Experimental Implementation of Generalized Transitionless Quantum Driving

TL;DR

This paper demonstrates that generalized Transitionless Quantum Driving (TQD) can be implemented with lower intensity fields and improved robustness against decoherence, using a trapped ion system to compare traditional and generalized TQD with adiabatic evolution.

Contribution

The study experimentally shows that gauge freedom in generalized TQD allows for optimized, less intense Hamiltonians that outperform traditional TQD and adiabatic methods in robustness and efficiency.

Findings

Generalized TQD reduces field intensity requirements.

Optimized TQD Hamiltonians are more robust against decoherence.

Performance of TQD surpasses adiabatic dynamics in fidelity.

Abstract

It is known that high intensity fields are usually required to implement shortcuts to adiabaticity via Transitionless Quantum Driving (TQD). Here, we show that this requirement can be relaxed by exploiting the gauge freedom of generalized TQD, which is expressed in terms of an arbitrary phase when mimicking the adiabatic evolution. We experimentally investigate the performance of generalized TQD in comparison with both traditional TQD and adiabatic dynamics. By using a $^{171}$Yb$^+$ trapped ion hyperfine qubit, we implement a Landau-Zener adiabatic Hamiltonian and its (traditional and generalized) TQD counterparts. We show that the generalized theory provides optimally implementable Hamiltonians for TQD, with no additional fields required. In addition, the energetically optimal TQD Hamiltonian for the Landau-Zener model is investigated under dephasing. Remarkably, even using less intense fields, optimal TQD exhibits fidelities that are more robust against a decohering environment, with performance superior than that provided by the adiabatic dynamics.