In this paper, we study the combined effects of the ideal amplification operator ([Formula: see text]) and m-photon added operator [Formula: see text] (or m-photon subtracted operator [Formula: see text]) on the thermal state ([Formula: see text]), with mean photon number (MPN [Formula: see text]). By only operating [Formula: see text] on [Formula: see text], we introduce a noiselessly amplified thermal state (ATS [Formula: see text]) with larger MPN [Formula: see text]. The selection of [Formula: see text] and g must ensure that the process is physical ([Formula: see text]). By operating [Formula: see text] and [Formula: see text] (or [Formula: see text]) on [Formula: see text] successively, we further introduce photon-added-ATS (ρ m+) or photon-subtracted-ATS (ρ m−). Then, we analyze their photon number distributions and prove that the purity of ρ m+ is equal to that of ρ m−. Meanwhile, we study their nonclassicality by examing Mandel parameter and second-order correlation function. Finally, we study their three quasiprobability distributions, whose negativities are other signatures of the nonclassicality. Our study demonstrates that photon addition has more pronounced effects on nonclassicality than photon subtraction. Our study will provide useful theoretical references for experiments and applications.
In this paper, we study the combined effects of the ideal amplification operator ([Formula: see text]) and m-photon added operator [Formula: see text] (or m-photon subtracted operator [Formula: see text]) on the thermal state ([Formula: see text]), with mean photon number (MPN [Formula: see text]). By only operating [Formula: see text] on [Formula: see text], we introduce a noiselessly amplified thermal state (ATS [Formula: see text]) with larger MPN [Formula: see text]. The selection of [Formula: see text] and g must ensure that the process is physical ([Formula: see text]). By operating [Formula: see text] and [Formula: see text] (or [Formula: see text]) on [Formula: see text] successively, we further introduce photon-added-ATS (ρ m+) or photon-subtracted-ATS (ρ m−). Then, we analyze their photon number distributions and prove that the purity of ρ m+ is equal to that of ρ m−. Meanwhile, we study their nonclassicality by examing Mandel parameter and second-order correlation function. Finally, we study their three quasiprobability distributions, whose negativities are other signatures of the nonclassicality. Our study demonstrates that photon addition has more pronounced effects on nonclassicality than photon subtraction. Our study will provide useful theoretical references for experiments and applications.
In this paper, we introduce the amplified thermal state (ATS) by operating [Formula: see text] on the thermal state (TS). Here, [Formula: see text] is the amplification factor and [Formula: see text] is the photon number operator. We study its properties, such as light intensity, signal-to-noise ratio (SNR), Fock matrix elements and Wigner function. In addition, we study its decoherence in photon-loss channel by analyzing evolution of all above properties. All considered properties are derived analytically and simulated numerically. Compared with the original TS, the amplification can enhance light intensity and SNR, remain the mixed character, and exhibit non-Gaussianity. While the decoherence will weaken light intensity and SNR, remain the mixed character, and return to Gaussian state.
Using the normally ordered form of thermal state characteristic of average photon number nc, we introduce the photon-added thermal state (PATS) and investigate its statistical properties, such as Mandel's Q-parameter, photon number distribution (PND), and Wigner function (WF). We then study its decoherence in a thermal environment with average thermal photon number [Formula: see text] and dissipative coefficient κ by deriving analytical expressions of the WF. The nonclassicality is discussed in terms of the negativity of the WF. It is found that the WF is always positive when [Formula: see text] for any number PATS. The expression for time evolution of the PND and the tomogram of PATS are also derived analytically, which are related to hypergeometric function and single variable Hermite polynomials.
By the use of nonclassical depth as a criterion for nonclassicality, we show that states generated by first adding (subtracting) multiphotons to an arbitrary state and then subtracting (adding) multiphotons from the resulting state is certainly nonclassical if the addition number of photons is equal to or larger than the subtraction number. The explicit expressions of nonclassical depth are found for both the single-photon-subtracted Gaussian state and the photon-added-then-subtracted thermal state. Based on the expressions, we show that the nonclassicality of the initial Gaussian state can be enhanced by the photon subtraction process. We also notice that the photon-added-then-subtracted thermal state is nonclassical if the initial thermal mean photon number is not zero, and the nonclassicality increases monotonously as the initial thermal mean photon number increases.
We investigate the nonclassicality and decoherence of a photon-subtraction-addition coherent state (a++a)m|a in a thermal environment. Its nonclassicality is discussed by deriving analytically Mandel's Q parameter, photon number distribution, and Wigner function. It is shown that if the condition |2z*+ -*|2 1 is satisfied, the Wigner function always presents the negativity for the one-order photon-subtraction-addition coherent state (m=1). Based on the evolution formula of Wigner function, we derive a compact expression for Wigner function in the thermal environment. It is found that when t(1/2)ln[(2N+2)/(2N+1)] there is no negativity for the case of m=1. In addition, the evolution of nonclassicality is discussed in terms of the negative volume of Wigner function.
We study the photon-number distributions (PND) of non-Gaussian states generated by subtracting m photons from or adding m photons to a displacement squeezed thermal state (DSTS). Compared with the PND of DSTS, PND of both m-photon-subtracted DSTS (PSDSTS) and m-photon-added DSTS (PADSTS) are modulated by a factor that is a monotonically increasing function of n, the photonnumber in the resulting non-Gaussian states. And the photon subtraction or addition essentially shifts the PND. We further demonstrate that both PND are periodic functions of the compound phase ϕ−θ/2 involved in complex squeezing and displacement parameters with a period πand exhibit more remarkable oscillations than that of DSTS. In the case of small squeezing and weak coherence, we investigate the negativity of Mandel’s Q parameter and the properties of PND of both PSDSTS and PADSTS. Our results indicate that generating new photon-number-controllable nonclassical states from a squeezed light with coherent component is effective by multiple-photon subtraction or addition when ϕ−θ/2=π/2.
State [Formula: see text] and state [Formula: see text] are same to state [Formula: see text], which is called as multi-photon-addition amplified coherent state (MPAACS) by us. Here, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] are photon number operator, creation operator, coherent state, gain factor, and an integer, respectively. We study mathematical and physical properties for these MPAACSs, including normalization, photon component analysis, Wigner function, effective gain, quadrature squeezing, and equivalent input noise. Actually, the MPAACS, which contains more nonclassicality, is an amplified version of photon-added coherent state (PACS) introduced by Agarwal and Tara [Phys. Rev. A 43, 492 (1991)]. Our work provides theoretical references for implementing amplifiers for light fields.