Tunneling driven by quantum light described via field Bohmian trajectories

Recent realization of an intense quantum light, namely bright squeezed vacuum, opened a new perspective on quantum light-matter interaction. Several theoretical works have appeared based on coherent state expansions of quantum state of light to investigate non-classical driving of high-harmonic generation in atomic gases and solids, or free-electron dynamics, but their predictions surprisingly coincide with what one could expect from essentially classical interpretations of the light statistics. A deeper theoretical insight into the underlying physics is necessary for understanding of observed experimental findings and predicting emerging effects relying on this new configuration. Here we present a theoretical framework to describe tunneling driven by quantum light, where the properties of such light are captured by a statistical ensemble of classical fields via a hydrodynamic, also referred to as Bohmian, formulation. Generalizing the quasiclassical theory of non-adiabatic tunneling driven by classical light, a single tunneling event is described by a bundle of tunneling solutions, each driven by a classical field corresponding to one realization in the ensemble. Quantum statistics of light are thus imprinted on the measured current. Fully quantum description of light via the Bohmian trajectories of its field provides a perfect fit to the description of the electron (under-) above-barrier dynamics in terms of (complex quasiclassical) real classical trajectories, resulting in a consistent and elegant theoretical approach. To illustrate this, we consider BSV-induced electron transport from the tip to the surface in the tunneling microscope configuration demonstrating the transition from the multiphoton to the direct tunneling regime.