Testing Lorentz Invariance Using an Odd-Parity Asymmetric Optical Resonator

We present the first experimental test of Lorentz invariance using the frequency difference between counter-propagating modes in an asymmetric odd-parity optical resonator. This type of test is $\sim10^{4}$ more sensitive to odd-parity and isotropic (scalar) violations of Lorentz invariance than equivalent conventional even-parity experiments due to the asymmetry of the optical resonator. The disadvantages of odd parity resonators have been negated by the use of counter-propagating modes, delivering a high level of immunity to environmental fluctuations. With a non-rotating experiment our result limits the isotropic Lorentz violating parameter $\tilde{\kappa}_{tr}$ to 3.4 $\pm$ 6.2 x $10^{-9}$, the best reported constraint from direct measurements. Using this technique the bounds on odd-parity and scalar violations of Lorentz invariance can be improved by many orders of magnitude.