Full counting statistics of electron transfer between superconductors.

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Mesoscopic Superconductivity

Background:

• The Keldysh-Green's function method is a powerful tool for studying quantum systems.
• Understanding particle transmission in mesoscopic superconductors is crucial for quantum electronics.
• Supercurrent statistics in short contacts require advanced theoretical frameworks.

Purpose of the Study:

• To extend the Keldysh-Green's function method for calculating particle transmission distributions in mesoscopic superconductors.
• To investigate the statistics of supercurrent in short superconducting contacts.
• To analyze the physical implications of negative probabilities in quantum measurements.

Main Methods:

• Extension of the Keldysh-Green's function formalism.
• Application to the analysis of supercurrent in short superconducting contacts.
• Investigation of Andreev bound state contributions to current.

Main Results:

• The extended method allows calculation of the full transmitted particle distribution.
• For supercurrent carried by Andreev bound states, a switching behavior between electron trains was observed.
• Negative "probabilities" were found in the supercurrent distribution for weak (gapless) superconductors at low temperatures.

Conclusions:

• The developed method provides a comprehensive approach to quantum transport in mesoscopic superconductors.
• The observed switching behavior is linked to the nature of Andreev bound states.
• Quantum mechanical considerations of the measurement device validate the measurability of negative probabilities, challenging classical intuition.