Validation of quantum adiabaticity through non-inertial frames and its trapped-ion realization

Area of Science:

• Quantum Mechanics
• Quantum Dynamics
• Quantum Information

Background:

• The adiabatic approximation is crucial for predicting quantum dynamics but faces challenges with resonance phenomena in oscillating systems.
• Existing quantitative adiabatic conditions have shown inconsistencies, necessitating novel approaches for adiabaticity.
• Standard adiabatic conditions often fail to accurately describe dynamics near resonance points.

Purpose of the Study:

• To introduce a novel validation mechanism for the adiabatic approximation.
• To demonstrate the effectiveness of this mechanism by employing a non-inertial reference frame.
• To extend the validation to multi-particle quantum systems and experimentally verify it using a trapped ion qubit.

Main Methods:

• Introduced a non-inertial reference frame transformation for quantum systems.
• Analyzed the validity of standard adiabatic conditions using an oscillating Hamiltonian for a single quantum bit (qubit).
• Evaluated adiabatic conditions in the non-inertial frame and experimentally tested the method with a trapped Ytterbium ion (¹⁷¹Yb⁺) qubit.

Main Results:

• Demonstrated that standard adiabatic conditions fail in the original frame for a qubit system near resonance.
• Showed that these conditions correctly describe adiabatic dynamics in the non-inertial frame, both at and away from resonance.
• Confirmed the extension of this validation mechanism to multi-particle systems and its experimental consistency with a trapped ion qubit.

Conclusions:

• A non-inertial reference frame provides a robust mechanism for validating adiabatic approximation conditions.
• This approach successfully reconciles inconsistencies in adiabaticity predictions, particularly around resonance.
• The findings offer a generalized method for understanding and predicting adiabatic quantum dynamics in various systems.