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High-Frequency Spin Entanglement Generation in Diamond

Periodic Reporting for period 1 - Hi-FrED (High-Frequency Spin Entanglement Generation in Diamond)

Reporting period: 2018-09-01 to 2020-08-31

The nitrogen vacancy (NV) centers in diamond are optically active impurities in high-purity diamond crystals and feature optically addressable electron spin with outstanding coherence times up to hundreds of milliseconds even at room temperature together with robust single photon emission. A crucial issue is the lack of an efficient, high-fidelity spin-photon interface. This issue has severely limited the implementation of NV centers in quantum technologies. This project aimed to establish the NV center in thin diamond structures as optically-coherent and radically improve the open cavity platform that can host such diamond samples with the aim of generating high flux of indistinguishable photons. The overarching goal of these actions is the generation of high-frequency spin-spin entanglement in spatially separated NV centers in diamond. This contributes to the research areas of quantum computing and quantum sensors which enhances Europe's capabilities in quantum technologies and fosters its staying at the front of the 'second quantum revolution'.
The NV center fabrication plan described in the original proposal had to be redesigned in early 2018 after a study has been published [1] on the quality of NV centers formed by nitrogen ion implantation, the method earlier selected to create NV centers in our project. The conclusion of this study indicated, that at least half (and most likely much more) of the NV centers formed in this way are not even potentially suitable for generating entanglement due to their zero-phonon linewidth inhomogeneous broadening, orders of magnitude larger than the desired radiative lifetime transform limit. In a parallel study, we further confirmed and described in more detail this finding2. Also, in a systematic study, we eliminated electron beam lithography and shallow etch as causes of spectral noise impacting NV centers optical quality. We determined that the step that is the most detrimental is the deep etching of the diamond. Finally, the lack of observation of a single NV center in a thin diamond structure formed by nitrogen ion implantation and featuring vanishing inhomogeneous broadening indicated that a completely new fabrication method might be necessary. The results of all these studies constituted a paradigm shift in the field of fabricating NV centers strongly impacting further development of the project, as a change of method for creating NV centers was strongly advisable.

In the redesigned research agenda our main research activity was focused on the creation of NV centers using a alternative approaches. As the new method, we selected the newly developed femtosecond laser-assisted creation of NV centers [3] and upgraded it by implementing a solid immersion lens in the process. After installation of a new setup and establishing fabrication procedures, we succeeded in fabricating NV centers with unprecedented quality (see the attached figure). Their zero-phonon line spectral linewidth, which is the key parameter determining suitability for applications of NV centers as sources of quantum light has a statistical distribution peaking at a record-low value of around 60 MHz. This includes the effect of long-term spectral diffusion induced by a 532 nm repump laser for charge state stabilization. About 95% of NVs feature a linewidth below 100 MHz, which is an excellent result not only when compared to NVs created with implantation, but also when comparing to all other fabrication methods. The SIL allowed for vacancy formation close to diamond surface without inducing surface graphitization.

The result of this experiment is the main scientific achievement of the project. We achieved the creation of nitrogen-vacancy centers in diamond with a minimally invasive technique presumably preserving the diamond’s crystal quality.

Regarding NV fabrication, we also joined the efforts of other colleagues who used the redesigned implantation method based on inverting the fabrication order and performing implantation after microstructuring2. Worth noticing, we observed two narrow (< 250MHz) linewidths in the 1.57 µm-thick area of a sample created with this method.

The second main goal of the project was a radical improvement of the microcavity parameters and resulting achievement of a higher coupling rate between the emitter and cavity together with a decrease of the unwanted losses. We showed that a quality factor well above 1·10^5 could be consistently achieved together with a finesse above 3·10^4, proving the high quality of the mirrors and mirror absorption together with the scattering losses at a satisfactorily low level. After insertion of the diamond, those parameters drop, which is due to originate mostly from surface roughness and another loss mechanism which is yet to be determined. The results are currently being described and soon will be submitted for publication [4].

Regarding the purely scientific objectives two out of three goals were accomplished laying solid foundations for realization of the third goal, which aimed at demonstrating entanglement between distant spins at a enhanced rate. Also, it has to be noted, that one of the main problems inhibiting implementation of milestones M3 and M4, which is the degradation of NV centers optical quality in very thin structures (below 3 micrometers thick) is of unknown but rather fundamental nature and despite efforts of several leading groups worldwide only limited progress has been achieved in the past years in improving the figures of merit.
All the major achievements described earlier represent a step forward in the state of the art. Of particular importance is the exceptionally high probability of finding narrow-linewidths NV centers in comparison to standard implantation and annealing1,2 and other creation methods like the one employing electron beam irradiation to create vacancies. This is crucial for tests of entanglement and is greatly beneficial for performing experiments with minimal pre-selection of NV centers. Also, the few measured NV centers where we measured polarization splitting between different NV centers levels indicate very low strain of the laser-written NV centers; however detailed statistical description of strain values is currently under study.

The results are contained in two currently prepaired manuscripts [4, 5] which will soon be submitted for publication. Also, results have been presented and discussed at international conferences and workshops.


1. Van Dam, S. B. et al. Optical coherence of diamond nitrogen-vacancy centers formed by ion implantation and annealing. Phys. Rev. B 99, (2019).
2. Kasperczyk, M. et al. Statistically modeling optical linewidths of nitrogen vacancy centers in microstructures. Phys. Rev. B 102, 75312 (2020).
3. Chen, Y. C. et al. Laser writing of coherent colour centres in diamond. Nat. Photonics 11, 77–80 (2017).
4. Flågan, S. et al. (in preparation).
5. Yurgens, V., ... & Jakubczyk, T. et al. Low-noise nitrogen-vacancy centers in diamond created using laser writing with a solid immersion lens. (to be submitted).