Dynamics of Quantum Collapse in Energy Measurements

TL;DR

This paper investigates how continuous energy measurements affect quantum system dynamics by modeling wavefunction collapse through a non-Hermitian Hamiltonian, demonstrating measurement-induced freezing of evolution.

Contribution

It introduces a method using restricted path integrals and an effective Schrödinger equation to analyze energy measurement effects in quantum systems, including numerical solutions.

Findings

Reproduces quantum Zeno effect in two-level systems

Predicts inhibition of spontaneous decay in quantum wells

Shows evolution freezing proportional to measurement accuracy

Abstract

The influence of continuous measurements of energy with a finite accuracy is studied in various quantum systems through a restriction of the Feynman path-integrals around the measurement result. The method, which is equivalent to consider an effective Schr\"odinger equation with a non-Hermitian Hamiltonian, allows one to study the dynamics of the wavefunction collapse. A numerical algorithm for solving the effective Schr\"odinger equation is developed and checked in the case of a harmonic oscillator. The situations, of physical interest, of a two-level system and of a metastable quantum-well are then discussed. In the first case the Zeno inhibition observed in quantum optics experiments is recovered and extended to nonresonant transitions, in the second one we propose to observe inhibition of spontaneous decay in mesoscopic heterostructures. In all the considered examples the effect of the continuous measurement of energy is a freezing of the evolution of the system proportional to the accuracy of the measurement itself.