[Paper Review] Landau-Zener-Stuckelberg interferometry in multilevel superconducting flux qubit

Xueda Wen, Yiwen Wang+8 more|arXiv (Cornell University)|Mar 10, 2010

Quantum and electron transport phenomena1 references3 citations

TL;DR

This paper presents a universal theoretical framework for Landau-Zener-Stuckelberg (LZS) interferometry in multilevel superconducting flux qubits under high-amplitude, high-frequency driving fields. By extending LZS theory to include multiple energy levels, the model explains complex interference patterns observed experimentally and predicts new quantum phenomena, enabling precise parameter extraction and dephasing mechanism probing in superconducting qubits.

ABSTRACT

Landau-Zener-Stuckelberg interferometry has been extensively investigated in quantum two-level systems, with particular interests on artificial system such as superconducting flux qubits. With increasing the driving field amplitude, more energy levels will be involved into the quantum evolution, which results in population inversion and many interesting interference patterns. These interference patterns can be used to obtain the parameters characterizing the system and probe dephasing mechanisms of the qubit. Most recently, experiments have been extended to the regime with higher-frequency and larger-amplitude driving field, in which the interference pattern exhibited more complicated characteristics. In this article, we give a universal description of the characteristics observed in both low-frequency and high-frequency regimes. Besides explaining the already observed experimental results, our theoretical model predicted many interesting phenomenon, which can be demonstrated by future experiments.

Motivation & Objective

• To develop a universal theoretical description of Landau-Zener-Stuckelberg interferometry in multilevel superconducting flux qubits beyond the two-level approximation.
• To explain the complex interference patterns observed in experiments with high-amplitude, high-frequency driving fields.
• To enable accurate extraction of system parameters and characterization of dephasing mechanisms in superconducting qubits through interference features.
• To predict novel quantum phenomena in the multilevel regime that can be tested in future experiments.

Proposed method

• Extension of the Landau-Zener-Stuckelberg theory to include multiple energy levels in a superconducting flux qubit under time-dependent driving.
• Use of a time-dependent Hamiltonian to model the avoided level crossings and non-adiabatic transitions during ramping of the driving field.
• Application of the LZS formula to multilevel systems, accounting for interference between multiple transition pathways.
• Numerical simulation of population dynamics and interference fringes across varying driving amplitudes and frequencies.
• Derivation of analytical expressions for interference patterns in both low- and high-frequency regimes.
• Comparison of theoretical predictions with existing experimental data to validate the model.

Experimental results

Research questions

• RQ1 How do multilevel effects modify Landau-Zener-Stuckelberg interference patterns in superconducting flux qubits under high-amplitude driving?
• RQ2 What universal features emerge in LZS interferometry when more than two levels are dynamically coupled?
• RQ3 How can interference patterns be used to extract physical parameters of the qubit system?
• RQ4 What new quantum phenomena are predicted by the multilevel LZS model that are absent in the two-level case?
• RQ5 How do high-frequency and high-amplitude driving fields alter the standard LZS interference behavior?

Key findings

• The theoretical model successfully explains the complex interference patterns observed in recent experiments with high-amplitude, high-frequency driving fields.
• The model predicts population inversion and non-trivial interference features in the multilevel regime, not captured by two-level approximations.
• Interference fringes are shown to be sensitive to system parameters, enabling their use as a diagnostic tool for qubit characterization.
• The framework unifies low- and high-frequency regimes of LZS interferometry in multilevel systems through a single theoretical description.
• The model predicts new quantum phenomena, such as multi-path interference and modified phase accumulation, which can be tested experimentally.
• The results demonstrate that multilevel effects significantly alter the standard LZS picture, especially under strong driving.