Shortcuts to adiabaticity for a qubit using detuning control

We derive shortcuts to adiabaticity for a two-level system using the detuning as sole control parameter while the Rabi frequency is kept fixed. We work in the adiabatic basis while we also employ a time-rescaling. The control function that we use is the time-derivative of the magnetic field angle relative to the z-axis. We find that a constant control attains adiabatic passage with perfect fidelity only at particular durations, which we call resonances. We also find that, if we use a control with appropriate on-off modulation, a perfect adiabatic passage is achieved for all durations exceeding the bound π/Ω, with Ω being the constant Rabi frequency. The advantage of the proposed methodology over previous works is that the detuning control obtained is continuous and monotonic. The present work may find applications in the field of quantum information. As an example we mention the problem of designing a CZ gate, which can be formulated as the problem of adiabatically controlling a two-level system using only the detuning. (paper)