Single-Photon-Added Coherent State Based Postselected Weak Measurement

Yusuf Turek

Yusuf Turek, Akbar Islam, Ahmad Abliz

Yi-Fang Ren, Yusuf Turek

We investigated precision measurements in a two-level system coupled to a single-photon-added coherent state (SPACS) under postselected weak measurement. We analyzed strategies for improving measurement precision, including parameter estimation and the signal-to-noise ratio (SNR) in postselected weak measurements, using the photon statistics of SPACS as the meter. Our results demonstrate that SPACS-based postselected weak measurements can outperform conventional measurement schemes in terms of precision. Additionally, we explicitly introduced an alternative weak measurement method, which is commonly applied in dispersive light-atom interactions. Our work presents a novel approach to addressing fundamental issues in quantum precision measurement based on photon statistics, and it provides a method for extracting the photon and phase shifts of radiation fields through the weak values of system observables.

Wen Jun Xu, Taximaiti Yusufu, Yusuf Turek

In this paper, ordinary and amplitude-squared squeezing as well as Wigner functions of single-photon-added coherent state after postselected von Neumann measurements are investigated. The analytical results show that the weak measurement procedure, which is characterized by postselection and weak value, can significantly change the principal squeezing feature of the single-photon-added coherent state. From the analysis of the Winger function we notice that in the strong measurement regime significant interference structures manifest and the negative regions become larger than the initial pointer state. Our results indicate that after postselected von Neumann measurement the degree of nonclassicality of single-photon-added coherent state is increased. It is anticipated that this work may provide alternate and effective methods for solving the state optimization problems based on the single-photon-added coherent state pointer via a postselected von Neumann measurement technique.

Gerard J Milburn

Qiang Hu, Taximaiti Yusufu, Yusuf Turek

State preparation via postselected weak measurements in a three-wave mixing process is studied. We assume the signal input mode is prepared in a vacuum state, coherent state, or squeezed vacuum state, while the idler input is prepared in a weak coherent state and passes the medium characterized by the second-order nonlinear susceptibility. It is shown that when the single photon is detected at one of the output channels of the idler beam's path, the signal output channel is prepared in a single-photon Fock state, single-photon-added coherent state, or single-photon-added squeezed vacuum state with very high fidelity, depending upon the input signal states and related controllable parameters. The properties of squeezing, signal amplification, second-order correlation, and the Wigner functions of the weak-measurement-based output states are also investigated. Our scheme promises to provide an alternate effective method for producing useful nonclassical states in quantum information processing.