We present the operating principle and the first observing run of a novel kind of direct detector for axions and axionlike particles in the galactic halo. Sensitive to the polarisation rotation of linearly polarised laser light induced by an axion field, our experiment is the first detector of its kind collecting scientific data. We discuss our peak sensitivity of 1.51×10^{-10}  GeV^{-1} (95% confidence level) to the axion-photon coupling strength in the axion mass range of 1.97-2.01 neV which is, for instance, motivated by supersymmetric grand-unified theories. We also report on effects that arise in our high-finesse in-vacuum cavity at an unprecedented optical continuous-wave intensity of 4.7  MW/cm^{2}. Our detector already belongs to the most sensitive direct searches within its measurement band, and our results pave the way towards surpassing the current sensitivity limits even of astrophysical observations in the mass range from 10^{-8} down to 10^{-16}  eV via quantum-enhanced laser interferometry, especially with the potential of scaling our detector up to kilometer length.