Driving can have no effect, if the phase is chosen appropriately

For expanding the quantum toolbox, it is important to develop coherent control of individual quantum systems. Our work relates to the possibility of controlling two-level quantum systems under the action of linear excitation. We take into account such factors as the phase difference between the incoming states, finite duration of driving, coupling to the dissipative environment. If starting from the ground state, the transition probability is described by the Landau-Zener-Stuckelberg-Majorana formula [1]. However, in a general superposition initial state, it becomes possible to greatly change the final result by means of quantum interference [2]. We can choose any value between the minimum and maximum values that can be achieved depending on the phase difference, the initial moment of time, at various system parameters. In the superposition state, depending on the tunable parameters, it is possible to obtain a full transition to one of the basis states or to remain in the same superposition state after the transition. Such keeping the occupation population even under driving is analogous to the transitionless driving of Ref. [3].

[1] O. V. Ivakhnenko, S. N. Shevchenko, F. Nori, "Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference", review article arXiv:2203.16348, (accepted Physics Reports) (2022).

[2] P. O. Kofman, O. V. Ivakhnenko, S. N. Shevchenko, and F. Nori, “Majorana’s approach to nonadiabatic transitions validates the adiabatic-impulse approximation,” arXiv:2208.00481 (2022).

[3] Berry, M. V. (2009), “Transitionless quantum driving,” J. Phys. A: Math. Theor. 42 (36), 365303.