Single-Atom Verification of the Optimal Trade-Off between Speed and Cost in Shortcuts to Adiabaticity

Abstract

The approach of shortcuts to adiabaticity enables the effective execution of adiabatic dynamics in quantum information processing with enhanced speed. Owing to the inherent trade-off between dynamical speed and the cost associated with the transitionless driving field, executing arbitrarily fast operations becomes impractical. To understand the accurate interplay between speed and energetic cost in this process, we propose theoretically and verify experimentally a new trade-off, which is characterized by a tightly optimized bound within $s$-parameterized phase spaces. Our experiment is carried out in a single ultracold ${}^{40}$Ca${}^{+}$ ion trapped in a harmonic potential. By exactly operating the quantum states of the ion, we execute the Landau-Zener model as an example, where the quantum speed limit as well as the cost are governed by the spectral gap. We witness that our proposed trade-off is indeed tight in scenarios involving both initially eigenstates and initially thermal equilibrium states. Our work helps understanding the fundamental constraints in shortcuts to adiabaticity and illuminates the potential of under-utilized phase spaces that have been traditionally overlooked.

6+5 pages, 3+3 figures

References in corpus (15)

• Quantum speed limits in open system dynamics
• Assisted finite-rate adiabatic passage across a quantum critical point: Exact solution for the quantum Ising model
• Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
• Shortcut to Adiabaticity in the Lipkin-Meshkov-Glick Model
• Environment assisted speed-up of the field evolution in cavity QED
• Generalized spin mapping for quantum-classical dynamics
• Demonstration of quantum brachistochrones between distant states of an atom
• Initialisation of single spin dressed states using shortcuts to adiabaticity
• Shortcuts to adiabaticity for quantum annealing
• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• Bang-bang shortcut to adiabaticity in the Dicke model as realized in a Penning trap experiment
• Geodesic path for the minimal energy cost in shortcuts to isothermality
• Implementing two-qubit gates at the quantum speed limit
• Quantum speed limits in arbitrary phase spaces
• Shortcut-to-adiabaticity-like techniques for parameter estimation in quantum metrology

Cited by in corpus (3)

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