

$${|\psi ⟩}_{\mathrm{f}}\propto |+⟩({\beta }_e|\downarrow ⟩+{\beta }_l|\uparrow ⟩)+|-⟩({\beta }_e|\downarrow ⟩-{\beta }_l|\uparrow ⟩),$$

$${\hat{H}}_{\mathrm{HF}}=\hslash A_{\parallel }\frac{{\hat{S}}_z}{2}\frac{{\hat{I}}_z}{2}+\hslash A_{\perp }\frac{{\hat{S}}_z}{2}\frac{{\hat{I}}_x}{2}$$

$${\tau }_k\approx \frac{2k+1}{2{\omega }_l}\left(1-\frac{1}{2}{\left(\frac{A_{\perp }}{2{\omega }_l}\right)}^2\right),$$

Full text

The realization of quantum networks is one of the central challenges in quantum science and engineering with potential applications to long-distance communication, non-local sensing and metrology, and distributed quantum computing Kimble (2008); Childress et al. (2005); Gottesman et al. (2012); Kómár et al. (2014); Monroe et al. (2014). Practical realizations of such networks require individual nodes with the ability to process and store quantum information in multi-qubit registers with long coherence times, and to efficiently interface these registers with optical photons. Cavity quantum electrodynamics (QED) is a promising approach to enhance interactions between atomic quantum memories and photons Stute et al. (2012); Reiserer and Rempe (2015); Kalb et al. (2015); Lodahl et al. (2015); Welte et al. (2018). Trapped atoms in optical cavities are one of the most developed cavity QED platforms for quantum processing, and have demonstrated gates between atoms and photons Reiserer et al. (2014) as well as interactions between multiple qubits mediated by the optical cavity Welte et al. (2017). While these experiments have demonstrated all of the individual components needed for a quantum network, combining them to realize a full-featured node remains an outstanding challenge.

Nanophotonic cavity QED systems with solid-state emitters are appealing candidates for realizing quantum nodes as they can be interfaced with on-chip electronic control and photonic routing, making them suitable for integration into large-scale networks Lodahl et al. (2015); Molesky et al. (2018). Numerous advances towards the development of such nodes have been made recently. Self-assembled quantum dots in GaAs have been efficiently interfaced with nanophotonic structures, enabling a fast, on-chip spin-photon interface Lodahl et al. (2015); Sun et al. (2016). Nitrogen-vacancy color centers in diamond (NVs) have demonstrated multi-qubit quantum processors with coherence times approaching one minute Bradley et al. (2019), and have been used to implement quantum error correction Waldherr et al. (2014) and teleportation Pfaff et al. (2014). Despite this rapid progress, functional nodes combining all the necessary ingredients in a single device have not yet been realized. For example, quantum memory times in quantum dots are limited to a few $\mathrm{\SIUnitSymbolMicro s}$ by the dense bath of surrounding nuclear spins Huthmacher et al. (2018). Conversely, an efficient nanophotonic interface to NVs remains elusive, in part due to the degradation of their optical properties inside nanostructures arising from electrical noise induced by the fabrication Faraon et al. (2012); Ruf et al. (2019).

In this Letter, we demonstrate an integrated network node combining all key ingredients required for a scalable quantum network. This is achieved by coupling a negatively charged silicon-vacancy color-center (SiV) to a diamond nanophotonic cavity and a nearby nuclear spin, illustrated schematically in Fig. 1(a). The SiV is an optically active point defect in the diamond lattice Hepp et al. (2014); Müller et al. (2014). Its $D_{3d}$ inversion symmetry results in a vanishing electric dipole moment of the ground and excited states, rendering optical transitions insensitive to electric field noise typically present in nanofabricated structures Sipahigil et al. (2014, 2016). We enhance interactions between SiVs and optical photons by incorporating them into nanocavities Nguyen et al. (2019), which are critically coupled to on-chip waveguides. Itinerant photons in a fiber network are adiabatically transferred to this waveguide, allowing for the collection of reflected photons with efficiencies exceeding $90\%$ Burek et al. (2017). After an initial optical characterization of the devices, a shorted, gold coplanar waveguide (CPW) is deposited in close proximity to a small subset of cavities [Fig. 1 (b), inset] Nguyen et al. (2019). This enables coherent microwave manipulation of the SiV ground state spin in a cryogenic environment ($T<$0.1\text{,}\mathrm{K}$$), where phonon-mediated dephasing and relaxation processes are mitigated Jahnke et al. (2015); Sukachev et al. (2017); Pingault et al. (2017).

In what follows, we characterize these devices in the context of the three key ingredients of a quantum network node: (i) an efficient spin-photon interface, (ii) a long-lived quantum memory, and (iii) access to multiple interacting qubits.

