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Gauge fields, geometric phases, and quantum adiabatic pumps.
Huan-Qiang Zhou1, Sam Young Cho, Ross H McKenzie
1Centre for Mathematical Physics, The University of Queensland, Queensland 4072, Australia. hqz@maths.uq.edu.au
Physical Review Letters
|November 13, 2003
Summary
Quantum adiabatic pumping efficiently moves charge and spin in nanoscale devices. This process is geometrically represented by gauge fields, with potential for demonstrating non-Abelian fields using scanning tunneling microscopy.
Area of Science:
- Quantum physics
- Condensed matter physics
- Nanoscale electronics
Background:
- Quantum adiabatic pumping of charge and spin has been demonstrated in nanoscale electronic devices.
- Pumping involves cyclic, slow variation of system parameters, keeping the quantum system in its ground state.
Purpose of the Study:
- To show that quantum pumping has a natural geometric representation.
- To explore the connection between quantum pumping and gauge fields.
- To identify experimental methods for demonstrating non-Abelian gauge fields in quantum pumping.
Main Methods:
- Theoretical analysis of quantum adiabatic pumping.
- Geometric representation using gauge fields (Abelian and non-Abelian).
- Proposal for experimental demonstration using scanning tunneling microscopy.
Main Results:
- Quantum pumping is shown to have a natural geometric representation in terms of gauge fields.
- Both Abelian and non-Abelian gauge fields are identified on the space of system parameters.
- Scanning tunneling microscopy through a magnetic atom is proposed as a method to demonstrate non-Abelian gauge fields.
Conclusions:
- Quantum adiabatic pumping exhibits a fundamental geometric structure related to gauge fields.
- The non-Abelian character of these gauge fields can potentially be observed experimentally.
- This work provides a new perspective on quantum pumping and its connection to geometric phase and topology.