Attosecond all-optical control and visualization of quantum interference between degenerate magnetic states by circularly polarized pulses

Controlling coherence and interference of quantum states is one of the central goals in quantum science. Different from energetically discrete quantum states, however, it remains a demanding task to visualize coherent properties of degenerate states (e.g., magnetic sublevels). It becomes further inaccessible in the absence of an external perturbation (e.g., Zeeman effect). Here, we present a theoretical analysis of all-optical control of degenerate magnetic states in the molecular hydrogen ion, $ {\rm H}_2^ + $H2+, by using two time-delayed co- and counterrotating circularly polarized attosecond extreme-ultraviolet (XUV) pulses. We perform accurate simulations to examine this model by solving the three-dimensional time-dependent Schrodinger equation. A counterintuitive phenomenon of quantum interference between degenerate magnetic sublevels appears in the time-dependent electronic probability density, which is observable by using x-ray-induced transient angular and energy-resolved photoelectron spectra. This work provides an insight into quantum interference of electron dynamics inside molecules at the quantum degeneracy level.