Scheme to measure the expectation value of a physical quantity in weak coupling regime

doi:10.1088/1674-1056/abd772

Abstract In quantum mechanics, the expectation value of an operator can be measured by using the projective measurement, if the coupling between the measured system and pointer is strong enough. However in the weak coupling regime, the pointer can not show all the eigenvalue of the physical quantity directly due to the overlapping among the pointer states, which makes the measurement of the expectation value difficult. In this paper, we propose an expectation value measurement method in the weak coupling regime inspired by the weak measurement scheme. Compared to the projective measurement, our scheme has two obvious advantages. Experimentally we use the internal state and motional state of a single trapped ⁴⁰Ca⁺ to establish the measurement scheme and realize the proof of principle demonstration of the scheme.

Keywords: weak measurement expectation value trapped ions

Received: 15 October 2020
Revised: 13 November 2020
Accepted manuscript online: 30 December 2020

PACS:	32.80.Qk	(Coherent control of atomic interactions with photons)
	03.65.Wj	(State reconstruction, quantum tomography)
	03.75.Be	(Atom and neutron optics)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12004430 and 61632021) and the National Basic Research Program of China (Grant No. 2016YFA0301903).

Corresponding Authors: ^†Corresponding author. E-mail: pxchen@nudt.edu.cn

Cite this article:

Jie Zhang(张杰), Chun-Wang Wu(吴春旺), Yi Xie(谢艺), Wei Wu(吴伟), and Ping-Xing Chen(陈平形) Scheme to measure the expectation value of a physical quantity in weak coupling regime 2021 Chin. Phys. B 30 033201

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