[Paper Review] Dissipative Landau-Zener tunneling in the crossover regime from weak to strong environment coupling

X. Dai, R. Trappen+23 more|arXiv (Cornell University)|Jul 5, 2022

Quantum and electron transport phenomena4 citations

TL;DR

This study experimentally demonstrates the crossover from weak to strong dissipation in Landau-Zener tunneling using a tunable superconducting flux qubit. By tuning the system-environment coupling, the work observes transitions between thermalization in the weak-coupling regime and dressed-state dynamics in the strong-coupling regime, providing new insights into open quantum system dynamics and quantum annealing.

ABSTRACT

Landau-Zener tunneling, which describes the transition in a two-level system during a sweep through an anti-crossing, is a model applicable to a wide range of physical phenomena. Realistic quantum systems are affected by dissipation due to coupling to their environments. An important aspect of understanding such open quantum systems is the relative energy scales of the system itself and the system-environment coupling, which distinguishes the weak- and strong-coupling regimes. Using a tunable superconducting flux qubit, we observe the crossover from weak to strong coupling to the environment in Landau-Zener tunneling. Our results confirm previous theoretical studies of dissipative Landau-Zener tunneling in the weak and strong coupling limits. We devise a spin bath model that effectively captures the crossover regime. This work is relevant for understanding the role of dissipation in quantum annealing, where the system is expected to go through a cascade of Landau-Zener transitions before reaching the target state.

Motivation & Objective

• To experimentally observe the crossover from weak to strong coupling between a quantum system and its environment in dissipative Landau-Zener tunneling.
• To investigate how environment-induced effects—such as thermalization and dressed-state transitions—evolve with increasing system-bath coupling strength.
• To provide experimental validation of theoretical models of open quantum systems in the intermediate coupling regime, previously unexplored experimentally.
• To assess the implications of these dynamics for quantum annealing, where non-adiabatic transitions and decoherence are critical performance bottlenecks.

Proposed method

• Employed a tunable superconducting flux qubit with capacitively shunted junctions to control the qubit's persistent current and level splitting.
• Used a flux-biased setup with a fast arbitrary waveform generator to sweep the qubit through an avoided level crossing, enabling Landau-Zener transitions.
• Performed measurements in the persistent current basis via flux-sensitive resonator readout, ensuring high-fidelity state detection with over 99% overlap with the energy eigenbasis.
• Characterized noise using T1 and T2 relaxation/dephasing measurements and fitted a circuit model to extract $I_p$ and $Δ$ as functions of flux bias.
• Simulated open system dynamics using the time-dependent AME (Adiabatic Master Equation) and PTRE (Polaron-Transformed Redfield Equation) formalisms to model weak and strong coupling regimes.
• Calculated the power spectral density (PSD) of $z$-loop flux noise from noise sensitivity and relaxation data, which was used as input in master equation simulations.

Experimental results

Research questions

• RQ1 How does the transition probability in dissipative Landau-Zener tunneling evolve as the system-environment coupling strength increases from weak to strong?
• RQ2 What are the dominant decoherence mechanisms in the intermediate coupling regime, and how do they differ from the weak-coupling thermalization and strong-coupling dressed-state scenarios?
• RQ3 To what extent do the AME and PTRE formalisms accurately describe experimental data across the full crossover from weak to strong coupling?
• RQ4 How does the presence of $1/f$ noise and non-Markovian effects influence the dynamics in the strong-coupling regime?

Key findings

• The experiment observed a smooth crossover from weak to strong coupling, with transition probabilities shifting from being dominated by thermalization to being governed by transitions between environment-dressed states.
• In the weak-coupling regime, the AME simulation with measured noise PSD accurately predicted the observed transition probabilities, confirming the role of environment-induced thermalization.
• In the strong-coupling regime, the PTRE formalism provided a better fit to experimental data than the AME, indicating that strong system-bath entanglement and non-Markovian effects are essential for accurate modeling.
• The inclusion of Lamb-shift terms in the master equation had negligible impact on the final ground-state probabilities, validating the use of the double-sided AME without such terms.
• The results demonstrate that the intermediate coupling regime exhibits non-trivial dynamics not captured by standard weak- or strong-coupling theories, highlighting the need for advanced open system frameworks.