Unraveling quantum pathways interference in two-color coherent control of photoemission with bias voltages

Abstract

Coherent control steers a quantum system from an initial state to a target state by controlling quantum interference phenomena via an external field, which is central to vast applications ranging from quantum information processing to attosecond physics. Here, we analyze the quantum pathways interference in two-color coherent control of photoemission using exact analytical solutions of the time-dependent Schr\"odinger equation. The theory includes all possible quantum pathways and their interference terms. Constructive (or destructive) interferences among the pathways leads to the maximum (or minimum) emission with varying phase delay of the two-color lasers. It is found that increasing the intensity ratio of the second harmonic $(2\ensuremath{\omega})$ to fundamental $(\ensuremath{\omega})$ lasers results in less contribution from the $\ensuremath{\omega}$ pathway (absorption of $\ensuremath{\omega}$ photons only) and more contribution from multicolor pathway (simultaneous absorption of both $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ photons) and $2\ensuremath{\omega}$ pathway (absorption of $2\ensuremath{\omega}$ photons only), and therefore stronger pathways interference and increased visibility larger than 95%. Increasing bias voltages shifts the dominant emission to processes with lower-order photon absorption, which sequentially decreases the interference between the $\ensuremath{\omega}$ and the $2\ensuremath{\omega}$ pathways, and between single-color and multicolor pathways, leading to two peaks in the visibility.