New methods of testing Lorentz violation in electrodynamics

We investigate experiments that are sensitive to the scalar and parity-odd coefficients for Lorentz violation in the photon sector of the standard model extension (SME). We show that of the classic tests of special relativity, Ives-Stilwell (IS) experiments are sensitive to the scalar coefficient, but at only parts in ${10}^5$ for the state-of-the-art experiment. We then propose asymmetric Mach-Zehnder interferometers with different electromagnetic properties in the two arms, including recycling techniques based on travelling wave resonators to improve the sensitivity. With present technology we estimate that the scalar and parity-odd coefficients may be measured with a sensitivity better than parts in ${10}^{11}$ and ${10}^{15}$ respectively.

Figure 1

Principle of the Ives-Stilwell experiment. The Doppler shifted resonant frequencies of a moving atom are measured in the parallel ${\nu }_p$, and antiparallel ${\nu }_a$ directions.

Figure 2

Mach-Zehnder (MZ) interferometer of length $L$, with two arms of permittivity ${ϵ}_{ra}$ and ${ϵ}_{rb}$, and permeability of ${\mu }_{ra}$ and ${\mu }_{rb}$ respectively.

Figure 3

Resonant recycling technique with travelling wave resonators in each arm of the interferometer.

Figure 4

Power-recycling technique where the output power at the bright port (BP) of the interferometer is fed back and added to the input. The dark port (DP) is the phase sensitive output.

Figure 5

Cross section of the transmission medium.

Figure 6

Schematic of a travelling wave resonator with electromagnetic asymmetry on the forward and reverse path of the resonator.

Figure 7

Sensitivity coefficient versus relative permittivity of Eq. (36).

Figure 8

Two possible resonant structures, which exhibit asymmetry around the x axis of a cylinder. The mode of propagation would be a travelling WG mode around the perimeter of the cylinder [44].