Quantum jumps and the theory of continuous quantum measurements

M. D. Srinivas

Yi-Xin Chen, SHANGGUAN WANGZUO, JI DA-REN +1 more

In this paper we investigate the quantum jump in a multi-level atom and construct a formal solution to the optical Block equation describing the interaction system of the multi-level atom with incident resonant laser. It is proved that pure state analysis theory is no longer applicable to a multi-level atom system, so a mixed one is developed, concluding that the resetting density of a multi-level atom should be described by mixed state analysis theory. We also discuss the continuous quantum measurement along with quantum jumping in a multi-level atom.

Alberto Barchielli

Therese Karmstrand, Franco Nori, Clemens Gneiting

Projective measurements are foundational for quantum physics in general and quantum information tasks in particular. However, their direct implementation is often not warranted. Here, we investigate under what conditions continuous monitoring that manifests in quantum jump trajectories realises projective measurements over time. Considering finite-dimensional quantum systems and single, diagonalisable jump operators, we show if and how the detected quantum jump statistics force, and allow inferring, the convergence of individual quantum trajectories towards eigenstates of an observable in the long-time limit. We identify a necessary non-degeneracy condition that is related to the presence of a strong symmetry with non-degenerate symmetry sectors. We derive analytical expressions for the rate of convergence and the time-error relationship in finite-time measurements. Our results provide a transparent framework for understanding the emergence of projective measurements from continuous monitoring, with direct implications for the optimisation of quantum measurement protocols in experiments.

Yi Xia

Abstract In this paper we investigate the quantum jump in a multi level atom and construct a formal solution to the optical Block equation describing the interaction system of the multi level atom with incident resonant laser.It is proved that pure state analysis theory is no longer applicable to a multi level atom system,so a mixed one is developed,concluding that the resetting density of a multi level atom should be described by mixed state analysis theory.We also discuss the continuous quantum measurement along with quantum jumping in a multi level atom.

E.G. Eberle