First Measurement of Neutron Birefringence in Polarized ¹²⁹Xe and ¹³¹Xe Nuclei

We present the first measurements of polarized neutron birefringence in transmission through nuclear-polarized $^{129}$Xe and $^{131}$Xe gas and determine the neutron incoherent scattering lengths $b_i(^{129}Xe)=0.186\pm(0.021)_{stat.}\pm(0.004)_{syst.}\space\text{ fm}$ and $b_i(^{131}Xe)=2.09\pm(0.29)_{stat.}\pm(0.12)_{syst.}\space\text{ fm}$ for the first time. These results determine the essential parameter needed for interpretation of spin-dependent neutron-scattering studies on polarized xenon ensembles, with possible future applications ranging from tests of time-reversal violation to mode-entangled neutron scattering experiments on nuclear-polarized systems.