Counterdiabatic formalism of shortcuts to adiabaticity

Abstract

A pedagogical introduction to counterdiabatic formalism of shortcuts to adiabaticity is given so that readers can access some of the more specialized articles in the rest of this theme issue without any barriers. A guide to references is given so that this article also serves as a mini-review. This article is part of the theme issue ‘Shortcuts to adiabaticity: theoretical, experimental and interdisciplinary perspectives’.

Shortcuts to adiabaticity: theoretical framework, relations between different methods, and versatile approximations

“…where {a tri k (t)} k=1,2,...,Ktr are time-dependent coefficients, which are scheduled by using the variational principle, equation (57), and K tr is an integer for truncation [34]. It can be the exact counterdiabatic Hamiltonian, but construction of the exact counterdiabatic Hamiltonian generally requires exponentially large K tr .…”

“…Note that the algebraic approach is equivalent to the variational approach when we adopt the same basis operators [65], i.e. when we make the same ansatz, equation ( 66), but we can directly obtain the set of linear equations (51), which is the result of the variational operation, equation (57). The algebraic approach can also give the exact counterdiabatic Hamiltonian when the set of the basis operators in the trial counterdiabatic Hamiltonian is identical to that in the exact counterdiabatic Hamiltonian.…”

“…We can also find a review focusing on fast-forward scaling [56]. Pedagogical introductions to counterdiabatic driving [57] and to invariant-based inverse engineering [58] are also available. However, the theory of shortcuts to adiabaticity is a rapidly growing research area.…”

Dynamical invariant formalism of shortcuts to adiabaticity

“…If we can find a pair of operators I(t) and H(t) satisfying equation (2.1), we can use it to construct a counterdiabatic driving. The counterdiabatic driving is formulated by introducing an additional counterdiabatic term H 1 (t) for a given original Hamiltonian H 0 (t) [5][6][7][8]. The total Hamiltonian is given by…”

“…We introduce an additional term to the Hamiltonian to prevent non-adiabatic transitions. The method is reviewed in an article of this issue [8].…”