Back to Search
Start Over
Phase Space Analysis of the Two-mode Binomial State Produced by Quantum Entanglement in a Beamsplitter
- Source :
- International Journal of Theoretical Physics. 58:2521-2530
- Publication Year :
- 2019
- Publisher :
- Springer Science and Business Media LLC, 2019.
-
Abstract
- Phase space analysis of quantum states is a newly developed topic in quantum optics. In this work we present Wigner phase space distributions for the two-mode binomial state produced by quantum entanglement between a vacuum state and a number state in a beamsplitter. By using two new binomial formulas involving two-variable Hermite polynomials and the so-called entangled Wigner operator, we find that the analytical Wigner function for the binomial state |ξ〉q ≡ D(ξ) |q, 0〉 is related to a Laguerre polynomial, i.e., $ W\left (\sigma _{,}\gamma \right ) =\frac {(-1)^{q}e^{-\left \vert \gamma \right \vert ^{2}-\left \vert \sigma \right \vert ^{2}}}{\pi ^{2}}L_{q}\left (\left \vert \frac {-\varsigma (\sigma -\gamma )+\sigma ^{\ast }+\gamma ^{\ast }} {\sqrt {1+|\varsigma |^{2}}}\right \vert ^{2}\right ) $ and its marginal distributions are proportional to the module-square of a single-variable Hermite polynomial. Also, the numerical results show that the larger number sum q of two modes lead to the stronger interference effect and the nonclassicality of the states |ξ〉q is stronger for odd q than for even q.
- Subjects :
- Physics
Hermite polynomials
Physics and Astronomy (miscellaneous)
Binomial (polynomial)
010308 nuclear & particles physics
General Mathematics
Operator (physics)
State (functional analysis)
01 natural sciences
Quantum state
Phase space
0103 physical sciences
Laguerre polynomials
Wigner distribution function
010306 general physics
Mathematical physics
Subjects
Details
- ISSN :
- 15729575 and 00207748
- Volume :
- 58
- Database :
- OpenAIRE
- Journal :
- International Journal of Theoretical Physics
- Accession number :
- edsair.doi...........6366e58fe85b8dbe5ce8de75037727de