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Strong Microwave Erbium Coupling

Periodic Reporting for period 1 - SMERC (Strong Microwave Erbium Coupling)

Reporting period: 2019-01-01 to 2020-12-31

Context
Building quantum machines that process information more efficiently than their classical counterpart is an active field of research worldwide. One of the architectures that is pursued is that of a quantum network, consisting of quantum nodes connected by coherent links. Each quantum node includes a small number (approximately 5 to 10) of very coherent qubits, possibly serving as quantum memory. Coherent interfacing between the nodes is done by exchanging photons, in the form of visible light or microwave signals. Such a quantum network would enable distributed quantum computing and long-distance quantum key distribution through quantum repeaters.
For quantum networks, crystals doped with erbium are one of the most appealing systems because of Erbium unique properties. Erbium is a member of the rare-earth elements, which can be found at the bottom of the periodic table. In particular, erbium can absorb and emit light at “telecom” wavelength, which is ideal for sending optical data through optical fibres. Indeed, this key property of erbium made the Internet possible through the use of erbium-doped lasers and amplifiers. Additionally, erbium ions have large magnetic moments. This is common property amongst many rare-earths; Neodymium magnets are used in many industrial applications. Erbium, however, has one of the largest magnetic moments of all the rare-earth elements. Because of this property erbium ions can couple strongly to both surrounding nuclei (providing a quantum register or “bus”) and also to microwave photons in a superconducting circuit. In this way, erbium could be used as a microwave-to-optical converter thanks to its telecom-wavelength optical transition.

Project objectives
In that context, project SMERC has been able to provide answers to the following questions : 1) Does the quantum “coherence” of the Erbium ion’s magnetic electron-spin transition persist for a long time? 2) Can erbium ions be strongly coupled to microwave photons in a superconducting resonator? The answers to these questions represent important milestones towards the realization of erbium-based quantum networks.
Project results
To answer these questions, we first had to choose a host material (ie: a crystal) to dope with Erbium ions. Our choice was Sheelite; with a chemical CaWO4 its also known as calcium-tungstate (see picture attached). Calcium-tungstate chosen because it has a very low concentration of nuclear spins. These nuclear spins are attributed to the tungsten (W) the calcium-tungstate crystal, and they destroy the fragile quantum coherence of the erbium ions’ magnetic electron-spin transition because of the magnetic noise they create. Indeed, before the SMERC project, the state-of-the-art for erbium electron-spin coherence time was only 50 microseconds [1], which is not very long compared to other commonly used systems, such as bismuth or phosphorus ions implanted in Silicon. To compete with these other systems, our goal was to measure erbium electron-spin coherence at the extremely low temperature of 10mK. This temperature is about 300 times colder than deep space (!!) and can only be reached using a special type of refrigerator known as a “dilution” refrigerator.
To perform these coherence measurements, we used a technique that was developed by the Quantronics Group at CEA Saclay several years ago [2]. A superconducting micro-resonator (fabricated on the crystal surface) is used to perform electron paramagnetic resonance (EPR). A diagram illustrating this spectroscopy is shown attached. These micro-resonators require very low power because their small size; typically, just a few nanowatts. This is critical to making EPR spectroscopy work at 10mK, because even a microwatt of heat can drastically raise the temperature of the crystal. To detect signals with such low-power we had to use a special type of quantum-limited microwave amplifier, known as a Josephson Parametric Amplifier (JPA) that operates with very little power.
For project SMERC, we applied this technique for the first time to a rare-earth doped crystal. We developed a process for making micro-resonators using a very thin sheet (about 100nm thick) of superconducting niobium deposited on the surface of the calcium-tungstate crystal that was doped with erbium. For these measurements we also had to achieve large “quality factors” with the niobium resonators, as the quality-factor directly impacts the detection sensitivity in EPR measurements. During this project we were able to demonstrate quality-factors of 50,000. This is comparable to state-of-the-art results for niobium resonators fabricated on other materials such as silicon and diamond.
In this way, we were able to measure a spin coherence time of 20ms in a CaWO4 crystal doped with 10 part-per-billion (ppb) erbium. This is a 400-fold improvement over the previous record for Erbium spin coherence in calcium-tungstate and consists the first major result of the project SMERC. We also performed a detailed study of erbium spin decoherence in a crystal with a higher erbium concentration of 18ppm. In this crystal we showed the quenching of spin decoherence due to the polarization of other paramagnetic impurities in the crystal, such as ytterbium and manganese.
The second important result of the project was to strongly-couple the erbium ions to the microwave photons in the resonator. This was realised by using the small volume in which the electromagnetic field of the resonator is concentrated. Combined with the large quality factors of our niobium resonators, we demonstrated strong coupling of an ensemble of erbium ions to a superconducting resonator [3].
Future Perspectives
In addition to strongly coupling of the ensemble of erbium ions in the crystal, it will be important to address individual erbium ions by selectively enhancing their coupling to the electromagnetic field in the resonator. For this goal, we have seen evidence of strong coupling to just a small fraction of the erbium ions within reach of the resonator; perhaps a few thousand or less. For this result, the “smoking-gun” was the observation of a rapid emission of photons from the erbium ions in question, when resonant with the niobium superconducting resonator. This rapid emission manifests as a shortened “relaxation lifetime” that can be observed with ESR spectroscopy. This is a signature of the Purcell-effect, which has only been observed for donors in silicon so far. Project SMERC has now provided the first evidence of Purcell-enhanced radiative-emission for crystals implanted with rare earth ions.
The results obtained within project SMERC pave the way for detecting individual erbium ions, by coupling them to a superconducting resonator. This will be a key enabling technology for erbium-based quantum networks both in the microwave and in the optical domain and this will help the development of the future quantum-Internet.

[1] S. Bertiana, et. al, Rare-earth solid-state qubits (2007) https://arxiv.org/abs/cond-mat/0703364
[2] Y. Kubo, et. al, Strong Coupling of a Spin Ensemble to a Superconducting Resonator (2010) https://arxiv.org/abs/1006.0251
[3] S. Probst, et. al Hyperfine spectroscopy in a quantum-limited spectrometer (2020) https://mr.copernicus.org/articles/1/315/2020/mr-1-315-2020.html
a) Calcium-tungstate unit cell, units in Angstroms. b) Er ions coupled to a 5um-wide resonator wire