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arXiv:cond-mat/0603802

Mesoscopic quantum measurements

D. V. Averin

Published Mar 29, 2006• 1 citation
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Abstract

The paper discusses dynamics of quantum measurements in mesoscopic solid-state systems. The aim is to show how the general ideas of the quantum measurement theory play out in the realistic models of actual mesoscopic detectors. The two general models of ballistic and tunneling detectors are described and studied quantitatively. Simple transformation cycle demonstrating wavefunction reduction in a mesosocpic qubit is suggested.

DOI
10.48550/arxiv.cond-mat/0603802

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The paper discusses dynamics of quantum measurements in mesoscopic solid-state systems. The aim is to show how the general ideas of the quantum measurement theory play out in the realistic models of actual mesoscopic detectors. The two general models of ballistic and tunneling detectors are described and studied quantitatively. Simple transformation cycle demonstrating wavefunction reduction in a mesosocpic qubit is suggested.
The transformation cycle and associated inequality are suggested for the basic demonstration of the wavefunction reduction in a mesoscopic qubit in measurements with quantum-limited detectors. Violation of the inequality would show directly that the qubit state changes in a way dictated by the probabilistic nature of the wavefunction and inconsistent with the dynamics of the Schrödinger equation: the qubit tunnels through an infinitely large barrier. Estimates show that the transformation cycle is within the reach of current experiments with superconducting qubits.
Recent experimental demonstrations of quantum coherence of the charge and flux states of Josephson junctions show that the quantum Josephson dynamics can be used to develop scalable quantum logic circuits. In this work, I review the basic concepts of Josephson tunneling and Josephson-junction qubits, and discuss two problems of this tunneling motivated by quantum computing applications. One is the theory of photon-assisted resonant flux tunneling in SQUID systems used to demonstrate quantum coherence of flux. Another is the problem of quantum measurement of charge with the SET electrometer. It is shown that the SET electrometer at the Coulomb blockade threshold is the quantum-limited detector with energy sensitivity reaching ħ/√3 in the resonant-tunneling regime.
We present and discuss some models for the quantum measuring process. Our models indicate that the coherent state approach to classical limits in quantum theories becomes a powerful method for a unified description of various measuring processes. Each detector in the models has a parameter N , the number of its dynamical variables; the whole process of an interaction between an object system and the detector is calculable for any finite number N . It is shown that the detector states after the interaction are characterized by a macroscopic parameter, which is closely connected with the “reliability” of the detector. The reliability plays an essential role in eliminating the quantum interference between two states corresponding to two different positions of the pointer. Finally, the quantum mechanics of the detector reduces to classical mechanics on suitable “phase space” as N becomes large, as is required.
In quantum measurement theory it is necessary to show how a quantum source conditions a classical stochastic record of measured results. We discuss mesoscopic conductance using quantum stochastic calculus to elucidate the quantum nature of the measurement taking place in these systems. To illustrate the method we derive the current fluctuations in a two terminal mesoscopic circuit with two tunnel barriers containing a single quasi bound state on the well. The method enables us to focus on either the incoming/ outgoing Fermi fields in the leads, or on the irreversible dynamics of the well state itself. We show an equivalence between the approach of BÜttiker and the Fermi quantum stochastic calculus for mesoscopic systems.