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arXiv:1201.3421 · Physical Review Letters

Four-Wave Mixing from Fe3+ Spins in Sapphire

Daniel Lloyd Creedon, Karim Benmessai, Warwick P. Bowen, Michael Edmund Tobar

Published Feb 29, 2012• 22 citations
arXivHTMLPDF

Abstract

Fe(3+) ions in sapphire exhibit an electron spin resonance which interacts strongly with high-Q whispering gallery modes at microwave frequencies. We report the first observation of a third-order paramagnetic nonlinear susceptibility in such a resonator at cryogenic temperatures and the first demonstration of four-wave mixing using this parametric nonlinearity. This observation of an all-microwave nonlinearity is an enabling step towards a host of quantum measurement and control applications which utilize spins in solids.

DOI
10.1103/physrevlett.108.093902

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Fe(3+) ions in sapphire exhibit an electron spin resonance which interacts strongly with high-Q whispering gallery modes at microwave frequencies. We report the first observation of a third-order paramagnetic nonlinear susceptibility in such a resonator at cryogenic temperatures and the first demonstration of four-wave mixing using this parametric nonlinearity. This observation of an all-microwave nonlinearity is an enabling step towards a host of quantum measurement and control applications which utilize spins in solids.
Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. The realisation of such devices by doping solid state cavities with paramagnetic ions imposes a trade-off between ion concentration and cavity coherence time. Here, we investigate an alternative approach involving interactions between photons and naturally occurring impurity ions in ultra-pure crystalline microwave cavities exhibiting exceptionally high quality factors. We implement a hybrid Whispering Gallery/Electron Spin Resonance method to perform rigorous spectroscopy of an undoped single-crystal sapphire resonator over the frequency range 8--19 GHz, and at external applied DC magnetic fields up to 0.9 T. Measurements of a high purity sapphire cooled close to 100 mK reveal the presence of Fe3+^{3+}3+, Cr3+^{3+}3+, and V2+^{2+}2+ impurities. A host of electron transitions are measured and identified, including the two-photon classically forbidden quadrupole transition (Δms=2Δm_s =2Δms​=2) for Fe3+^{3+}3+, as well as hyperfine transitions of V2+^{2+}2+.
Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. The realization of such devices by doping solid-state cavities with paramagnetic ions imposes a tradeoff between ion concentration and cavity coherence time. Here, we investigate an alternative approach involving interactions between photons and naturally occurring impurity ions in ultrapure crystalline microwave cavities exhibiting exceptionally high quality factors. We implement a hybrid whispering gallery/electron spin resonance method to perform rigorous spectroscopy of an undoped single-crystal sapphire resonator over the frequency range 8--19 GHz, and at external applied DC magnetic fields up to 0.9 T. Measurements of high-purity sapphire cooled close to 100 mK reveal the presence of Fe3+{}^{3+}3+, Cr3+{}^{3+}3+, and V2+{}^{2+}2+ impurities. A host of electron transitions are measured and identified, including the two-photon classically forbidden quadrupole transition ($\ensuremath{\Delta}{m}_{s}=2$) for Fe3+{}^{3+}3+, as well as hyperfine transitions of V2+{}^{2+}2+.
Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. The realisation of such devices by doping solid state cavities with paramagnetic ions imposes a trade-off between ion concentration and cavity coherence time. Here, we investigate an alternative approach involving interactions between photons and naturally occurring impurity ions in ultra-pure crystalline microwave cavities exhibiting exceptionally high quality factors. We implement a hybrid Whispering Gallery/Electron Spin Resonance method to perform rigorous spectroscopy of an undoped single-crystal sapphire resonator over the frequency range 8{19 GHz, and at external applied DC magnetic fields up to 0.9 T. Measurements of a high purity sapphire cooled close to 100 mK reveal the presence of Fe3+, Cr3+, and V2+ impurities. A host of electron transitions are measured and identified, including the two-photon classically forbidden quadrupole transition (Δms = 2) for Fe3+, as well as hyperfine transitions of V2+.
We present experimental observations of bimodal solitons in a solid state three-level maser cooled to millikelvin temperatures. The maser is built on a highly dilute Fe3+{\text{Fe}}^{3+}Fe3+ spin ensemble hosted by a high-purity Al2O3{\text{Al}}_{2}{\text{O}}_{3}Al2​O3​ crystal constituting a high-quality factor whispering-gallery-mode resonator. The maser is pumped through one of these modes, near 31 GHz, generating two signals near 12.04 GHz from two distinct modes, 8 MHz apart. The system demonstrates three regimes, namely, a continuous-wave regime, a dense soliton regime, and a sparse soliton regime. These results open other avenues for studying nonlinear wave phenomena using microwave systems as well as different applications of solitons in this part of the electromagnetic spectrum.
The microwave properties of a crystalline sapphire dielectric whispering gallery mode resonator have been measured at very low excitation strength (E/ℏω≈1) and low temperatures (T≈30 mK). The measurements were sensitive enough to observe saturation due to a highly detuned electron spin resonance, which limited the loss tangent of the material to about 2×10−8 measured at 13.868 and 13.259 GHz. Small power dependent frequency shifts were also measured which correspond to an added magnetic susceptibility of order 10−9. This work shows that quantum limited microwave resonators with Q-factors >108 are possible with the implementation of a sapphire whispering gallery mode system.
Nonlinear microwave resonators are a versatile tool in quantum information processing, enabling parametric amplification, continuous variable quantum computing, and engineered mode interactions. Many of these applications especially benefit from cubic nonlinearities enabling three-wave mixing; at the same time, they are limited by quartic nonlinearities giving rise to undesired Kerr effects. A recurrent challenge is therefore to engineer resonators with a finite cubic nonlinearity while suppressing quartic terms. Here, we investigate a superconducting resonator hosting two weak links fabricated from an aluminum-capped indium arsenide nanowire. We characterize the Kerr nonlinearity as a function of magnetic flux and gate bias, showing that it can be tuned to zero with either control parameter. Furthermore, we experimentally demonstrate three-wave mixing in a semiconductor-superconductor hybrid device, establishing nonzero cubic nonlinearity. An effective model based on Andreev bound states qualitatively captures the observed trends. Our results validate semiconductor-superconductor hybrid devices as a promising platform for tunable nonlinear superconducting circuits, with applications in parametric amplification, quantum control of bosonic modes, and engineering interactions between microwave modes.