Poynting vector controversy in axion modified electrodynamics

Abstract

The most sensitive haloscopes that search for axion dark matter through the two photon electromagnetic anomaly, convert axions into photons through the mixing of axions with a large background DC magnetic field. In this work we apply Poynting theorem to the resulting axion modified electrodynamics and identify two possible Poynting vectors, one which is similar to the Abraham Poynting vector in electrodynamics and the other to the Minkowski Poynting vector. Inherently the conversion of axions to photons is a non-conservative process with respect to the created oscillating photonic degree of freedom. We show that Minkowski Poynting theorem picks up the added non-conservative terms while the Abraham does not. The non-conservative terms may be categorised more generally as "curl forces", which in classical physics are non-conservative and non-dissipative forces localised in space, not describable by a scalar potential and exist outside the global conservative physical equations of motion. To understand the source of energy conversion and power flow in the detection systems, we apply the two different Poynting theorems to both the resonant cavity haloscope and the broadband low-mass axion haloscope. Our calculations show that both Poynting theorems give the same sensitivity for a resonant cavity axion haloscope, but predict markedly different sensitivity for the low-mass broadband capacitive haloscope. Hence we ask the question, can understanding which one is the correct one for axion dark matter detection, be considered under the framework of the Abraham-Minkowski controversy? In reality, this should be confirmed by experiment when the axion is detected. However, many electrodynamic experiments have ruled in favour of the Minkowski Poynting vector when considering the canonical momentum in dielectric media. In light of this, we show that the axion modified Minkowski Poynting vector should indeed be taken seriously for sensitivity calculation for low-mass axion haloscopes in the quasi static limit, and predict orders of magnitude better sensitivity than the Abraham Poynting vector equivalent.