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Sapphire whispering gallery mode resonators at millikelvin temperature

Daniel Lloyd Creedon, Yarema Reshitnyk, Jean-Michel Le Floch, Warrick G. Farr, John M. Martinis, T. Duty, Michael Edmund Tobar

Published Aug 1, 2011• 0 citations
Publisher

Abstract

Single crystal sapphire exhibits extremely high electrical and mechanical Q-factors (~109at 4K), which are important characteristics for electromechanical experiments at the quantum limit. We report the first cool down of a bulk sapphire sample below super fluid liquid helium temperature (1.6K) to as low as 25mK. The electromagnetic properties were characterized at microwave frequencies over a broad range of excitation powers. At high powers we report the observation of thermal bistability in millikelvin sapphire due to the material properties such as the T3dependence on thermal conductivity and the ultra-low dielectric loss tangent of the material. We identify "magic temperatures" between 80 to 2100 mK, the lowest ever measured, at which the onset of bistability is suppressed. At very low excitation strength (E/ ω~1) measurements were sensitive enough to measure saturation effects due to a highly detuned electron spin resonance, which limited the loss tangent of the material to about 2>;-8at 13.868 and 13.259 GHz. Small power dependent frequency shifts were also measured, which corresponds to an added magnetic susceptibility of order 10-9. This work shows that quantum limited microwave resonators with Q-factors >;108are possible by implementing sapphire whispering gallery modes. These phenomena at low temperatures make sapphire suitable for a host of quantum metrology applications.

DOI
10.1109/iqec-cleo.2011.6193643

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Single crystal sapphire exhibits extremely high electrical and mechanical Q-factors (109at 4K), which are important characteristics for electromechanical experiments at the quantum limit. We report the first cool down of a bulk sapphire sample below super fluid liquid helium temperature (1.6K) to as low as 25mK. The electromagnetic properties were characterized at microwave frequencies over a broad range of excitation powers. At high powers we report the observation of thermal bistability in millikelvin sapphire due to the material properties such as the T3dependence on thermal conductivity and the ultra-low dielectric loss tangent of the material. We identify "magic temperatures" between 80 to 2100 mK, the lowest ever measured, at which the onset of bistability is suppressed. At very low excitation strength (E/ ω1) measurements were sensitive enough to measure saturation effects due to a highly detuned electron spin resonance, which limited the loss tangent of the material to about 2>;-8at 13.868 and 13.259 GHz. Small power dependent frequency shifts were also measured, which corresponds to an added magnetic susceptibility of order 10-9. This work shows that quantum limited microwave resonators with Q-factors >;108are possible by implementing sapphire whispering gallery modes. These phenomena at low temperatures make sapphire suitable for a host of quantum metrology applications.
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.
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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+.
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.
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.
Low-loss, high frequency acoustic resonators cooled to millikelvin temperatures are a topic of great interest for application to hybrid quantum systems. When cooled to 20 mK, we show that resonant acoustic phonon modes in a bulk acoustic wave quartz resonator demonstrate exceptionally low loss (with Q-factors of order billions) at frequencies of 15.6 and 65.4 MHz, with a maximum f · Q product of 7.8 × 1016 Hz. Given this result, we show that the Q-factor in such devices near the quantum ground state can be four orders of magnitude better than previously attained. Such resonators possess the low losses crucial for electromagnetic cooling to the phonon ground state, and the possibility of long coherence and interaction times of a few seconds, allowing multiple quantum gate operations.