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Dynamics of quantum measurement via electron transport in quantum dot systems: many-particle wavefunction approach

George Stavisskii, Leonid Fedichkin

TL;DR

This work develops a principled many-particle wavefunction approach to model quantum measurement with quantum point contacts that have rich internal structure. It derives master equations for a two-dimensional bottleneck PC and couples it to a qubit via Coulomb interaction, enabling analysis of the current noise spectrum $S(\omega)$ and the qubit’s reduced dynamics. The authors obtain analytical insights in incoherent and coherent regimes, reveal a resonance near $\omega=2\Omega_{0}$, and demonstrate qubit-induced noise asymmetries, while extending the framework to general quantum-dot graphs through a diagonalization strategy. Relaxation to a bosonic bath is shown to be essential for physically consistent noise statistics, smoothing qubit-induced features. The formalism provides a versatile toolkit for extracting qubit parameters from detector noise and for designing PC-based quantum measurement schemes across complex mesoscopic architectures.

Abstract

Measurement of a charge qubit via point contacts with complex internal structures is considered. In this context, a fully formalized derivation of the many-body wave function method is presented, together with the corresponding master equations for point contacts possessing an arbitrary number of internal states. The focus is placed on the current noise power spectrum and its dependence on the qubit dynamics and the point contact parameters.

Dynamics of quantum measurement via electron transport in quantum dot systems: many-particle wavefunction approach

TL;DR

This work develops a principled many-particle wavefunction approach to model quantum measurement with quantum point contacts that have rich internal structure. It derives master equations for a two-dimensional bottleneck PC and couples it to a qubit via Coulomb interaction, enabling analysis of the current noise spectrum and the qubit’s reduced dynamics. The authors obtain analytical insights in incoherent and coherent regimes, reveal a resonance near , and demonstrate qubit-induced noise asymmetries, while extending the framework to general quantum-dot graphs through a diagonalization strategy. Relaxation to a bosonic bath is shown to be essential for physically consistent noise statistics, smoothing qubit-induced features. The formalism provides a versatile toolkit for extracting qubit parameters from detector noise and for designing PC-based quantum measurement schemes across complex mesoscopic architectures.

Abstract

Measurement of a charge qubit via point contacts with complex internal structures is considered. In this context, a fully formalized derivation of the many-body wave function method is presented, together with the corresponding master equations for point contacts possessing an arbitrary number of internal states. The focus is placed on the current noise power spectrum and its dependence on the qubit dynamics and the point contact parameters.

Paper Structure

This paper contains 13 sections, 101 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Point contact as a framework for Many-body wavefunction approach
  3. Point contact detector with 2-d "bottleneck"
  4. In - coherent case
  5. Coherent case
  6. PC 2-d "bottleneck" near quantum dot qubit
  7. Current noise power-spectrum in presence of qubit
  8. Stationary state approximation
  9. Noise power spectrum approximation
  10. Qubit dynamics via interaction with PC 2-d "bottleneck"
  11. Generalization for any graph structures in the "bottleneck"
  12. Including relaxation in non-unitary dynamics
  13. Conclusions

Figures (10)

  • Figure 1: PC-2D quantum bottleneck energy band diagrammatic representation.
  • Figure 2: Terms in transition Hamiltonian, which give contribution to the "alpha" term. Indexes denote many-body wavefunction argument of the contributing term.
  • Figure 3: Terms in transition Hamiltonian, which give contribution to the $\alpha \beta$ term. Indexes denote many-body wavefunction argument of the contributing term.
  • Figure 4: Terms in transition Hamiltonian, which give contribution to the $0$ term. Indexes denote many-body wavefunction argument of the contributing term.
  • Figure 5: Residue theorem explanation. $\gamma_{R}$ is the half-circle contour, $E_{\lambda}$ is the bias cutoff, $\gamma_{I}$ is the actual integration contour, $z_{1}$ and $z_{2}$ are poles of simplified integrand in (10).
  • ...and 5 more figures