Linear and Nonlinear Effects of Electron Paramagnetic Resonance in High-Q Cryogenic Sapphire Microwave Resonators Daniel L. Creedon a , Karim Benmessai a , Warwick P. Bowen b , Michael E. Tobar a a ARC Centre of Excellence for Engineered Quantum Systems, University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia; b ARC Centre of Excellence for Engineered Quantum Systems, University of Queensland, St. Lucia QLD 4072, Australia ABSTRACT Cryogenic sapphire resonators operating in Whispering Gallery Modes have very high Q-factors (> 10 9 ) at microwave frequencies . Such a property makes them useful for a host of applications, which are only possible due to the additional inclusion of residual paramagnetic impurities that annul the frequency-temperature dependence of sapphire. More recently, residual Fe 3+ impurities with parts-per-billion concentration within the lattice have been shown to create a three level system corresponding to the spin states of the ion. By pumping at 31.3 GHz, a stable 12.04 GHz maser signal (stability of parts in 10 1 4) has been created without any stabilization circuitry. In addition, we have observed the fundamental thermal noise limit near 4 K by operating such masers in a bimodal configuration. Annealing one resonator in air has led to conversion of Fe 2+ ions in the lattice to Fe 3+ , leading to an orders of magnitude increase in active ion concentration. At the post-annealing Fe 3+ concentration of 150 ppb , we observe nonlinear effects such as a degenerate four-wave mixing due to a χ (3) magnetic nonlinearity as well as stable frequency comb generation. Keywords: Four wave mixing, nonlinearity, Whispering Gallery modes, maser 1. INTRODUCTION Since the development of the first laser, 1 a multitude of nonlinear effects have been observed in optical systems. Optical second- 2 and third-harmonic generation, 3, 4 optical sum-frequency generation, 5 optical parametric os- cillation and amplification, 6, 7 Raman lasing, 8 and two-photon absorption 9 are all well-characterised nonlinear effects which have been instrumental in the development of the past few decades of modern optics. High quality optical cavities allow the effect of the nonlinearity to be greatly enhanced, and have lead to many new appli- cations including the implementations of frequency combs through parametric frequency conversion effects. 10–12 Optical nonlinearities are crucial for switching and modulation in modern communications technology, and are an enabling capability for future implementations of optical computer technologies, including the possibility of a quantum computer based on encoded single photons. 13 Recently, dramatic progress has been made in us- ing microwave systems for quantum information and measurement, with nonlinearities playing a critical role. Josephson junctions in particular, which operate at microwave frequencies, act as a nonlinear inductor which per- mits uneven spacing of energy levels, leading to individual addressability of energy states using an external field. This, and other strongly nonlinear systems are currently of considerable interest for a new generation of quantum measurement experiments including quantum-limited amplification, 14 single quadrature squeezing with tunable nonlinear Josephson metamaterials, 15 readout of superconducting flux qubits, 16 and frequency conversion with quantum-limited efficiency. 17 An addressable quantum memory with coherence times long enough for quantum computing applications could potentially be achieved through the manipulation of electron spins in a crystal lat- tice host, which typically occurs at microwave frequencies, and can have characteristic relaxation times of order seconds. This, along with the potential for large collective couplings, have provoked great interest in electron Further author information: (Send correspondence to M.E.T.) E-mail: michael.tobar@uwa.edu.au, Telephone: +61 8 6488 3982 Invited Paper Laser Resonators, Microresonators, and Beam Control XIV, edited by Alexis V. Kudryashov, Alan H. Paxton, Vladimir S. Ilchenko, Lutz Aschke, Kunihiko Washio, Proc. of SPIE Vol. 8236, 82361R · © 2012 SPIE · CCC code: 0277-786X/12/$18 · doi: 10.1117/12.912115 Proc. of SPIE Vol. 8236 82361R-1 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 12/06/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx