High cooperativity in coupled microwave resonator ferrimagnetic insulator hybrids (1207.6039v2)

Abstract: We report the observation of strong coupling between the exchange-coupled spins in gallium-doped yttrium iron garnet and a superconducting coplanar microwave resonator made from Nb. The measured coupling rate of 450 MHz is proportional to the square-root of the number of exchange-coupled spins and well exceeds the loss rate of 50 MHz of the spin system. This demonstrates that exchange coupled systems are suitable for cavity quantum electrodynamics experiments, while allowing high integration densities due to their extraordinary high spin densities. Our results furthermore show, that experiments with multiple exchange-coupled spin systems interacting via a single resonator are within reach.

• The paper establishes strong coupling between exchange-coupled YIG:Ga spins and an Nb resonator with an effective rate of 450 MHz.
• The paper employs an input-output formalism to extract coupling and loss rates, confirming a high cooperativity of approximately 1350.
• The paper highlights the potential for integrating multiple spin systems, paving the way for advanced CQED and quantum memory applications.

High Cooperativity in Coupled Microwave Resonator Ferrimagnetic Insulator Hybrids

This paper presents a compelling case for the strong coupling observed between exchange-coupled spins in gallium-doped yttrium iron garnet (YIG:Ga) and a superconducting coplanar microwave resonator fabricated from niobium (Nb). The paper, conducted by Huebl et al., reports an effective coupling rate of 450 MHz, which is notably higher than the spin relaxation rate (50 MHz) and resonator decay rate (3 MHz).

The researchers argue that the observed strong coupling is indicative of the suitability of exchange-coupled systems for cavity quantum electrodynamics (CQED) applications, particularly because these systems allow integration densities on the scale similar to the Bohr magneton per atom. A crucial implication of this finding is the feasibility of integrating multiple exchange-coupled spin systems through a single resonator, paving the way for sophisticated communication between magnetic subsystems or the exchange of quantum information.

Theoretical and Experimental Context

Consistent with the theoretical predictions by Soykal and Flatté, the authors emphasize the benefits of ferromagnetic systems. Advantages include high spin density and nearly full polarization below the Curie temperature, a contrast to paramagnetic systems which necessitate thermal polarization. In this paper, the Nb resonator interacted with the exchange-locked spins of YIG:Ga, confirmed through the measurement of a strong coupling regime where the effective coupling strength is proportional to the square root of the number of exchange-coupled spins ($g_{\rm{eff}} = g\sqrt{N}$).

The experimental apparatus was meticulously calibrated to ensure superconductivity within the resonator while maintaining temperatures around 50 mK. The transmission characteristics indicated a pronounced avoided crossing—a haLLMark of strong coupling—thus validating the theoretical model of coupled harmonic oscillators. The authors employed an input-output formalism to rigorously extract the coupling and loss rates, achieving a cooperativity $C = g_{\rm{eff}}^2/\kappa\gamma \approx 1350$.

Numerical Results and Implications

The numerical analysis and subsequent experimental validation reveal that the effective coupling rate reaches 8% of the baseline resonator frequency. Moreover, the performance of YIG:Ga in the strong-coupling regime holds promise for significantly enhancing cooperativity in pure YIG configurations. In practical terms, these findings highlight the potential for exploiting such hybrid systems in quantum memory applications where large coupling rates facilitate the compact integration of multiple magnetic quanta systems.

Future Prospects and Developments

This work opens avenues for further exploration into the macroscale quantum coherence properties of ferromagnetic insulators like YIG. It also suggests a research trajectory aimed at employing multiple magnetically coupled systems for advanced CQED schemes. Future exploration should consider low-temperature damping characteristics of YIG-based systems to fully exploit their coupling potential and coherence longevity.

In conclusion, the results reported by Huebl et al. mark a significant advancement in understanding and utilizing exchange-coupled systems within microwave resonator environments, providing substantial groundwork for subsequent research in the domain of solid-state quantum information processing and storage technologies.