The efficient spin-photon interface is enabled by coupling to a diamond nanophotonic cavity. For critically-coupled cavities, the presence of an SiV modulates the bare nanocavity reflection spectrum with the strength of this modulation parametrized by the cavity cooperativity $C=4g^{2}/(\kappa\gamma)\sim 38$ (with the single photon Rabi frequency, cavity, and atomic energy decay rate $\{g,\kappa,\gamma\}=2\pi\times\{5.6,33,0.1\}$ $\mathrm{G}\mathrm{H}\mathrm{z}$). For $C>1$, we expect high-contrast modulation for a small detuning ($\Delta$) between the cavity and the SiV resonance near $737$\mathrm{n}\mathrm{m}$$. An external field $B_{\mathrm{ext}}$ lifts the degeneracy of the SiV spin-$\frac{1}{2}$ sub-levels, creating spin-dependent reflection: photons at the frequency of maximum contrast ($f_{Q}$) are reflected from the cavity only when the SiV is in a specific spin state ([Fig. 2(a)], $\ket{\uparrow}$). In previous works, spin readout of the SiV was performed with $B_{\mathrm{ext}}$ parallel to the SiV symmetry axis, where the spin-conserving transitions are highly cycling Sukachev et al. (2017). The high collection efficiency into a tapered fiber allows for fast single-shot readout of the SiV even in a misaligned field [Fig. 2(b)], which is necessary for the nuclear spin control described below. We observe a readout fidelity of $F=0.92$ in $13\text{\,}\mathrm{\SIUnitSymbolMicro s}$ even when only a few ($\sim 10$) photons are scattered.

We next demonstrate that the SiV spin in a nanocavity is a suitable quantum memory. Microwave pulses at $f_{\uparrow\downarrow}=$ $6.7\text{\,}\mathrm{GHz}$ coherently manipulate the SiV spin qubit. The resulting Rabi oscillations, which can be driven in excess of $80\text{\,}\mathrm{MHz}$ while maintaining acceptable sample temperatures Nguyen et al. (2019), are shown in the inset of Fig. 2(c). These rotations are used to probe the coherence properties of the spin via dynamical decoupling sequences [Fig. 2(c)] Ryan et al. (2010); de Lange et al. (2010). We measure the coherence time of the SiV inside the nanocavity to be $T_{2}>$ $1.5\text{\,}\mathrm{ms}$ and scale with the number of decoupling pulses as $T_{2}\propto N^{2/3}$. The coherence scaling observed here differs from that observed in bulk diamond Sukachev et al. (2017), and is similar to NVs near surfaces Myers et al. (2014). This suggests that SiV memory in nanostructures is limited by an electron spin bath, for example residing near the surface of the nanostructure or resulting from implantation-induced damage Nguyen et al. (2019).

We now combine the efficient spin-photon interface and control over the SiV spin state to demonstrate heralded storage of photonic qubit states in the spin-memory, a key feature of a network node Kalb et al. (2015). Fig. 3(a) outlines the experimental scheme, where photonic qubits are prepared using time-bin encoding and mapped onto the SiV spin. In our experiments, the SiV is first initialized into a superposition state $\ket{\rightarrow}\propto\ket{\uparrow}+\ket{\downarrow}$ by optical pumping followed by a microwave $\frac{\pi}{2}$-pulse. A pair of weak coherent pulses separated by $\delta t=$ $30\text{\,}\mathrm{ns}$ at frequency $f_{Q}$ are then sent to the cavity. The single photon sub-space corresponds to an incoming qubit state $\ket{\Psi_{\mathrm{i}}}\propto\beta_{e}\ket{e}+\beta_{l}\ket{l}$, where $\ket{e}$ ($\ket{l}$) denotes the presence of a photon in the early (late) time-bin. As a photon can only be reflected from the device if the SiV is in state $\ket{\uparrow}$ [Fig. 2(a)], particular components of the initial product state can be effectively ”carved out” Welte et al. (2017). We invert the SiV spin with a $\pi$-pulse between the arrival of the two time bins at the cavity, such that a photon detection event indicates that the final state has no $\ket{e\uparrow}$ or $\ket{l\downarrow}$ component. This leaves the system in the final spin-photon entangled state $\ket{\Psi_{\mathrm{f}}}\propto\beta_{e}\ket{e\downarrow}+\beta_{l}\ket{l\uparrow}$.

