Quantum measurement in the charge representation

Abstract

Counting statistics of charge transfers in a point contact interacting with an arbitrary quantum system is studied. The theory for the charge specific density matrix is developed, allowing the evaluation of the probability of the outcome of any joint measurement of the state of the quantum system and the transferred charge. Applying the method of charge projectors, the master equation for the charge specific density matrix is derived in the tunneling Hamiltonian model of the point contact. As an example, the theory is applied to a quantum measurement of a two-state system: The evolution of the charge specific density matrix in the presence of Nyquist or Schottky noise is studied and the conditions for the realization of a projective measurement are established.

16 pages, 4 figures

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• Transport Statistics of Interacting Double Dot Systems: Coherent and Non-Markovian Effects
• Nonequilibrium isolated molecule limit
• Interference effects in the counting statistics of electron transfers through a double quantum dot
• Geometrical effects and signal delay in time-dependent transport at the nanoscale
• Statistics of charge transfer in a tunnel junction coupled to an oscillator
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• Time-dependent magnetotransport in an interacting double quantum wire with window coupling
• Single-electron counting spectroscopy: simulation study of porphyrin in a molecular junction
• Non-Markovian dynamics of a nanomechanical resonator measured by a quantum point contact
• Electron transport through a quantum dot assisted by cavity photons
• Improved position measurement of nano electromechanical systems using cross correlations
• Role of coherence in transport through engineered atomic spin devices
• Non-Markovian theory for the waiting time distributions of single electron transfers
• Influence of superconducting leads energy gap on electron transport through double quantum dot by Markovian quantum master equation approach
• The effect of noise fluctuation of a quantum tunneling device coupled to a substrate