Noiselessly amplified thermal states and after multi-photon addition or subtraction

Abstract

In this paper, we introduce a noiselessly amplified thermal state (ATS), by operating the noiseless amplification operator ($g^{\hat{n}}$) on the thermal state (TS) with corresponding mean photon number (MPN) $\bar{n}$. Actually, the ATS is an new TS with MPN $\bar{N}=g^2\bar{n}/[1-\bar{n}\left(g^2-1\right)]$. Furthermore, we introduce photon-added-ATS (PAATS) and photon-subtracted-ATS (PSATS) by operating $m$-photon addition (${\hat{a}}^{†m}$) and $m$-photon subtraction (${\hat{a}}^m$) on the ATS, respectively. We study photon number distributions (PNDs), purities, and Wigner functions (WFs) for all these states.

8 pages, 8 figures