Entanglement, measurement, and conditional evolution of the Kondo singlet interacting with a mesoscopic detector

TL;DR

This paper explores how a mesoscopic detector affects the quantum coherence and entanglement of a Kondo singlet in a quantum dot, revealing how measurement influences its state and relaxation dynamics.

Contribution

It introduces the concept of conditional evolution of the Kondo singlet under measurement and analyzes how entanglement and phase coherence are affected by the detector.

Findings

Phase coherence of the Kondo singlet is destroyed by charge-sensitive scattering.

Measurement causes the system to become disentangled and the singlet to evolve into a fixed-electron state.

Relaxation time depends only on charge-dependent transmission, with phase information erased.

Abstract

We investigate various aspects of the Kondo singlet in a quantum dot (QD) electrostatically coupled to a mesoscopic detector. The two subsystems are represented by an entangled state between the Kondo singlet and the charge-dependent detector state. We show that the phase-coherence of the Kondo singlet is destroyed in a way that is sensitive to the charge-state information restored both in the magnitude and in the phase of the scattering coefficients of the detector. We also introduce the notion of the `conditional evolution' of the Kondo singlet under projective measurement on the detector. Our study reveals that the state of the composite system is disentangled upon this measurement. The Kondo singlet evolves into a particular state with a fixed number of electrons in the quantum dot. Its relaxation time is shown to be sensitive only to the QD-charge dependence of the transmission probability in the detector, which implies that the phase information is erased in this conditional evolution process. We discuss implications of our observations in view of the possible experimental realization.