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

Chinese Physics B

Optical field's quadrature excitation studied by new Hermite-polynomial operator identity

Hong-Yi Fan, Rui He, Cheng Da, Zu-feng Liang

Published Aug 1, 2013• 5 citations
Publisher

Abstract

We study the optical field's quadrature excitation state X m |0〉, where X = ( a + a † )/√2 is the quadrature operator. We find it is ascribed to the Hermite-polynomial excitation state. For the first time, we determine this state's normalization constant which turns out to be a Laguerre polynomial. This is due to the integration method within the ordered product of operators (IWOP). The normalization for the two-mode quadrature excitation state is also completed by virtue of the entangled state representation.

DOI
10.1088/1674-1056/22/8/080301

Related papers

ENTANGLED STATE REPRESENTATION, NEW TWO-VARIABLE HERMITE-POLYNOMIAL-OPERATOR IDENTITIES FOR TWO-MODE QUADRATURE'S PHYSICAL QUANTITY CALCULATION

Hong-Yi Fan, Jieyu Jiang

By virtue of the entangled state representation and the technique of integration within an ordered product (IWOP) of operators we derive some new two-variable Hermite-polynomial-operator identities, their application for calculating moment and cumulant for two-mode quadratures in quantum field theory are presented. The new operator identities make all calculations neat and concise.

Modern Physics Letters A•Dec 2, 2011•3 citations

New operator identities with regard to the two-variable Hermite polynomial by virtue of entangled state representation

Hong‐Chun Yuan, Heng-Mei Li, Xuefen Xu

By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.

Chinese Physics B•Jun 1, 2013•8 citations

Entangled state representation for deriving new operator identities regarding to two-variable Hermite polynomial

Hong-Yi Fan, Hong-chun Yuan

In this paper, by virtue of the entangled state representation we concisely derive some new operator identities regarding to two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.

arXiv:1011.5943•Nov 27, 2010•0 citations

A new kind of special function and its application

Hong-Yi Fan, Zhi-Long Wan, Ze Wu +1 more

By virtue of the operator Hermite polynomial method and the technique of integration within the ordered product of operators we derive a new kind of special function, which is closely related to one- and two-variable Hermite polynomials. Its application in deriving the normalization for some quantum optical states is presented.

Chinese Physics B•Sep 29, 2015•7 citations

New operator-ordering identities and associative integration formulas of two-variable Hermite polynomials for constructing non-Gaussian states

Hong-Yi Fan, Zhen Wang

For directly normalizing the photon non-Gaussian states (e.g., photon added and subtracted squeezed states), we use the method of integration within an ordered product (IWOP) of operators to derive some new bosonic operator-ordering identities. We also derive some new integration transformation formulas about one- and two-variable Hermite polynomials in complex function space. These operator identities and associative integration formulas provide much convenience for constructing non-Gaussian states in quantum engineering.

Chinese Physics B•Jul 31, 2014•5 citations

New Applications of Two-mode Hermite Polynomials in Quantum Optics Theory

Fan Hong‐Yi

We emphasize the importance of two-mode Hermite poly-nomials in quantum optics theory,we consider it as the prominent function in studying the entangled state of continuum variables and two-mode squeezed state,and that possesses a clear physical meaning.By virtue of the two-mode Hermite polynomials and combining operators' integration technique within normal and antinormal orderings,we derive some new operator identities and mutual invertible integration transformation,and prove that squeezed two-mode number state is just the two-mode Hermite polynomial excited squeezed two-mode vacuum state.

Acta Sinica Quantum Optica•Jan 1, 2012•0 citations
We study the optical field's quadrature excitation state X m |0〉, where X = ( a + a † )/√2 is the quadrature operator. We find it is ascribed to the Hermite-polynomial excitation state. For the first time, we determine this state's normalization constant which turns out to be a Laguerre polynomial. This is due to the integration method within the ordered product of operators (IWOP). The normalization for the two-mode quadrature excitation state is also completed by virtue of the entangled state representation.
By virtue of the entangled state representation we concisely derive some new operator identities with regard to the two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of the TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.
In this paper, by virtue of the entangled state representation we concisely derive some new operator identities regarding to two-variable Hermite polynomial (TVHP). By them and the technique of integration within an ordered product (IWOP) of operators we further derive new generating function formulas of TVHP. They are useful in quantum optical theoretical calculations. It is seen from this work that by combining the IWOP technique and quantum mechanical representations one can derive some new integration formulas even without really performing the integration.
For directly normalizing the photon non-Gaussian states (e.g., photon added and subtracted squeezed states), we use the method of integration within an ordered product (IWOP) of operators to derive some new bosonic operator-ordering identities. We also derive some new integration transformation formulas about one- and two-variable Hermite polynomials in complex function space. These operator identities and associative integration formulas provide much convenience for constructing non-Gaussian states in quantum engineering.
We emphasize the importance of two-mode Hermite poly-nomials in quantum optics theory,we consider it as the prominent function in studying the entangled state of continuum variables and two-mode squeezed state,and that possesses a clear physical meaning.By virtue of the two-mode Hermite polynomials and combining operators' integration technique within normal and antinormal orderings,we derive some new operator identities and mutual invertible integration transformation,and prove that squeezed two-mode number state is just the two-mode Hermite polynomial excited squeezed two-mode vacuum state.