Nonlinear Stimulated Raman Exact Passage by Resonance-Locked Inverse Engineering.

We derive an exact and robust stimulated Raman process for nonlinear quantum systems driven by pulsed external fields. The external fields are designed with closed-form expressions from the inverse engineering of a given efficient and stable dynamics. This technique allows one to induce a controlled population inversion which surpasses the usual nonlinear stimulated Raman adiabatic passage efficiency.

A quadratic transformation for a special confluent Heun function.

We report a functional identity involving a quadratic transformation of the argument for the confluent Heun function. This identity is the first of its kind to be discovered for the confluent Heun function, and it has the potential to be useful in a variety of applications.

Exact solution of the 1D Dirac equation for a pseudoscalar interaction potential with the inverse-square-root variation law.

We present the exact solution of the one-dimensional stationary Dirac equation for the pseudoscalar interaction potential, which consists of a constant and a term that varies in accordance with the inverse-square-root law. The general solution of the problem is written in terms of irreducible linear combinations of two Kummer confluent hypergeometric functions and two Hermite functions with non-integer indices. Depending on the value of the indicated constant, the effective potential for the Schrödinger-type equation to which the problem is reduced can form a barrier or well. This well can support an infinite number of bound states. We derive the exact equation for the energy spectrum and construct a rather accurate approximation for the energies of bound states. The Maslov index involved turns out to be non-trivial; it depends on the parameters of the potential.