Landau-Zener Transitions and Rabi Oscillations in a Cooper-Pair Box: Beyond Two-Level Models

TL;DR

This paper explores quantum interference in a superconducting Cooper-pair box using a three-level model, revealing new Landau-Zener and Rabi oscillation behaviors beyond traditional two-level approximations.

Contribution

It introduces a three-level framework to analyze Landau-Zener and Rabi oscillations, uncovering new interference patterns and conditions for effective two-level dynamics in Cooper-pair boxes.

Findings

Landau-Zener probabilities show 'step' and 'beats'-like interference patterns.

Resonance tuning maps the three-level system to a two-level Rabi model.

Off-resonance Rabi oscillations involve second-order tunneling processes.

Abstract

We investigate quantum interference effects in a superconducting Cooper-pair box by taking into account the possibility of tunneling processes involving one and two Cooper pairs. The quantum dynamics is analysed in a framework of three-level model. We compute Landau-Zener probabilities for a linear sweep of the gate charge and investigate Rabi oscillations in a periodically driven three-level system under in- and off- resonance conditions. It was shown that the Landau-Zener probabilities reveal two different patterns: "step" and "beats"-like behaviours associated with the quantum interference effects. Control on these two regimes is provided by change of the ratio between two characteristic time scales of the problem. We demonstrate through the analysis of a periodically driven three-level system, that if a direct transition between certain pairs of levels is allowed and fine-tuned to a resonance, the problem is mapped to the two-level Rabi model. If the transition between pair of levels is forbidden, the off-resonance Rabi oscillations involving second order in tunneling processes are predicted. This effect can be observed by measuring a population difference slowly varying in time between the states of the Cooper-pair box characterised by the same parity.