Anisotropic rare-earth spin ensemble strongly coupled to a superconducting resonator

Abstract: Interfacing photonic and solid-state qubits within a hybrid quantum architecture offers a promising route towards large scale distributed quantum computing. Ideal candidates for coherent qubit interconversion are optically active spins magnetically coupled to a superconducting resonator. We report on a cavity QED experiment with magnetically anisotropic Er3+:Y2SiO5 crystals and demonstrate strong coupling of rare-earth spins to a lumped element resonator. In addition, the electron spin resonance and relaxation dynamics of the erbium spins are detected via direct microwave absorption, without aid of a cavity.

Anisotropic Rare-earth Spin Ensemble Strongly Coupled to a Superconducting Resonator

The paper by Probst et al. presents a significant investigation into the interaction between anisotropic rare-earth spin ensembles, specifically Er$^{3+}$:Y$_2$SiO$_5$ crystals, and superconducting resonators. The research provides valuable insights into optically active spins within hybrid quantum architectures, a crucial aspect for achieving large-scale distributed quantum computing. The primary focus of the study is to demonstrate and analyze the strong coupling of rare-earth spins to lumped element resonators (LERs), a pivotal step towards coherent qubit interconversion between solid-state and photonic systems.

Main Contributions

The authors successfully demonstrate the strong collective coupling between the Erbium(Er$^{3+}$) ions within Y$_2$SiO$_5$ crystals and superconducting LERs. They achieve this by strategically using the magnetic anisotropy of the rare-earth ions, which exhibit significant g-tensor variation depending on the orientation of their electronic orbitals in the crystal field. This anisotropy provides different coupling strengths and relaxation dynamics contingent on the alignment of the crystal axis with respect to the DC and AC magnetic fields.

Using two different Er:YSO crystal orientations, the experimental setup integrates these crystals onto a superconducting chip equipped with multiple LERs coupled to a transmission line. Each resonator operates across a microwave frequency band between 4.5 and 5.2 GHz, with demonstrably high-quality factors. The experiment meticulously maps and analyzes the electron spin resonance (ESR) and relaxation dynamics without the need for cavity enhancement, which marks a significant methodological advancement.

Key Results and Observations

1. Strong Coupling Regime: The research achieves a coupling strength up to $2v/2\pi = 68 \, \text{MHz}$ and spin linewidth $\Gamma_2^{\star}/\pi = 24 \, \text{MHz}$, yielding a cooperativity parameter $C\approx 36$, indicative of strong coupling conditions.
2. Magnetic Anisotropy Utilization: The study leverages the strong magnetic anisotropy of the Erbium ions, enabling maximal coupling when the interplay of DC and AC fields is optimized.
3. Improved Spin Linewidth: The experiments report a narrowly measured inhomogeneous linewidth of 12 MHz for the high-field transition, offering improved coherence characteristics beneficial for hybrid quantum systems.
4. Absence of Cavity Effects: The strong ESR signal observed without cavity enhancement challenges current methodologies, reinforcing the potential of rare-earth doped crystals for direct microwave absorption applications.
5. Spin Relaxation Dynamics: Detailed measurements of electron spin relaxation dynamics reveal a relaxation time $T_1 = 4.3 \, \text{sec}$, offering insights into decoherence processes within the hybrid system's operational temperature ranges.

Implications and Future Directions

The implications of this experiment are robust, highlighting the viability of rare-earth ion doped crystals as quantum memory elements within broader quantum networks. By thoroughly examining the anisotropic g-factors and corresponding coupling efficiencies, the study opens potential pathways for designing more efficient quantum media converters. This could significantly bridge the gap between microwave and optical communication within disparate quantum systems, enhancing scalability.

Future research may explore further optimizations in spin ensemble handling, the integration of different host materials, and the potential reduction of inhomogeneities in the spin transition profiles. Additionally, advancements in quantum transduction techniques may benefit from these foundational studies, accelerating developments in quantum repeater and quantum network node technologies.

In summary, Probst et al.'s research offers a detailed analysis of rare-earth spin ensemble interactions with superconducting resonators, paving the way for enhanced hybrid quantum system implementations. The orchestration of spin ensembles using magnetic anisotropy principles presents a promising approach for achieving coherent qubit interconversion, further advancing the frontier of distributed quantum computing architectures.