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arXiv:1311.4961 · Physical Review B

Spin bath maser in a cryogenically cooled sapphire whispering gallery mode resonator

Jeremy Bourhill, Karim Benmessai, Maxim Goryachev, Daniel Lloyd Creedon, Warrick G. Farr, Michael Edmund Tobar

Published Dec 3, 2013• 11 citations
arXivHTMLPDF

Abstract

We report the observation of a mechanism of maser generation in an ensemble of intercoupled, inhomogeneously broadened two-level systems, enhanced by high quality factor electromagnetic cavity modes. In this form of population inversion, an inseparable quantum system leads to cavity-enhanced stimulated emission arising from interactions within an ensemble of two-level systems, as opposed to a traditional ensemble of noninteracting identical three-level systems. The effect is observed in a cryogenically cooled whispering gallery mode sapphire resonator containing dilute Fe${}^{3+}$ impurity ions. These ions exhibit strong spin-lattice interaction, leading to both electron spin resonance broadening and phonon mediated spin-spin coupling. The maser effect is due to a $|1/2\ensuremath{\rangle}\ensuremath{\rightarrow}|3/2\ensuremath{\rangle}$ energy transition in an electron spin angular momentum observed at zero external magnetic field. Both continuous and oscillating regimes are observed with corresponding thresholds both in detuning frequency and incident power.

DOI
10.1103/physrevb.88.235104

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Dec 7, 2013•0 citations
We report the observation of a mechanism of maser generation in an ensemble of intercoupled, inhomogeneously broadened two-level systems, enhanced by high quality factor electromagnetic cavity modes. In this form of population inversion, an inseparable quantum system leads to cavity-enhanced stimulated emission arising from interactions within an ensemble of two-level systems, as opposed to a traditional ensemble of noninteracting identical three-level systems. The effect is observed in a cryogenically cooled whispering gallery mode sapphire resonator containing dilute Fe3+{}^{3+}3+ impurity ions. These ions exhibit strong spin-lattice interaction, leading to both electron spin resonance broadening and phonon mediated spin-spin coupling. The maser effect is due to a ∣1/2\ensuremath⟩\ensuremath→∣3/2\ensuremath⟩|1/2\ensuremath{\rangle}\ensuremath{\rightarrow}|3/2\ensuremath{\rangle}∣1/2\ensuremath⟩\ensuremath→∣3/2\ensuremath⟩ energy transition in an electron spin angular momentum observed at zero external magnetic field. Both continuous and oscillating regimes are observed with corresponding thresholds both in detuning frequency and incident power.
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.
Employing a sapphire whispering gallery mode resonator, we demonstrate features of the spin-photon interaction in cavities with broken time-reflection symmetry. The broken symmetry leads to a lifting of the degeneracy between left-handed and right-handed polarized cavity photons, which results in an observable gyrotropic effect. In the high-QQQ cavity limit, such a situation requires a modification of the Tavis-Cummings Hamiltonian to take into account conservation of spin angular momentum and the corresponding selection rules. As a result, the system is represented by a system of two linearly coupled bosonic modes, with each one coupled to its own subensemble of two-level systems with different energy splittings. In the experimental example, these subensembles originate from Fe3+{\text{Fe}}^{3+}Fe3+ impurity ions effectively seen as a two-level system at the interaction frequency. The temperature dependence of the population of each subensemble (in terms of effective susceptibility of the medium) is determined experimentally in accordance with the theoretical predictions revealing various paramagnetic impurity types in the solid. The regimes of backscatterer and spin ensemble domination are discussed and compared.
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.
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+, 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+.