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

Journal of Shangluo University

Analyzing on Separability of Two Different Multi-mode Even Coherent State Light Fields

Ying Li

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The distance functions Do(rj,rj')which is between two different multi-mode even coherent state light fields is obtained by using the concept of Ludwig Kn?芽ll's et.al.defined.Based on De(rj rj'),the separability of multi-mode even coherent sate light fields is analyzed by the multi-mode coherent state light fields these build up them.

Related papers

The Distance Between Multi-mode Vacuum States and Multi-mode Coherent States

Ying Li

Based on Ludwig Knoll et. al. definition, the general distance function D(rj) between multi-mode vacuum state and multi-mode coherent state is got. A ccoding to D (rj) relationships about distance function and parameters of multi -mode vacuum state and multi -mode coherent state are discussed in this paper, differentiates of multi-mode vacuum state and multi-mode coherent state is proved.

Journal of Shangluo University•Jan 1, 2003•0 citations

The Distance Between Two Multi-mode Coherent States

Chen Yong-zhuang

The distance D(rj rj′ θj) between the two multi-mode coherent state |Z1q and |Z′2q is studied. Relationships between D(rj rj′ θj) and parameters amount D(rj rj′ θj) are discussed carefully. It is found that the size of the D(rj rj′ θj) has relation with the distance of every coherent state which displaced in complex space and it represents cyclically mutation with their initialy phases differential θ changing under some condition.

Journal of Shangluo University•Jan 1, 2002•0 citations

Multi-mode, multi-photon coherent states

Jacob Katriel, A. I. Solomon

A two-mode photon operator satisfying the canonical boson commutation relations is used to define two-mode coherent states for the Weyl, SU(2) and SU(1,l) groups. In all these cases squeezing is determined by an appropriate correlation, which we evaluate. The generalisation to multi-mode, many-photon states is indicated. In this letter we introduce a formalism for describing coherent states, tailored to the multi-mode case. We shall present the two-mode case for definiteness, although the generalisation to several modes will be obvious. Similarly, we show at the end of this note how to accommodate multi-photon states with little extra effort. States associ- ated with the Weyl group (two-mode coherent states), and the groups SU.(2) and SU(1,l) will be given; and we show that (for a specific representation) the last case reduces to the two-mode sqaeezed states of Caves and Schumaker (1986). In the conventional quantum optics approach, a mode of the electromagnetic field is represented by a creation (annihilation) operator a(at), with commutation relation (a, a') = 1. Our starting point in considering the two-mode case is to introduce a two-mode operator A analogous to the single-mode operator a. We do this by defining (Katriel and Hummer 1981) A = (max(Al, A2) + 1)'2ala2 , (1) Here al, a2 are the (annihilation) operators referring to each mode; they obey the basic commutation relation (ai, ait) = 6, but commute with each other. The number operators AI, A2 are defined in the usual way, Ai = aitai and functions of Ai will be evaluated in simultaneous eigenstates of rii, where of course they equal the functions of the corresponding eigenvalues. Now, we may show easily that (A, A') = 1. We note that AA = AtA = min(A1, h2). (The generalisation of (1) to three (or more) modes, which we shall not pursue, is immediate on replacing one of the two single-mode operators by a two-mode one.) Note that all the states defined here give variance-free single-mode operators; since At always creates equal numbers of 1 and 2 modes

Quantum Optics Journal of the European Optical Society Part B•Dec 1, 1989•3 citations

The Distance for coherent states and their superposition stetes

Gao Rong-fa

Ganeral distance function D (r,r_0,φ).between a coherent state |α_0and a superposition cpjeremt state of stidoed nu Ludwig Knll's definition.Acorrding to D (r,r_0, φ),the separabiloity relationship amount |α_0 to)and |Ψ are dicussed.It's found that the simiilitude degrees of |α_0)and |Ψ correlete wity distance of every coherent state is displaced in copmlex plane the difference of |α_0 and |Ψand superposition phase;The similitudes of odd,even and |α_0and |Ψ are studied carefully.

Journal of Shangluo University•Jan 1, 2004•0 citations

Characteristics Equal-Order N-th Y Squeezing of a New Type of Multi-mode Superposition Light Fields

HU Zhuo-rui

According to the linear superposition principle mechanics,the four-state superposition multi-mode superposition state light field |Ψ~((4))_(oe)Ⅷ〉_q is composed by multi-mode imaginary odd and complicit conjugation coherent states,and its general results of N-th power Y squeezing are got out by the multi-mode squeezing state theory.By numeric analyzing,it is found that: when parameters squeezed order N,total number of multi-mode q,average photon numbers of every mode state R~2_j and modulo of superposition probability amplitudes r_o(r_e) are taken different values,the state |Ψ~((4))_(oe)Ⅷ〉_q will represent by the equal-order N-Y minimum uncertainty states,half coherent states effect,half squeezing state effect,the first or the second orthogonal component represent N-th power Y squeezing.6 refs.

