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ACTA PHOTONICA SINICA

Nonclassical Property and Decoherence of Photon-added Chaotic Field

Lu Dao

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

Photon-added chaotic field is constructed by creation operator roling in chaotic field.Nonclassical property and decoherence of photon-added chaotic field are analysed.Master equations of density operators can be concisely solved by the technique of integration with in an ordered product of operators and virtue of thermo-entangled state representation.We get the evolution formula of the field density operator which is in photon-added chaotic field initially.The evolutions of its Wigner function and the evolutions of Prepresentation are given.The nonclassical property is discussed by calculating its Wigner function in phase space.Numerical results show that the photon-added chaotic field displays nonclassical property initially,and its nonclassical property is weakened with dissipation time increasing.On the other hand,its nonclassical property is also weakened with added photon number increasing.

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International Journal of Modern Physics B•Apr 29, 2014•9 citations
Photon-added chaotic field is constructed by creation operator roling in chaotic field.Nonclassical property and decoherence of photon-added chaotic field are analysed.Master equations of density operators can be concisely solved by the technique of integration with in an ordered product of operators and virtue of thermo-entangled state representation.We get the evolution formula of the field density operator which is in photon-added chaotic field initially.The evolutions of its Wigner function and the evolutions of Prepresentation are given.The nonclassical property is discussed by calculating its Wigner function in phase space.Numerical results show that the photon-added chaotic field displays nonclassical property initially,and its nonclassical property is weakened with dissipation time increasing.On the other hand,its nonclassical property is also weakened with added photon number increasing.
Master equations of density operators can be concisely solved by virtue of thermo entangled state representation and the technique of integration within an ordered product of operators.The solution of master equations of density operators is given.We get the Wigner function evolution formula in phase space and photon number distribution formula of the state,which is a superposition of vacuum state and single-photon state initially in laser process.By numerical calculation we plot its Wigner function and photon number distribution evolution curves,when cavity gain constant and cavity loss constant are both equal to certain values.The effect of decoherence on nonclassical property of the state is discussed by comparing negative area size and the depth of negativity of Wigner function.Numerical results show that the negativity area size and the depth of negativity of its Wigner function decrease and then vanish with dissipation.In addition,we calculate the variation of negative volume of Wigner function with dissipation time.We find that it decreases with dissipation time increasing.These results show that the nonclassical properties of the state are weakened and then disappear with dissipation time increasing.
We propose a new photon field in quantum field theory, named Laguerre-polynomial-weighted chaotic field. This field will emerge when an initial photon-added chaotic field, which is represented by its density operator [Formula: see text], dissipates in an amplitude damping channel described by time evolution equation [Formula: see text], where κ is a damping coefficient, that is, the initial field will evolve into [Formula: see text] with [Formula: see text], where Ls is the s-order Laguerre-polynomial, and : : denotes normal ordering. We employ the method of summation within an ordered product of operators to obtain our result.
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.
Based on the Kraus operator of laser theory which we derived in [2] and by virtue of the technique of integration within ordered product of operators we exactly calculate the evolving result of a chaotic field, governed by the master equation describing the laser process, we find that the initial density operator evolves into a new chaotic field, with where g and κ represent the cavity gain and loss of the laser, respectively. When g = 0, the system reduces to an amplitude dissipative channel, and f' becomes −ln [(e−f − 1) e2κt + 1]. The law of photon number decay in this process is evaluated, and the corresponding Wigner function's evolution is also demonstrated.
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.
We put forward the photon-added squeezing-enhanced thermal states (PASETS) theoretically by adding photon to the squeezed enhancing thermal states (SETS) repeatedly. Based on the normally ordered density operator of PASETS, we investigate the nonclassical behavior of the PASETS by evaluating, both analytically and numerically, Mandel's Q-parameter, photon-number distribution (PND), and Wigner function (WF). It is found that smaller squeezing parameter r and thermal photon number nc can lead to more chance of the appearance of sub-Poissonian statistics. And it is shown that the PND of PASETS exhibit more remarkable oscillations than that of SETS in stronger squeezing case. The WF exhibit partial negativity in phase space and the squeezing parameter r can result in both squeezing and rotating effect. By investigating the fidelity between PASETS and SETS shows that the fidelity tender to steady values in the high value of squeezing parameter or thermal photon number. In addition, the decoherence effect on the PASETS is examined by the time-evolution of the analytical WF in thermal channel. The results show that the PASETS shall lose nonclassicality and non-Gaussianity and reduce to classical states with Gaussian distribution after sufficient time interaction with the thermal noise. And larger photon-added number or thermal photon number shall render shorter decoherence time.