The reflected photon enters a time-delay interferometer, where one arm passes through a delay line of length $\delta t$, allowing the two time-bins to interfere and erase which-time-bin information. As can be seen by expressing the final state in the corresponding photon basis:

[TABLE]

a detection event on either the ‘$+$’ or ‘$-$’ arm of the interferometer represents a measurement in the X-basis ($\ket{\pm}\propto\ket{e}\pm\ket{l}$), effectively teleporting the initial photonic state onto the electron (up to a known local rotation). We experimentally verify generation of the entangled state $\ket{\psi}_{\mathrm{f}}$ for input states $\ket{\psi}_{\mathrm{i}}=\ket{\pm}$ by measuring spin-photon correlations Nguyen et al. (2019), and use it to extract a teleportation fidelity of $0.92(6)$.

After detection of the heralding photon, we store the teleported photonic states (initially prepared in $\{\ket{+}$ or $\ket{-}\}$) in spin memory for $20\text{\,}\mathrm{\SIUnitSymbolMicro s}$ by applying an additional decoupling $\pi$-pulse on the SiV spin. The overall fidelity of teleportation and storage is $F=0.87(6)$ after corrected for readout errors [Fig. 3(b)]. The quantum storage time can be extended by additional decoupling sequences [Fig. 2(c)], enabling entanglement distribution up to a $T_{2}$-limited range of $500\text{\,}\mathrm{km}$.

In order to extend this range and to enable more generic quantum communication protocols, we next demonstrate a two-qubit register based on the cavity coupled SiV electronic spin and a nearby 13C nuclear memory. The 13C isotope of carbon is a spin-$\frac{1}{2}$ nucleus which has $\sim 1\%$ natural abundance in diamond, and is known to exhibit exceptional coherence times Bradley et al. (2019). While direct radio-frequency manipulation of nuclear spins is impractical due to heating concerns Nguyen et al. (2019), control over 13C spins can be achieved by adapting electron mediated techniques developed for Nitrogen vacancy (NV) centers Dutt et al. (2007); Kolkowitz et al. (2012); Taminiau et al. (2014); Abobeih et al. (2018). The physical principle of the SiV-13C interaction is depicted in Fig. 4(a). The SiV generates a spin-dependent magnetic field $\mathbf{B}_{\mathrm{SiV}}$ at the position of the 13C, which is located a few lattice sites away. This is described by a hyperfine interaction Hamiltonian:

[TABLE]

where $\hat{S}_{z,x}$ ($\hat{I}_{z,x}$) are the Pauli operators for the electron (nuclear) spin, and $A_{\parallel,\perp}$ are the coupling parameters related to the parallel and perpendicular components of $B_{\mathrm{SiV}}$ with respect to the bias field $B_{\mathrm{ext}}$ Rowan et al. (1965); Kolkowitz et al. (2012); Taminiau et al. (2014). Hyperfine interactions manifest themselves in spin-echo measurements as periodic resonances Taminiau et al. (2014), shown in Fig. 4(b) for an XY8-2 decoupling sequence $\pi/2-(\tau-\pi-\tau)^{16}-\pi/2$, where $\tau$ is the free evolution time. The coherence envelope for this sequence is $T_{2}(N=16)=$603\text{,}\mathrm{\SIUnitSymbolMicro s}$$ [Fig. 4(b), upper panel].

For weakly coupled 13C ($A_{\perp}\ll\omega_{l}$, and $A_{\parallel}\ll\omega_{l}$, as used in this letter), the positions of the resonances Taminiau et al. (2014)

[TABLE]

where $\omega_{l}$ is the larmor frequancy of a bare 13C, are insensitive to specific 13C hyperfine parameters at first order, rendering them indistinguishable at early times ($\tau_{k}\ll$ $4\text{\,}\mathrm{\SIUnitSymbolMicro s}$, [Fig. 4(b), red inset]). Individual 13C can be isolated at longer times Taminiau et al. (2014); Nguyen et al. (2019), and are used to engineer gates between a single 13C and the SiV [Fig. 4(b), green inset] 111This is in contrast with the NV center, which is a spin-1 system and therefore features a linear shift of the resonances with coupling strength $A_{\parallel}$ in the $S=\{0,-1\}$ sub-system.. The fundamental two-qubit gate associated with such interaction is a conditional $\pm\pi/2$ rotation of the 13C-spin around the $X$ axis ($R_{x}^{\pm\pi/2}$), which is a maximally entangling gate. Together with unconditional rotations of the nuclear spin (which are also generated via dynamical decoupling sequences), and MW rotations on the SiV, these sequences form a universal set of gates for the register Taminiau et al. (2014).

