Robust Quantum-Network Memory Using Decoherence-Protected Subspaces of Nuclear Spins

The realization of a network of quantum registers is an outstanding challenge in quantum science and technology. We experimentally investigate a network node that consists of a single nitrogen-vacancy center electronic spin hyperfine coupled to nearby nuclear spins. We demonstrate individual control and readout of five nuclear spin qubits within one node. We then characterize the storage of quantum superpositions in individual nuclear spins under repeated application of a probabilistic optical internode entangling protocol. We find that the storage fidelity is limited by dephasing during the electronic spin reset after failed attempts. By encoding quantum states into a decoherence-protected subspace of two nuclear spins, we show that quantum coherence can be maintained for over 1000 repetitions of the remote entangling protocol. These results and insights pave the way towards remote entanglement purification and the realization of a quantum repeater using nitrogen-vacancy center quantum-network nodes.

Popular Summary

A future quantum internet that links network nodes through quantum entanglement will enable ultrasecure communication, the clustering of quantum computers, and quantum-secured computing in the cloud. In recent years, several point-to-point quantum links have been demonstrated. However, in order to realize a true quantum network, a node needs to contain robust memories that can reliably store previously established quantum entanglement while a new connection with another node is being set up. Here, we investigate the physics of one of the most promising quantum network platforms: single nuclei in a diamond lattice surrounding an electron that provides an interface to light.

Our experimental setup, which is conducted at 4 K, focuses on the individual control and readout of five ${}^{13}\mathrm{C}$ nuclear spin qubits within one node. These nuclear spins have coherence times on the order of tens of milliseconds. We unravel the main limitation to the performance of such nuclear quantum memories, and we overcome this limitation by creating a novel type of memory that is composed of multiple individual nuclei prepared in special resilient quantum states.

Our results demonstrate a clear path toward the first demonstration of key quantum network protocols, thereby constituting a critical step toward a future quantum internet.

Figure 1

(a) Layered quantum-network architecture. Individual electronic spins (purple spin symbols) are entangled probabilistically over large distances using photons (red curly lines). Each electronic spin is hyperfine coupled to a quantum register of surrounding nuclear spins (yellow) that can be deterministically controlled (green arrows). (b) Electron-nuclear coupling. The nuclear spins precess in an external magnetic field $\overrightarrow{B}$. The precession axis and frequency, ${\omega }_0$ or ${\omega }_{-1}$ (black vectors), depend on the state of the electronic spin, $|0⟩$ or $|-1⟩$, via the hyperfine interaction with parallel component $A_{\parallel }$ and perpendicular component $A_{\perp }$ (green vectors). (c) Experimental sequence to generate entanglement between remote NV electronic spins [20]. By optical pumping on the “reset” transition, the spin is initialized in $|0⟩$ at time $t_r$. Subsequently, a spin superposition state is created via a microwave $\pi /2$ pulse. Spin-photon entanglement is then generated via two optical excitations, separated by a microwave $\pi$ pulse that inverts the spin state $|0⟩\leftrightarrow |-1⟩$. (d) NV electronic orbital and spin level scheme at cryogenic temperature. The ground states $|0⟩$ ($|\pm 1⟩$) are optically coupled to the excited states $|E_{x,y}⟩$ ($|E_{1,2}⟩$ and $|A_{1,2}⟩$, red arrows), respectively. These states decay either directly (red dashed arrows) or via the metastable spin singlet states $|S⟩$ (blue dashed arrows) to one of the ground states.

Figure 2

NV electronic spin initialization. (a) Probability that the electronic spin is pumped to $|0⟩$ as a function of the repump laser pulse duration when the spin is initially prepared in $|-1⟩$. The inset shows the used pulse sequence. We observe a double-exponential decay (solid fit curves), with a time scale and relative amplitude that depends on the used “reset” transition. Reduced laser power leads to slower initialization time scales. (b) Probability that the NV is found in state $|0⟩$, $|+1⟩$, and $|-1⟩$ for 2000-nW repump power in the $|E_{1,2}⟩$ (left) or $|A_{1,2}⟩$ (right) configuration. The solid lines are calculated using a rate equation model described in the text. For long repumping time, the calculated population in the metastable singlet states (green dotted curve) dominates the repumping process.

Figure 3

Dephasing of ${}^{13}\mathrm{C}$ nuclear spins. (a) Optimization of the dynamical decoupling sequence timing. Different nuclear spins (colors) are initialized in a balanced superposition state and the entanglement sequence is performed $N=200$ times. The duration of the second wait interval is swept and the length of the Bloch vector $XY$ projection is measured. All measured nuclear spins exhibit the same broad optimum around $0.4\mu \mathrm{s}$, as can be seen from the Gaussian fit curves. (b) Dephasing of nuclear spins when the number of random reset processes is increased. The data show measurement results of all five individually controlled nuclear spins, where increasing coupling strength leads to steeper decay curves. The solid lines are exponential fits.

Figure 4

Encoding of a quantum bit in decoherence-protected subspaces. (a) Encoding in nuclear spin 2 or 3 (cyan and green) shows similar decay with increasing $N$. Encoding in a decoherence-protected (decoherence-enhanced) subspace leads to strongly decreased (enhanced) dephasing shown in red (magenta). The initial fidelity in the two-spin case is slightly reduced because encoding and readout require more control operations on the nuclear spins. (b) Number of sequence repetitions that are possible before the nuclear qubit Bloch vector length drops to $1/e$ of its initial value, for qubits encoded in single nuclear spins (empty circles) and in two-spin states (filled circles) of different effective coupling strengths $\mathrm{\Delta }\omega$. The four depicted data sets are taken for increasing repump duration, caused by a reduced repump laser power. The solid curves are fits according to the model we present in the text.