Gauge-invariant absorption of light from a coherent superposition of states

Absorption and emission of light is studied theoretically for excited atoms in coherent superposition states subjected to isolated attosecond pulses the extreme ultraviolet range. A gauge-invariant formulation transient absorption theory motivated using energy operator from Yang's gauge theory. The interaction, which simultaneously couples both bound continuum states, simulated by solving time-dependent Schr\"odinger equation hydrogen neon atoms. strong dependence on angular momentum relative phase observed. Perturbation used disentangle fundamental processes a rule established interpret complex behavior. It found that nonresonant transitions are source asymmetry phase, while resonant contribute symmetrically superpositions states.