We characterize the 13C via Ramsey spectroscopy [Fig. 4(c)]. The nuclear spin is initialized and read out via the optically addressable SiV spin by transferring population between the SiV and 13C Nguyen et al. (2019). Depending on the SiV state before the Ramsey sequence, we observe oscillations of the nuclear spin at its eigenfrequencies $\omega_{\uparrow,\downarrow}^{2}=\left(\omega_{l}\pm A_{\parallel}/2\right)^{2}+\left({A_{\perp}}/{2}\right)^{2}$), allowing us to determine the hyperfine parameters \{\omega_{l},A_{\parallel},A_{\perp}\}=2\pi\{2.0,0.70,-0.35\}$$\mathrm{MHz}. This coherence persists for $T_{2}^{*}>$ $2\text{\,}\mathrm{ms}$ Nguyen et al. (2019), and can be further extended to $T_{2}>$ $0.2\text{\,}\mathrm{s}$ by applying a single dynamical decoupling $\pi$-pulse on the nucleus, demonstrating the exceptional memory of the 13C nuclear spin [Fig. 4(d)].

We benchmark the two-qubit register by demonstrating an SiV-controlled X-gate (CNOT) on the 13C-spin by combining a $R_{x}^{\pm\pi/2}$ with an unconditional nuclear $\pi/2$ rotation Nguyen et al. (2019). This gate results in a spin flip of the 13C only if the SiV spin is in the state $\left|\downarrow\right\rangle$ [Fig. 4(e)]. We use this gate to prepare a Bell state by initializing the register in $\left|\downarrow\downarrow\right\rangle$, and applying a $\pi/2$-rotation gate on the SiV spin followed by a CNOT gate. Correlation measurements yield a concurrence of $\mathcal{C}=0.22(9)$ corresponding to a Bell state fidelity of $F=0.59(4)$ after correcting for readout errors Nguyen et al. (2019).

Our experiments demonstrate the first prototype of a nanophotonic quantum network node combining all necessary ingredients in a single physical system. We emphasize that both spin-photon and spin-spin experiments are performed in the same device under identical conditions (cavity detuning and bias field), thereby providing simultaneous demonstration of all key requirements for a network node.

The main limitation on the demonstrated fidelities are related to the specific 13C in the proximity of the SiV, requiring an unfavorable alignment of the external magnetic field in order to isolate a single 13C. Specifically, the fidelity of two-qubit gates is limited by residual coupling to bath nuclei, SiV decoherence during the gate operations, and under/over-rotations of the nuclear spin arising from the granularity of spin-echo sequences. To reduce these errors, fine-tuned adaptive pulse sequences can be used to enhance sensitivity to specific nearby 13C, and tailor the rotation angle and axis of rotation Casanova et al. (2015); Schwartz et al. (2018). Alternatively, replacing gold with superconducting microwave coplanar waveguides will significantly reduce ohmic heating, and allow direct radio-frequency control of nuclear spins. These improvements could also enable the realization of a deterministic two-qubit register based on 29SiV, which contains both electronic and nuclear spins in a single defect Nguyen et al. (2019); Rogers et al. (2014).

The fidelity of the heralded photon storage is limited primarily by single shot readout and imperfect critical coupling of the cavity. The improvements of the nuclear spin control mentioned above would allow for working in an external magnetic field aligned to the SiV axis, which would improve readout fidelity from $F\sim 0.90$ (reported here) to $0.99$ Evans et al. (2018); Nguyen et al. (2019). The impedance mismatch of the cavity used in this experiment also gives rise to residual reflections which are not entangled with the SiV. Over-coupled cavities enable the use of a SiV spin-dependent phase flip for reflected photons, improving both the fidelity and success probability of spin-photon interactions.

In conjunction with recent advances in controlling emitter inhomogeneity via electromechanical tuning Machielse et al. (2019), these techniques should allow for chip-scale fabrication of quantum network nodes, laying the groundwork for the realization of scalable quantum repeater Briegel et al. (1998); Childress et al. (2005) architectures. The ability to store quantum information in highly coherent 13C nuclei, as well as the opportunity to extend these results to other group-IV color-centers, may open up the possibility of operating such nodes at at temperatures $>$ $1\text{\,}\mathrm{K}$ Metsch et al. (2019); Siyushev et al. (2017); Trusheim et al. (2019, 2018). Finally, the efficient quantum network node demonstrated in this Letter could enable generation of multi-dimensional cluster states of many photons, which could facilitate realization of novel, ultra-fast one-way quantum communication architectures Buterakos et al. (2017).

We would like to thank M. Markham, A. Bennett and D. Twitchen from Element Six Inc. for providing the diamond substrates used in this work, as well as F. Jelezko, R. Evans and A. Sipahigil for insightful discussions. This work was supported by DURIP grant No. N00014-15-1-28461234 through ARO, NSF, CUA, AFOSR MURI, and ARL. M.K.B. and D.S.L were supported by DoD NDSEG, B.M. and E.N.K. were supported by NSF GRFP, and R.R. was supported by the Alexander von Humboldt Foundation. Devices were fabricated at Harvard CNS, NSF award no. 1541959.