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Counting statistics for arbitrary cycles in quantum pumps.

Y Makhlin1, A D Mirlin

  • 1Institut für Theoretische Festkörperphysik, Universität Karlsruhe, 76128 Karlsruhe, Germany.

Physical Review Letters
|January 22, 2002
PubMed
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We analyze current noise in adiabatic pumps, linking charge transport to geometric loop properties on spheres. This framework simplifies analysis and reveals how loop areas determine average current and minimal variance.

Area of Science:

  • Condensed Matter Physics
  • Quantum Transport
  • Mesoscopic Physics

Background:

  • Adiabatic quantum pumps are devices designed to transport charge without an applied voltage.
  • Understanding noise properties is crucial for characterizing the efficiency and limitations of quantum transport devices.
  • Previous studies often focused on specific pump geometries, lacking a unifying theoretical framework.

Purpose of the Study:

  • To investigate noise-related properties of electrical current in adiabatic pumps.
  • To establish a unifying theoretical framework for analyzing charge transport in various adiabatic pump realizations.
  • To formulate conditions for quantized charge transport.

Main Methods:

  • Utilizing a symmetry in the problem to connect charge transport statistics to the geometry of loops on a sphere.

Related Experiment Videos

  • Extending this geometric analogy to higher-dimensional manifolds for multi-channel systems.
  • Relating average current and minimal variance to enclosed areas on a sphere and minimal surfaces (soap films).

    • Main Results:

    • A unifying geometric framework is established for analyzing adiabatic pumps.
    • The average current and minimal variance are directly related to the areas enclosed by loops on a sphere and minimal surfaces.
    • Conditions for the quantization of pumped charge have been formulated.

    Conclusions:

    • The geometric approach provides a simplified and unified method for studying charge transport in adiabatic pumps.
    • The findings offer insights into noise reduction and control in quantum transport.
    • The derived conditions for charge quantization are essential for designing efficient quantum devices.