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Ultrasensitive microwave spectroscopy of spin ensembles in solids for hybrid quantum systems

Warrick G. Farr

Published May 1, 2015• 0 citations
OpenAlex

Abstract

Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. In this thesis, a novel spectroscopic technique using electron spin resonance (ESR) is presented. Microwave whispering gallery modes (WGM) in cylindrical dielectric resonators are used to probe paramagnetic impurities at millikelvin temperatures under the influence of an applied dc magnetic field. This technique couples the naturally high quality factor and the relatively high magnetic filling factor of WGMs in crystalline hosts. Precision spectroscopy has been performed on a number of dielectric samples including, sapphire, ruby, quartz, yttrium orthosilicate (YSO) and yttrium aluminium garnet (YAG). Spectroscopic characterisation of sapphire reveals trace ion impurities at parts per billion, which have been used to control strong coupling between the WGM doublets. Moreover, time-reversal symmetry breaking has been observed when a WGM interacts with an ESR, a result of selection rules being created as a consequence of conservation of angular momentum. Following this, interactions between WGM microwave photons and spin resonances are shown in a range of systems. Results achieved include coupling between WGM photons and Cr3+ ions in ruby with normal mode splitting on the order of 600 MHz at 13.9 GHz, the coupling of iron group ion impurities to WGM photons in YSO, which also revealed a strong coupling regime with very low magnetic field, and coupling of Er3+ to WGMs in YAG with evidence of dilute ferromagnetism - the first observation of such an effect outside of iron group doped semiconductors. In addition a novel double-post re-entrant cavity is presented, which is able to focus the rf magnetic field into a small sample, in this case a sub-millimetre sized Yttrium Iron Garnet (YIG) ferrite microsphere that supports magnon resonances. Ultra-high cooperatively of 105 between photon and magnon modes is demonstrated at millikelvin temperatures and microwave frequencies. A coupling strength (normal mode splitting) of 2 GHz at 20 GHz, equivalent to 76 cavity linewidths, is achieved for the bright cavity mode. This constitutes about 10% of the photon energy and shows that ultra-strong coupling is possible in spin systems at microwave frequencies.

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Progress in the emerging field of engineered quantum systems requires the development of devices that can act as quantum memories. In this thesis, a novel spectroscopic technique using electron spin resonance (ESR) is presented. Microwave whispering gallery modes (WGM) in cylindrical dielectric resonators are used to probe paramagnetic impurities at millikelvin temperatures under the influence of an applied dc magnetic field. This technique couples the naturally high quality factor and the relatively high magnetic filling factor of WGMs in crystalline hosts. Precision spectroscopy has been performed on a number of dielectric samples including, sapphire, ruby, quartz, yttrium orthosilicate (YSO) and yttrium aluminium garnet (YAG). Spectroscopic characterisation of sapphire reveals trace ion impurities at parts per billion, which have been used to control strong coupling between the WGM doublets. Moreover, time-reversal symmetry breaking has been observed when a WGM interacts with an ESR, a result of selection rules being created as a consequence of conservation of angular momentum. Following this, interactions between WGM microwave photons and spin resonances are shown in a range of systems. Results achieved include coupling between WGM photons and Cr3+ ions in ruby with normal mode splitting on the order of 600 MHz at 13.9 GHz, the coupling of iron group ion impurities to WGM photons in YSO, which also revealed a strong coupling regime with very low magnetic field, and coupling of Er3+ to WGMs in YAG with evidence of dilute ferromagnetism - the first observation of such an effect outside of iron group doped semiconductors. In addition a novel double-post re-entrant cavity is presented, which is able to focus the rf magnetic field into a small sample, in this case a sub-millimetre sized Yttrium Iron Garnet (YIG) ferrite microsphere that supports magnon resonances. Ultra-high cooperatively of 105 between photon and magnon modes is demonstrated at millikelvin temperatures and microwave frequencies. A coupling strength (normal mode splitting) of 2 GHz at 20 GHz, equivalent to 76 cavity linewidths, is achieved for the bright cavity mode. This constitutes about 10% of the photon energy and shows that ultra-strong coupling is possible in spin systems at microwave frequencies.
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 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+.
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+.
Interaction of Whispering Gallery Modes (WGMs) with dilute spin ensembles in solids is an interesting paradigm of Hybrid Quantum Systems potentially beneficial for Quantum Signal Processing applications. Unexpected ion transitions are measured in single crystal Y2SiO5 using WGM spectroscopy with large Zero Field Splittings at 14.7 GHz, 18.4 GHz, and 25.4 GHz, which also feature considerable anisotropy of the g-tensors as well as two inequivalent lattice sites, indicating spins from Iron Group Ion (IGI) impurities. The comparison of undoped and Rare-Earth doped crystals reveal that the IGIs are introduced during co-doping of Eu3+ or Er3+ with concentration at much lower levels of order 100 ppb. The strong coupling regime between an ensemble of IGI spins and WGM photons have been demonstrated at 18.4 GHz and near zero field. This approach together with useful optical properties of these ions opens avenues for “spins-in-solids” Quantum Electrodynamics.
Multiple-post reentrant 3D lumped cavity modes have been realized to design the concept of a discrete Whispering Gallery and Fabry-Pérot-like Modes for multimode microwave Quantum Electrodynamics experiments. Using the magnon spin-wave resonance of a submillimeter-sized Yttrium-Iron-Garnet sphere at millikelvin temperatures and a four-post cavity, we demonstrate the ultra-strong coupling regime between discrete Whispering Gallery Modes and a magnon resonance with a strength of 1.84 GHz. By increasing the number of posts to eight and arranging them in a D4 symmetry pattern, we expand the mode structure to that of a discrete Fabry-Pérot cavity and modify the Free Spectral Range (FSR). We reach the superstrong coupling regime, where spin-photon coupling strength is larger than FSR, with coupling strength in the 1.1 to 1.5 GHz range.
We report the study of interactions between cavity photons and paramagnetic Cr3+{\mathrm{Cr}}^{3+}Cr3+ spins in a ruby (Cr3+:Al2O3){(\mathrm{Cr}}^{3+}:{\mathrm{Al}}_{2}{\mathrm{O}}_{3})(Cr3+:Al2​O3​) whispering gallery mode (WGM) resonator. Examining the system at microwave frequencies and millikelvin temperatures, spin-photon couplings up to 610 MHz or about 5% of photon energy are observed between the impurity spins and high quality factor (Q>105)(Q>{10}^{5})(Q>105) WGM. Large tunability and spin-spin interaction allows operation in the strong coupling regime. The system exhibits behavior not predicted by the usual Tavis-Cummings model because of interactions within the two-level spin bath, and the existence of numerous photonic modes.