Single rare-earth ions are hard to observe and even harder to use as qubits. However, with the help of coupling to an optical cavity and clever engineering of selection rules, a big step has been taken to establish their new role in the quantum world.
Rare-earth ions (REIs) in crystals are excellent candidates for optically addressable quantum memory. This is because of their optically active 4f electrons, shielded from environmental distortions by a Faraday cage comprised of filled 5s and 5p electron shells1. Record-long decoherence times of six hours have been demonstrated in an ensemble of europium doped into yttrium orthosilicate (YSO)2. However, to make REI-based quantum architectures fully scalable one has to address the ions at the level of single atoms. Now, writing in Nature Communications and Nature, respectively, Mouktik Raha and colleagues3 and Jonathan M. Kindem and colleagues4 have not only reported the detection of individual REIs, but also implemented a protocol for single shot readout of its spin.
Revealing the spin state of a REI qubit by its fluorescence is a hard task since the number of emitted photons is extremely small, typically on the order of a few tens per second. However, this can be circumvented by placing a REI in a tiny high quality (high-Q) optical resonator and exploiting the so-called Purcell effect — the significant speedup of spontaneous emission into the resonator mode. The workhorses of Raha and colleagues are erbium ions doped into YSO, while those of Kindem and colleagues are ytterbium ions in yttrium orthovanadate (YVO).
Both groups use high-Q photonic crystal resonators to enhance the REI fluorescence. Specifically, Raha and colleagues use erbium ions close to the surface of YSO, which are evanescently coupled to the resonator mode. Even though the ions are not inside the maximum electric field of the mode, the high Q-factor of the resonator (around 60,000) and small volume of its mode lead to Purcell enhancement with a factor of 700. Using cavities carved in YVO, Kindem and colleagues achieve an enhancement by a factor of 100. This means that, in the respective experiments, the ion spontaneously emits photons into the resonator mode 700 and 100 times faster than it does in free space. This significant speedup of emission facilitates single-ion detection.
The second important ingredient of the work by Raha and colleagues is engineering of the optical selection rules in such a way that only spin-conserving optical transitions are enhanced by the resonator. The authors take advantage of the well-defined optical polarization of the resonator mode at the location of the erbium ion. Placing the ion in an external magnetic field leads to a mixing of the spin components of the ground and emitting electronic states of erbium. The degree of mixing can be controlled by the direction of the magnetic field, so that for certain direction of the field the resonator mode experiences a Purcell enhancement only for spin-conserving optical transitions, as shown in Fig. 1. The transitions accompanied by a spin flip are unaffected, meaning that, even if the spin-conserving and spin-flip optical transitions had the same probability before coupling to the resonator, the Purcell enhancement makes the spin-conserving transition 700 times more probable. Thus, before the electron spin flips by taking the wrong (spin-non-conserving) path, the ion is able to emit on average 700 photons while keeping its electron spin state.
Finally, the two spin-conserving optical transitions have different optical wavelengths and can be addressed separately by a narrow-band single-mode laser. If, say, the electron is in the ground state \(\left| \uparrow \right\rangle\) and one shines the laser in resonance with the \(\left| \uparrow \right\rangle - \left| \uparrow \right\rangle\) transition, the erbium ion keeps emitting fluorescence photons until it accidentally jumps into the |↓〉 state. By observing this fluorescence, one can immediately say that the spin is in state \(\left| \uparrow \right\rangle\). However, if there is no fluorescence emitted, one concludes that the spin is in state \(\left| \downarrow \right\rangle\). This simple but elegant strategy allows the observation of quantum jumps of erbium electron spin in real time — with very far reaching implications for quantum computing architectures based on REIs.
While both groups of authors have used similar methods for cavity-enhanced emission, and have measured spin relaxation using the coupled spin–cavity system, Kindem and colleagues went one step beyond — measuring spin dephasing and even exploring the spin dephasing limits in YVO with spin decoupling techniques.
Besides the intriguing physics and engineering achievements behind the observation of spin quantum jumps, the ability to read out the quantum state of the spin is of fundamental importance for quantum information processing. Certain algorithms that are critical for scalability, such as error correction, rely on single-shot readout. While the detection and coherent control of REI has been elusive for a long time, with the invention of efficient resonators for REI-based systems published now, REIs are quickly catching up with the leading contenders in the field. Starting from the first detection of single REI reported eight years ago5, most basic qubit functionalities have now been shown, although some key steps such as spin–photon and entanglement of remote REIs remain out of reach for now. However, owing to the diversity of REI species, the possibility of their tight packing into the crystal and the ultra-long coherence times, the future of REI-based quantum hardware looks bright.
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Kindem, J. M. Nature https://doi.org/10.1038/s41586-020-2160-9 (2020).
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Kolesov, R., Wrachtrup, J. A rare quantum leap. Nat. Phys. 16, 503–504 (2020). https://doi.org/10.1038/s41567-020-0871-3