St\"uckelberg interference in a superconducting qubit under periodic latching modulation

TL;DR

This paper investigates Landau-Zener-Stückelberg interference in a superconducting qubit under periodic latching modulation, developing new theoretical models and experimentally validating the phenomena with a transmon device.

Contribution

It introduces a novel adiabatic-impulse model for abrupt level switching and compares it with RWA and numerical simulations, extending understanding beyond sinusoidal modulation.

Findings

Rich interference spectrum observed experimentally

Good agreement between theory and experiment

Distinct features identified for slow and fast modulation regimes

Abstract

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