Gauge freedom in observables and Landsberg's nonadiabatic geometric phase: Pumping spectroscopy of interacting open quantum systems
Journal article, 2017

We set up a general density-operator approach to geometric steady-state pumping through slowly driven open quantum systems. This approach applies to strongly interacting systems that are weakly coupled to multiple reservoirs at high temperature, illustrated by an Anderson quantum dot. Pumping gives rise to a nonadiabatic geometric phase that can be described by a framework originally developed for classical dissipative systems by Landsberg. This geometric phase is accumulated by the transported observable (charge, spin, energy) and not by the quantum state. It thus differs radically from the adiabatic Berry-Simon phase, even when generalizing it to mixed states, following Sarandy and Lidar. As a key feature, our geometric formulation of pumping stays close to a direct physical intuition (i) by tying gauge transformations to calibration of the meter registering the transported observable and (ii) by deriving a geometric connection from a driving-frequency expansion of the current. Furthermore, our approach provides a systematic and efficient way to compute the geometric pumping of various observables, including charge, spin, energy, and heat. These insights seem to be generalizable beyond the present paper's working assumptions (e.g., Born-Markov limit) to more general open-system evolutions involving memory and strong-coupling effects due to low-temperature reservoirs as well. Our geometric curvature formula reveals a general experimental scheme for performing geometric transport spectroscopy that enhances standard nonlinear spectroscopies based on measurements for static parameters. We indicate measurement strategies for separating the useful geometric pumping contribution to transport from nongeometric effects. A large part of the paper is devoted to an explicit comparison with the Sinitsyn-Nemenmann full-counting-statistics (FCS) approach to geometric pumping, restricting attention to the first moments of the pumped observable. Covering all key aspects, gauge freedom, pumping connection, curvature, and gap condition, we argue that our approach is physically more transparent and, importantly, simpler for practical calculations. In particular, this comparison allows us to clarify how in the FCS approach an "adiabatic" approximation leads to a manifestly nonadiabatic result involving a finite retardation time of the response to parameter driving.

Topological Insulators

Dots

Electron Pump

Adiabatic Response

Mixed States

Matter

Dissipative Systems

Full Counting Statistics

Transport

Condensed

Berry Phase

Author

T. Pluecker

RWTH Aachen University

JARA - Fundamentals of Future Information Technologies

Maarten Wegewijs

Forschungszentrum Jülich

RWTH Aachen University

JARA - Fundamentals of Future Information Technologies

Janine Splettstoesser

Chalmers, Microtechnology and Nanoscience (MC2), Applied Quantum Physics

Physical Review B

24699950 (ISSN) 24699969 (eISSN)

Vol. 95 15 Article nr 155431 - 155431

Areas of Advance

Nanoscience and Nanotechnology (2010-2017)

Subject Categories

Physical Sciences

Nano Technology

DOI

10.1103/PhysRevB.95.155431

More information

Latest update

6/29/2020