Nonadiabatic Control of Geometric Pumping

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Nonlinear dynamics

Background:

• Geometric pumping describes charge transport driven by time-periodic control parameters.
• The adiabatic approximation simplifies calculations but limits applicability to slow parameter changes.
• Understanding nonadiabatic effects is crucial for precise control of quantum systems.

Purpose of the Study:

• To derive the exact pumping current beyond the adiabatic approximation.
• To explore a geometrical interpretation of nonadiabatic pumping currents.
• To investigate methods for controlling and enhancing geometric currents.

Main Methods:

• Exact calculation of pumping current for arbitrary periodic control parameters.
• Development of a geometrical interpretation for nonadiabatic currents.
• Application of shortcuts to adiabaticity with an assisting field.

Main Results:

• The exact pumping current was obtained, going beyond the adiabatic approximation.
• A geometrical interpretation for the nontrivial part of the current was established in the nonadiabatic regime.
• A smooth connection between adiabatic Berry phase theory and Floquet theory was found.
• Shortcuts to adiabaticity were shown to enhance the geometric current.

Conclusions:

• Nonadiabatic effects in geometric pumping can be precisely calculated and offer a geometrical interpretation.
• The developed method bridges low-frequency adiabatic and high-frequency Floquet theories.
• Shortcuts to adiabaticity provide an effective strategy for controlling and amplifying geometric currents.