Fast and robust population transfer in two-level quantum systems with dephasing noise and/or systematic frequency errors

Abstract

We design, by invariant-based inverse engineering, driving fields that invert the population of a two-level atom in a given time, robustly with respect to dephasing noise and/or systematic frequency shifts. Without imposing constraints, optimal protocols are insensitive to the perturbations but need an infinite energy. For a constrained value of the Rabi frequency, a flat pi pulse is the least sensitive protocol to phase noise but not to systematic frequency shifts, for which we describe and optimize a family of protocols

Robust coherent superposition of states using quasiadiabatic inverse engineering

“…These equations are equivalent to those obtained by the invariant dynamical theory [31], [20,21,24]. The inverse engineering is achieved by choosing the parameters θ(t) and β(t) first, and then constructing the Hamiltonian (obtaining the corresponding Ω(t) and ∆(t)) inversely through Eqs.…”

“…We substitute Eqs. (2) or (3) directly into the Schrödinger equation and obtain the following auxiliary differential equations [20,21,23,24,25]:…”

“…In Refs. [20,21,24,25], the inverse engineering was used together with perturbation theory calculations to design evolutions that are robust against particular errors. Here, we apply the quasiadiabatic condition to achieve system robustness.…”

“…Shortcut to adaibaticity (STA) has been proposed as a set of techniques to speed up the slow adiabatic processes, while keeping or enhancing robustness [19,20,21,22]. Also, a similar technique called designer evolution of quantum systems by inverse engineering (DEQSIE) [23] has also been developed for synthesizing Hamiltonians for the desired quantum state evolution.…”

“…However, the process does not always lead to the exact target state. On the other hand, the invariant-based inverse engineering STA [20,21] allows one to freely design the system evolution from the desired initial state to the final state. In this paper, the invariant-based inverse engineering and quasiadiabatic condition are combined for the first time for the production of coherent superposition of states.…”