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The European Physical Journal Applied Physics

Analysis of the whispering gallery mode sapphire Fe3+maser under magnetic field

M. Mrad, P.Y. Bourgeois, Michael Edmund Tobar, Y. Kersalé, V. Giordano

Published Jan 2, 2012• 5 citations
Publisher

Abstract

This article describes the influence of the magnetic field on a small amount of residual Fe3+ ion impurities contained in a sapphire resonator excited on a whispering gallery mode and cooled down to 4 K. The energy levels and transition probabilities between pairs of levels of the system are calculated in order to determine the effect of the magnetic field on the maser output power and also on the pump power threshold.

DOI
10.1051/epjap/2012110366

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arXiv:1201.3421•Physical Review Letters•Feb 29, 2012•22 citations
This article describes the influence of the magnetic field on a small amount of residual Fe3+ ion impurities contained in a sapphire resonator excited on a whispering gallery mode and cooled down to 4 K. The energy levels and transition probabilities between pairs of levels of the system are calculated in order to determine the effect of the magnetic field on the maser output power and also on the pump power threshold.
The molecular structure of a 3d 5 configuration ion in a trigonal ligand field is theoretically established on the basis of the 252\times252 complete energy matrice. The optical absorption and the electron paramagnetic resonance spectra of the Fe3+ ion in the sapphire crystal (α-Al2 O3) have been studied by diagonalizing the complete energy matrice. The calculated results are in very good agreement with previous experimental observations. The strength of the transition probabilities between pairs of the energy levels have been calculated to determine the possibility to achieve a population inversion in the ground state by applying optical pumping to the crystal. Preliminary results based on the computed transition parameters and on the maser rate equations model show that a 31 GHz maser signal can be effectively generated depending on the cryogenic resonator design.
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 $|1/2\ensuremath{\rangle}\ensuremath{\rightarrow}|3/2\ensuremath{\rangle}$ 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.
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.
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.
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.