Poynting vector controversy in axion modified electrodynamics

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 direct current (DC) magnetic field. In this work we apply the 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 nonconservative process with respect to the created oscillating photonic degree of freedom. We show that the Minkowski Poynting theorem picks up the added nonconservative terms while the Abraham does not. The nonconservative terms may be categorized more generally as “curl forces,” which in classical physics are nonconservative and nondissipative forces localized 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 relevant 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 favor 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 quasistatic limit, and predict orders of magnitude better sensitivity than the Abraham Poynting vector equivalent.

Figure 1

Schematic of axion conversion in an ADMX style haloscope. Such haloscopes are based on radio frequency cavity resonators, where an external DC magnetic field, ${\overrightarrow{B}}_0$, has a nonzero dot product with the nondissipative electric field of the radio frequency mode in the cavity, $\mathrm{Re}({\mathbf{E}}_1)$. For a cylindrical cavity the sensitive modes are from the $T{M}_{0,n,0}$ mode family, where $n$ is the radial mode number. The axial and azimuthal mode numbers must be zero. Finite losses mean part of the electric field, $\mathrm{Im}({\mathbf{E}}_1)$, is in phase with the magnetic field, ${\mathbf{B}}_1$, characterized by the loss angle $\delta$, which for a high-$Q$ system is very small and related by $\tan \delta \sim \frac{1}{Q_1}$.

Figure 2

Schematic of axion conversion in a capacitive haloscope.

Figure 3

Left, equivalent parallel $LCR$ circuit representation of an axion coupling to a resonant cavity haloscope. Right, the equivalent series $LCR$ circuit representation.