A Trajectory Description of Quantum Processes. I. Fundamentals

Ángel S. Sanz, Salvador Miret-Artés

Ángel S. Sanz, Salvador Miret-Artés

Ángel S. Sanz, Salvador Miret-Artés

Eric R. Bittner, Donald Jack Kouri, Sean Derrickson +1 more

The invention of lasers in the early sixties triggered the development of the rich field of nonlinear optics. Similarly, the development of lasers with ultrahigh intensities, that is, when the light electric field is larger than the attraction between electrons and nuclei, has boosted extreme nonlinear optics to a relevant and promising discipline in physics. Besides its technological potentialities, strong field physics is also challenging at a fundamental level, leading to the reconsideration of the basic processes of light-matter interactions. Also, the complexity of the exact solutions of the nonperturbative equations has encouraged the development of simple approaches based in semiclassical concepts that offer invaluable insight into the basic processes involved. In this sense, Bohmian trajectories offer an interesting extension of the semiclassical treatment, since their description is purely quantum and , yet, they retain the intuitiveness of a classical description. In this chapter we study the interaction of a hydrogen atom with short and intense laser pulses. By first using a simplified one-dimensional model, we show how Bohmian trajectories can be used in the calculation of the above-threshold ionization (ATI) and harmonic generation spectra. We also present a full three-dimensional (3D) model to study the interaction of an atom with beams bearing orbital angular momentum (OAM) and use the trajectories to gain physical insight into the absorption of angular momentum.

Hai-Woong Lee

Fattah Sakuldee, Simon Milz, Felix A. Pollock +1 more

Abstract We develop a notion of stochastic quantum trajectories. First, we construct a basis set of trajectories, called elementary trajectories , and go on to show that any quantum dynamical process, including those that are non-Markovian, can be expressed as a linear combination of this set. We then show that the set of processes divide into two natural classes: those that can be expressed as a convex mixture of elementary trajectories and those that cannot be. The former are shown to be entanglement breaking processes (in each step), while the latter are dubbed coherent processes . This division of processes is analogous to separable and entangled states. In the second half of the paper, we show, with an information theoretic game, that when a process is non-Markovian, coherent trajectories allow for decoupling from the environment while preserving arbitrary quantum information encoded into the system. We give explicit expressions for the temporal correlations (quantifying non-Markovianity) and show that, in general, there are more quantum correlations than classical ones. This shows that non-Markovian quantum processes are indeed fundamentally different from their classical counterparts. Furthermore, we demonstrate how coherent trajectories (with the aid of coherent control) could turn non-Markovianity into a resource. In the final section of the paper we explore this phenomenon in a geometric picture with a convenient set of basis trajectories.