Schr\"{o}dinger-cat states in Landau-Zener-St\"{u}ckelberg-Majorana interferometry: a multiple Davydov Ansatz approach

TL;DR

This paper introduces a novel approach using the multiple Davydov Ansatz to study Landau-Zener transitions in a qubit-photon system, revealing detailed photon dynamics and transition pathways beyond common approximations.

Contribution

It develops an efficient variational method to analyze complex photon-qubit interactions and uncovers new insights into transition probabilities and pathways in Landau-Zener-Stückelberg-Majorana interferometry.

Findings

Exact photon dynamics during LZ transition are obtained.

Asymptotic transition probabilities are characterized for Schrödinger-cat initial states.

Photon-assisted interference effects are explored with sinusoidal driving.

Abstract

Employing the time-dependent variational principle combined with the multiple Davydov $\mathrm{D}_2$ Ansatz, we investigate Landau-Zener (LZ) transitions in a qubit coupled to a photon mode with various initial photon states at zero temperature. Thanks to the multiple Davydov trial states, exact photonic dynamics taking place in the course of the LZ transition is also studied efficiently. With the qubit driven by a linear external field and the photon mode initialized with Schr\"odinger-cat states, asymptotic behavior of the transition probability beyond the rotating-wave approximation is uncovered for a variety of initial states. Using a sinusoidal external driving field, we also explore the photon-assisted dynamics of Landau-Zener-St\"{u}ckelberg-Majorana interferometry. Transition pathways involving multiple energy levels are unveiled by analyzing the photon dynamics.