Stückelberg interference in a superconducting qubit under periodic latching modulation

Abstract

When the level separation of a qubit is modulated periodically across an\navoided crossing, tunneling to the excited state - and consequently\nLandau-Zener-St\\"uckelberg interference - can occur. The types of modulation\nstudied so far correspond to a continuous change of the level separation. Here\nwe study periodic latching modulation, in which the level separation is\nswitched abruptly between two values and is kept constant otherwise. In this\ncase, the conventional approach based on the asymptotic Landau-Zener (LZ)\nformula for transition probabilities is not applicable. We develop a novel\nadiabatic-impulse model for the evolution of the system and derive the\nresonance conditions. Additionally, we derive analytical results based on the\nrotating-wave approximation (RWA). The adiabatic-impulse model and the RWA\nresults are compared with those of a full numerical simulation. These\ntheoretical predictions are tested in an experimental setup consisting of a\ntransmon whose flux bias is modulated with a square wave form. A rich spectrum\nis observed, with distinctive features correspoding to two regimes:\nslow-modulation and fast-modulation. These experimental results are shown to be\nin very good agreement with the theoretical models. Also, differences with\nrespect to the well known case of sinusoidal modulation are discussed, both\ntheoretically and experimentally.\n