Comment on "Test of constancy of speed of light with rotating cryogenic optical resonators"

A recent experiment by Antonini et. al. [Phys. Rev. A {\bf 71}, 050101R 2005], set new limits on Lorentz violating parameters in the frame-work of the photon sector of the Standard Model Extension (SME), $\tilde{\kappa}_{e-}^{ZZ}$, and the Robertson-Mansouri-Sexl (RMS) framework, $\beta-\delta-1/2$. The experiment had significant systematic effects caused by the rotation of the apparatus which were only partly analysed and taken into account. We show that this is insufficient to put a bound on $\tilde{\kappa}_{e-}^{ZZ}$ and the bound on $\beta-\delta-1/2$ represents a five-fold improvement not a ten-fold improvement as claimed. (For reply see Phys. Rev. A 72, 066102 (2005) DOI: 10.1103/PhysRevA.72.066102)Comment: 2 page

Frequency Conversion in a High Q-factor Sapphire Whispering Gallery Mode Resonator due to Paramagnetic Nonlinearity

Nonlinear frequency conversion is a well known and widely exploited family of effects in optics, often arising from a Kerr nonlinearity in a crystal medium. Here, we report high stability frequency conversion in the microwave regime due to a $\chi^{(3)}$ nonlinearity in sapphire introduced by a dilute concentration of paramagnetic spins. First, we produce a high stability comb from two microwave fields at 12.029 and 12.037 GHz corresponding to two high $Q$-factor Whispering Gallery (WG) modes within the Electron Spin Resonance (ESR) bandwidth of the Fe$^{3+}$ ion. The resulting comb is generated by a cascaded four-wave mixing effect with a 7.7 MHz repetition rate. Then, by suppressing four-wave mixing by increasing the threshold power, third harmonic generation is achieved in a variety of WG modes coupled to various species of paramagnetic ion within the sapphire

High Resolution Flicker-Noise-Free Frequency Measurements of Weak Microwave Signals

Amplification is usually necessary when measuring the frequency instability of microwave signals. In this work, we develop a flicker noise free frequency measurement system based on a common or shared amplifier. First, we show that correlated flicker phase noise can be cancelled in such a system. Then we compare the new system with the conventional by simultaneously measuring the beat frequency from two cryogenic sapphire oscillators with parts in 10^15 fractional frequency instability. We determine for low power, below -80 dBm, the measurements were not limited by correlated noise processes but by thermal noise of the readout amplifier. In this regime, we show that the new readout system performs as expected and at the same level as the standard system but with only half the number of amplifiers. We also show that, using a standard readout system, the next generation of cryogenic sapphire oscillators could be flicker phase noise limited when instability reaches parts in 10^16 or betterComment: Accepted for publication in IEEE Transactions on Microwave Theory & Technique

High Q-factor Sapphire Whispering Gallery Mode Microwave Resonator at Single Photon Energies and milli-Kelvin Temperatures

The microwave properties of a crystalline sapphire dielectric whispering gallery mode resonator have been measured at very low excitation strength (E/hf=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 2e-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 1e-9. This work shows that quantum limited microwave resonators with Q-factors > 1e8 are possible with the implementation of a sapphire whispering gallery mode system