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A Scalable Quantum Network based on Individual Erbium Ions

Periodic Reporting for period 2 - QuantumNet (A Scalable Quantum Network based on Individual Erbium Ions)

Reporting period: 2019-09-01 to 2021-02-28

A future quantum network will consist of quantum processors that are connected by quantum channels, just like conventional computers are wired up to form the Internet. In contrast to classical devices, however, the entanglement and non-local correlations available in a quantum-controlled system facilitate novel fundamental tests of quantum theory and numerous applications. In particular, quantum networks can fundamentally enhance computational power, ensure provably-secure communication, and simulate complex quantum systems to aid the search for new materials and drugs.
While pioneering experiments have demonstrated the entanglement of two quantum nodes separated by up to 1.3 km, accessing the full potential of quantum networks requires scaling of these prototypes to more nodes and larger distances. This requires the development of a new technology that overcomes the bottlenecks of existing physical systems. To this end, we harness the exceptional properties of individual Erbium ions embedded in silicon and silicate crystals. The key steps towards increasing the size of quantum networks based on this platform are, first, the implementation of efficient quantum network nodes at a telecommunication wavelength, second, increasing the number of quantum bits in such node via frequency-selective addressing, and, third, the implementation of efficient protocols to generate entanglement between the nodes. Based on these advances, we plan to demonstrate a prototype quantum repeater, a milestone advancement towards global quantum networks.
We have built two experimental setups to study and control the interaction of Erbium dopants with photons at telecommunication wavelength. In the first setup, we have realized a Fabry-Perot resonator that enables an unprecedented Purcell enhancement. We have encountered unexpected problems in the sample fabrication caused by surface amorphization of YSO under reactive ion etching. We have overcome these challenges by developing a suited polishing recipe, followed by van-der-Waals bonding to a dielectric mirror. We have achieved the targeted cavity finesse, exceeding 105, and stabilized the resonator in a closed-cycle cryostat. We have demonstrated that Erbium dopants preserve their exceptional coherence upon resonator integration. Still, we have observed unexpectedly large spectral diffusion, likely caused by previously undetected impurities or nuclear spins in the host. We have summarized these findings in a publication, arXiv:2006.14229 (2020), accepted for publication in PRX.

In the second setup, we have started to investigate an alternative host material that avoids the mentioned challenges, crystalline silicon. In stark contrast to previous work, we have shown that Erbium can be integrated at well-defined lattice sites using an optimized implantation and annealing procedure. This has allowed us to achieve a three-orders of magnitude improved inhomogeneous distribution, which should be sufficient for the control of individual ions. We have summarized these findings in a publication, arXiv:2005.01775 (with referees).

Finally, we have investigated spin-spin interactions within rare-earth doped crystals. In contrast to the expectation of the community, we have demonstrated that these interactions cannot be efficiently decoupled my microwave control, which poses a severe limitation to quantum memory experiments with dense ensembles. We have summarized these results in
arXiv:2005.08822 (with referees). Our findings thus highlight the importance of our cavity-enhanced single-ion approach that can overcome the mentioned limitation.

In summary, we have successfully completed most of the targeted work packages (ensemble spectroscopy, laser stabilization, spin readout and ground state control, spin-spin interactions within a node, construction of setup B, sample and setup optimization).
We have shown that the emission of erbium dopants can be strongly enhanced by a resonator while at the same time preserving their excellent optical coherence properties. Compared to competing experiments with cryogenic Fabry-Perot resonators, we have increased the stability and the finesse approximately hundredfold. Compared to state-of-the-art systems with rare-earth dopants in nanophotonic resonators, we observe an increase of the optical coherence by two to three orders of magnitude.
In addition, we have demonstrated that ion implantation allows one to integrate erbium into silicon at well-defined lattice sites, in striking contrast to the findings of numerous previous works. Recently, we have succeeded in single-ion spectroscopy in this novel materials platform, opening unique perstpectives for the realization of integrated quantum networks based on established fabrication processes of the semiconductor industry.

We expect that in spite of additional delay caused by the COVID-crisis, we can still complete most of the work packages of the original proposal. This includes in particular the control of single spins, frequency-domain multiplexing of many spins in one device, and the generation of spin-photon and spin-spin entanglement. Albeit some of these topics have by now been addressed in competing physical platforms, we expect that our results in each of them will further push the state of the art towards the realization of global quantum networks via quantum repeaters.