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Modern Physics Letters B

Amplified thermal state: Properties and decoherence

Zheng‐Yin Zhao, Xue-xiang Xu

Published Aug 11, 2021• 2 citations
Publisher

Abstract

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.

DOI
10.1142/s0217984921504480

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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.
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.
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.
Two “amplified” quantum states, that is, amplified coherent state (ACS) and amplified squeezed vacuum (ASV), are considered in this paper by applying operator [Formula: see text] on coherent state (CS) and squeezed vacuum (SV), respectively. Here [Formula: see text] [Formula: see text] denotes a amplification factor and [Formula: see text]) denote the creation (annihilation) operator. Along these two lines, we make a comparative analysis of properties for ACS and ASV. The considered properties include density matrix elements, Wigner function, mean photon number, second-order autocorrelation function, and quadrature squeezing. We derive analytical expressions and make numerical simulations for all the properties. The noteworthy results include: (1) the ACS has antibunching and squeezing characters; (2) the ASV will have the bunching and antibunching effect in small initial squeezing.
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.
We investigate nonclassicality and decoherence of field states generated with the non-Gaussian operation of photon addition to a two-mode squeezed thermal state (TSTS) using the normally ordered density operator of the photon-added TSTS (PTSTS). The normalization factor of the PTSTS is just a Jacobi polynomial of the squeezing parameter γ and the average photon number n¯ of the thermal field. We show that the fields in such states exhibit remarkable quantum features, such as sub-Poissonian photon statistics, the anti-bunching effect, and photon-number distribution. The nonclassicality is discussed in phase space based on the partial negativity of the Wigner function (WF) with two-variable Hermite polynomials. The results show that the non-Gaussian WF always exhibits the quantum interference structure caused by the two-mode squeezing operation and has some negative regions for any value of n¯, γ, and the photon-addition numbers m, n. In addition, the effect of decoherence on the PTSTS in the thermal channel is studied by analytically deriving the time-evolution WF. We find that the WF becomes Gaussian (corresponding to a classical thermal state) at long times, losing its nonclassicality as a result of decoherence, and a larger m (or n) leads to a longer decoherence time κt.
We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation (AC) and creation-then-annihilation operation (CA) to the thermal state (TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number, Mandel Q -parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS.