A scalable technique for designing shortcuts to adiabaticity with Lie algebras

Many experiments in atomic and molecular physics rely on slow adiabatic processes. It is desirable to find dynamics which produce the same populations, but more rapidly. Invariant based shortcuts to adiabaticity (STA) have proven a popular method for finding such processes. In this talk, we present a general method for deriving STA protocols for Lie algebras with few dimensions. The approach is similar to that presented by Torrontegui et al. [1], which multiplies the pseudo-inverse of a matrix that depends on the invariant to the invariant to solve for the Hamiltonian. By contrast, our method restricts invariants to solutions of a linear differential equation in time. This makes our technique easy to scale up, as it relies only on tensor network contractions and row reduction. However, this comes at the cost of guaranteed solutions. As an example, we apply this technique to a Bose-Hubbard model with tunable interaction and hopping energies.

[1] E. Torrontegui, S. Martinez-Garaot, and J.G. Muga, Phys. Rev. A 89, 043408 (2014).