We theoretically investigate the atomic-orbital-resolved vortex-shaped photoelectron momentum distributions (PMDs) and ionization probabilities by solving the two-dimensional time-dependent Schrödinger equation (2D-TDSE) of neon in a pair of delayed counter-rotating circularly polarized attosecond pulses. We found that the number of spiral arms in vortex patterns is twice the number of absorbed photons when the initial state is the ψm=±1 state, which satisfy a change from c2n+2 to c2n (n is the number of absorbed photons) rotational symmetry of the vortices if the 2p state is replaced by 2p+ or 2p− states. For two- and three-photon ionization, the magnetic quantum number dependence of ionization probabilities is quite weak. Interestingly, single-photon ionization is preferred when the electron and laser field corotate and ionization probabilities of 2p− is much larger than that of 2p+ if the proper time delay and wavelength are used. The relative ratio of ionization probabilities between 2p− and 2p+ is insensitive to laser peak intensity, which can be controlled by changing the wavelength, time delay, relative phase and amplitude ratio of two attosecond pulses.

We comparatively study the effect of orbital symmetry on vortex patterns in photoelectron momentum distributions (PMDs) of perfectly aligned H2 and N2 molecules and their companion atom Ar exposed to a pair of delayed counter-rotating circularly polarized lasers by numerically solving the two-dimensional time-dependent Schrödinger equation. We show that vortex patterns in PMDs strongly depend on the orbital symmetry of atoms and molecules, and numbers of spiral arms in PMDs of N2, H2, and Ar are quite different even though they have nearly identical ionization potentials. We also confirm that vortex structures in PMDs of the highest occupied molecular orbit (HOMO)-2 for N2 are quite different from those of the HOMO but similar to those of Ar. Furthermore, vortex patterns in PMDs of molecules are also sensitive to internuclear distances and alignment angles, which provides more possibilities for controlling the coherent interference of electronic wave packets in comparison with atoms.

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