Quantum Zeno Effect and Atomic Population Inversion

Jiu-Ming Li

doi:10.11648/j.ajmp.20180705.12

Abstract

Quantum Zeno effect can be applied to quantum information processing，and can reveal the nature of quantum measurement. In addition, it has also many potential applications. This suggests that studying the quantum Zeno effect has great theoretical and experimental significance. In this work, the system of a two-level atom interacting with a single mode field is considered and the dynamics of the system subjected to successive projection measurements is studied, and the quantum Zeno effect is presented. Moreover, the influence of the quantum Zeno effect on atomic population inversion is discussed. Based on Schrödinger equation, the survival probability of the initial state of the two-level atom subjected to frequently repeated measurements can be obtained. The survival probability depends on the time interval between measurements. It is seen that the exponential decay of the system under slowly frequent measurements is presented instead of the naturally oscillatory process. For slowly repeated measurements the atomic population inversion and the survival probability of initial state decline rapidly at the early time and then both of them become unchanged. As the time intervals of the measurements are sufficiently short, the quantum Zeno effect occurs. These results have also shown how the measurement can inhibit the atomic population inversion.

Highlights

The development of quantum information and quantum computing over the last two decades has led to increasing attention to quantum Zeno effect (QZE) in the literature [1,2,3,4]
An opposite effect known as quantum anti-Zeno effect (QAZE), i.e., the acceleration of the decay process caused by frequent measurement, has been pointed out
After the frequent projection measurements for a two-level atoms, Francica et al have demonstrated how both quantum and classical correlations are affected by the QZE and QAZE [1]

Summary

Introduction

The development of quantum information and quantum computing over the last two decades has led to increasing attention to quantum Zeno effect (QZE) in the literature [1,2,3,4]. The QZE is a quantum effect that unstable quantum systems are induced to the reduction of the quantum decay rate even stop due to the frequent measurements at short time intervals [5,6,7,8,9,10]. Unlike previous most of the research is on the basis of the interaction with atoms, Peise and Lücke et al used laser beams to realize no interaction measurements, resulting in the indirect QZE, inhibiting decay of ultracold atoms [12]. Because of these theories and experiments, the QZE has been widely used in various quantum protocols. It is shown that when the measured time interval is short enough, the QZE will be generated, and the influence of QZE on the population inversion is investigated

Model and Hamiltonian

The Role of Quantum Measurement in Atomic Population Inversion

Numerical Analysis

Conclusion