Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2304.05324 · Journal of Modern Optics

Non-classicality of photon-added-then-subtracted and photon-subtracted-then-added states

Arpita Chatterjee

Published Mar 16, 2012• 8 citations
arXivHTMLPDF

Abstract

We formulate the density matrices of a quantum state obtained by first adding multi-photons to and then subtracting multi-photons from any arbitrary state as well as performing the same process in the reverse order. Considering the field to be initially in a thermal (or in an even coherent) state, we evaluate the photon number distribution, Wigner function and Mandel's Q parameter of the resulting field. We show graphically that the order in which multi-photons are added and subtracted has a noticeable effect on the temporal behavior of these statistical properties.

DOI
10.1080/09500340.2012.670278

Related papers

Nonclassicality of photon-subtracted and photon-added-then-subtracted Gaussian states

Yang Yang, Fuli Li

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.

Journal of the Optical Society of America B•Mar 27, 2009•46 citations

Nonclassicality of the photon addition-then-subtraction coherent state and its decoherence in the photon-loss channel

Zhen Wang, Hong‐Chun Yuan, Hong-Yi Fan

In this paper the photon addition-then-subtraction coherent state (PASCS) is put forward by first adding multiphotons to and then subtracting multiphotons from the coherent state. By taking advantage of the technique of integration within an ordered product of operators, the analytical expressions of the normalization constant, photon-number distribution, Mandel’s Q parameter, the P function, the Q function, and the Wigner function (WF) of the PASCS are derived. The fidelity between the PASCS and the initial coherent state is also deduced and its nonclassicality discussed. In addition, the time evolution of the WF is derived analytically and the decoherence of the PASCS in the photon-loss channel is studied.

Journal of the Optical Society of America B•Jul 19, 2011•34 citations

Nonclassicality of Any Number Photon Added-then-subtractedand Subtracted-then-added Coherent States

廖小鸽 LIAO Xiao-ge, 张浩亮 ZHANG Hao-liang, 胡利云 HU Li-yun

We study the nonclassical properties of arbitrary number photon creation-then-annihilation operation(CA) and annihilation-then-creation operation(AC) to the coherent states,and give the analytical expression.Because of the noncoummutativity of between annihilation operator and the creation operator,the states generated by AC operation and CA operation have different nonclassical properties.We firstly derive the analytical expressions of normalization factor for these states,and then study the statistics characteristics by some nonclassical properties,such as the Mandel Q parameters,the photon number distribution and the Wigner function.It is shown that these states have a very distinct nonclassical properties,and the nonclassical state generated by AC operation can present more clear nonclassicality than those generated by the CA operation.

Acta Sinica Quantum Optica•Jan 1, 2013•0 citations

NONCLASSICALITY AND DECOHERENCE OF PHOTON-ADDED THERMAL STATE

Wang Shu-Jing, Xue-xiang Xu, Ma Shan-Jun

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.

International Journal of Quantum Information•Dec 1, 2010•1 citation

Photon-added and photon-subtracted displaced Fock states and their non-classical properties

Si Kun, Miao Zhang, Jia Huan-Yu

A new kind of quantum optical state, photon-added and -subtracted displaced Fock states, is introduced by applying the inverse of bosonic creation and annihilation operators to displaced Fock states. The quantum statistical properties of these states are investigated by numerical methods. Numerical results indicate that these states reveal some interesting non-classical properties, such as anti-bunching effects, sub-Poisson distributions and negativities of their Wigner functions.

Chinese Physics B•Nov 1, 2009•3 citations

Photon-number distributions of non-Gaussian states generated by photon subtraction and addition

Shuai Wang, Hong-Yi Fan, Liyun Hu

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.

Journal of the Optical Society of America B•Apr 23, 2012•16 citations
We formulate the density matrices of a quantum state obtained by first adding multi-photons to and then subtracting multi-photons from any arbitrary state as well as performing the same process in the reverse order. Considering the field to be initially in a thermal (or in an even coherent) state, we evaluate the photon number distribution, Wigner function and Mandel's Q parameter of the resulting field. We show graphically that the order in which multi-photons are added and subtracted has a noticeable effect on the temporal behavior of these statistical properties.
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.
In this paper the photon addition-then-subtraction coherent state (PASCS) is put forward by first adding multiphotons to and then subtracting multiphotons from the coherent state. By taking advantage of the technique of integration within an ordered product of operators, the analytical expressions of the normalization constant, photon-number distribution, Mandel’s Q parameter, the P function, the Q function, and the Wigner function (WF) of the PASCS are derived. The fidelity between the PASCS and the initial coherent state is also deduced and its nonclassicality discussed. In addition, the time evolution of the WF is derived analytically and the decoherence of the PASCS in the photon-loss channel is studied.
We study the nonclassical properties of arbitrary number photon creation-then-annihilation operation(CA) and annihilation-then-creation operation(AC) to the coherent states,and give the analytical expression.Because of the noncoummutativity of between annihilation operator and the creation operator,the states generated by AC operation and CA operation have different nonclassical properties.We firstly derive the analytical expressions of normalization factor for these states,and then study the statistics characteristics by some nonclassical properties,such as the Mandel Q parameters,the photon number distribution and the Wigner function.It is shown that these states have a very distinct nonclassical properties,and the nonclassical state generated by AC operation can present more clear nonclassicality than those generated by the CA operation.
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 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.