Journal of Chang'an University•Jan 1, 2006•0 citations

Equal power higher-order sum-squeezing in nonsymmetry multi-mode quantum superposition state

Meng Ji-de

Based on the superposition theory in the quantum mechanics, the nonsymmetry multi-mode Quantum superposition state light field |ψ1f(2)q is constituted by complex conjugate multi-mode coherent state light field \{zj(a)*}q and reversed state |{-Zj(b)*}q of complex conjugate multi-mode coherent state. By using higer-order squeezing theory in multi-mode state, It is studied that equal power higher-order sum-squeezing properties in the |ψ1f(2)q,it is found: 1) When Rj(a) = Rj(b) = Rj and ψj(a) - ψj(b) = ±(2k1 + 1)π(k1 = 0, 1, 2, 3, ...... ), the two quardrature phase components in the |ψ1f(2)q are all in N - H smallest uncertain state; 2) When Rj (a) = Rj(b) = Rj and ψj(a) = ψj(b) = ψj equal power higher-order sum-squeezing in \ψ1f(2)q looks like the results in the literature 3; 3) When Rj(a)#Rj(b) and ψj(a) =ψj(b) = ψj and the certain conditions are saisfied by and , The two quardrature phase components in |ψ1f(2)q all present respectively equal power higher-order oum-squeezing effect which changes periodically whether qN is odd number or even number, but squeezing-intensity under qN is odd number is bigger then squeezing-intensity under qN is even number.

Chinese Journal of Quantum Electronics•Jan 1, 2004•0 citations
The distance functions Do(rj,rj')which is between two different multi-mode even coherent state light fields is obtained by using the concept of Ludwig Kn?芽ll's et.al.defined.Based on De(rj rj'),the separability of multi-mode even coherent sate light fields is analyzed by the multi-mode coherent state light fields these build up them.
A two-mode photon operator satisfying the canonical boson commutation relations is used to define two-mode coherent states for the Weyl, SU(2) and SU(1,l) groups. In all these cases squeezing is determined by an appropriate correlation, which we evaluate. The generalisation to multi-mode, many-photon states is indicated. In this letter we introduce a formalism for describing coherent states, tailored to the multi-mode case. We shall present the two-mode case for definiteness, although the generalisation to several modes will be obvious. Similarly, we show at the end of this note how to accommodate multi-photon states with little extra effort. States associ- ated with the Weyl group (two-mode coherent states), and the groups SU.(2) and SU(1,l) will be given; and we show that (for a specific representation) the last case reduces to the two-mode sqaeezed states of Caves and Schumaker (1986). In the conventional quantum optics approach, a mode of the electromagnetic field is represented by a creation (annihilation) operator a(at), with commutation relation (a, a') = 1. Our starting point in considering the two-mode case is to introduce a two-mode operator A analogous to the single-mode operator a. We do this by defining (Katriel and Hummer 1981) A = (max(Al, A2) + 1)'2ala2 , (1) Here al, a2 are the (annihilation) operators referring to each mode; they obey the basic commutation relation (ai, ait) = 6, but commute with each other. The number operators AI, A2 are defined in the usual way, Ai = aitai and functions of Ai will be evaluated in simultaneous eigenstates of rii, where of course they equal the functions of the corresponding eigenvalues. Now, we may show easily that (A, A') = 1. We note that AA = AtA = min(A1, h2). (The generalisation of (1) to three (or more) modes, which we shall not pursue, is immediate on replacing one of the two single-mode operators by a two-mode one.) Note that all the states defined here give variance-free single-mode operators; since At always creates equal numbers of 1 and 2 modes
Ganeral distance function D (r,r_0,φ).between a coherent state |α_0and a superposition cpjeremt state of stidoed nu Ludwig Knll's definition.Acorrding to D (r,r_0, φ),the separabiloity relationship amount |α_0 to)and |Ψ are dicussed.It's found that the simiilitude degrees of |α_0)and |Ψ correlete wity distance of every coherent state is displaced in copmlex plane the difference of |α_0 and |Ψand superposition phase;The similitudes of odd,even and |α_0and |Ψ are studied carefully.
According to the linear superposition principle mechanics,the four-state superposition multi-mode superposition state light field |Ψ~((4))_(oe)Ⅷ〉_q is composed by multi-mode imaginary odd and complicit conjugation coherent states,and its general results of N-th power Y squeezing are got out by the multi-mode squeezing state theory.By numeric analyzing,it is found that: when parameters squeezed order N,total number of multi-mode q,average photon numbers of every mode state R~2_j and modulo of superposition probability amplitudes r_o(r_e) are taken different values,the state |Ψ~((4))_(oe)Ⅷ〉_q will represent by the equal-order N-Y minimum uncertainty states,half coherent states effect,half squeezing state effect,the first or the second orthogonal component represent N-th power Y squeezing.6 refs.
Based on the superposition theory in the quantum mechanics, the nonsymmetry multi-mode Quantum superposition state light field |ψ1f(2)q is constituted by complex conjugate multi-mode coherent state light field \{zj(a)*}q and reversed state |{-Zj(b)*}q of complex conjugate multi-mode coherent state. By using higer-order squeezing theory in multi-mode state, It is studied that equal power higher-order sum-squeezing properties in the |ψ1f(2)q,it is found: 1) When Rj(a) = Rj(b) = Rj and ψj(a) - ψj(b) = ±(2k1 + 1)π(k1 = 0, 1, 2, 3, ...... ), the two quardrature phase components in the |ψ1f(2)q are all in N - H smallest uncertain state; 2) When Rj (a) = Rj(b) = Rj and ψj(a) = ψj(b) = ψj equal power higher-order sum-squeezing in \ψ1f(2)q looks like the results in the literature 3; 3) When Rj(a)#Rj(b) and ψj(a) =ψj(b) = ψj and the certain conditions are saisfied by and , The two quardrature phase components in |ψ1f(2)q all present respectively equal power higher-order oum-squeezing effect which changes periodically whether qN is odd number or even number, but squeezing-intensity under qN is odd number is bigger then squeezing-intensity under qN is even number.