Holographic detection of parity in atomic and molecular orbitals

We introduce a novel and concise methodology to detect the parity of atomic and molecular orbitals based on photoelectron holography, which is more general than the existing schemes. It fully accounts for the Coulomb distortions of electron trajectories, does not require sculpted fields to retrieve phase information and, in principle, is applicable to a broad range of electron momenta. By comparatively measuring the differential photoelectron spectra from strong-field ionization of N$_{2}$ molecules and their companion atoms of Ar, some photoelectron holography patterns are found to be dephased for both targets. This is well reproduced by the full-dimensional time-dependent Schr\"{o}dinger equation and the Coulomb quantum-orbit strong-field approximation (CQSFA) simulation. Using the CQSFA, we trace back our observations to different parities of the 3$p$ orbital of Ar and the highest-occupied molecular orbital of N$_{2}$ via interfering Coulomb-distorted quantum orbits carrying different initial phases. This method could in principle be used to extract bound-state phases from any holographic structure, with a wide range of potential applications in recollision physics and spectroscopy.