Sum and Difference Squeeze Properties of Entangle Coherent States

Yongxin Zhan Department of physics, Sichuan Agriculture university, Sichuan, Ya An, 625014, China Tel: 86-835-288-5166 E-mail: zyx073515@163.com By the national natural science foundation in key projects funded (60601005) Abstract A kind of entangle coherent states is constructed. According to dual mode field’s sum and difference operators defined by Mark Hillery, its squeezing properties are investigated by means of numerical calculation. Results show that the states appear sum and difference squeezing effect under the given conditions.


Introduction
The quantum entangle is a basic characteristics different with non-classical physics in quantum mechanics.Since entangle states have been put forward by Einstein, Podolsky (Einstein A, Podolsky B, Rosen N. 1935), Rosen and Schrödinger (Schrödinger E. 1935) to verify completeness of quantum mechanics, they have been attracting extensive attention in physical field.Recently, following the development of quantum information, the entangle states are considered as a kind of important physical resource.Up to now, they have been applied in the region such as quantum computation, teleportation (Bennett C H, Brassard G, Crepeau C, et al. 1993), dense coding (Bennett C H, Wiesner S J. 1992) and quantum key distribution (Ekert A K. 1991).
The research on non-classical effects of optical field is one of important subject in quantum optics.Squeezing effects of optical field reflects a kind of non-classic properties.They have extensive application in optical communication, high precision measurement and weak signal detection (Loudon R, Knight P L. 1987) (Wall D F. 1983).They have become focus in quantum optics.
In the paper (Zhou Lan, Kuang Leman. 2002), entangle degree, dual and single mode squeezing of entangle coherent states have studied and their relations have been discussed.In the paper (Fu H C, Wang X G, Solomon A I. 2001), the relations of entangle degree,squeezing and ant-bunching of entangle coherent states have investigated.In the paper, sum and difference squeeze effects of entangle coherent states are discussed by using sum and difference operator introduced by Mark Hillery (Hillery M. 1989).

Entangle coherent states
According to paper (Mann A, Sanders B C, Munro W J. 1995) (Wang Xiao-guang. 2002), a kind of entangle coherent states is considered where μ and ν are complex constants, and ν , N is normalized coefficient.For convenience, μ and ν are assumed real.Using complete property, N can read For convenience, the first and second mode of dual mode coherent states (1) are notated as a and b , respectively.

Sum squeezing of entangle coherent states
By the paper (Hillery M. 1989), two orthogonal hermite operators are introduced 1 2 ab a b V Where a , a + , b and b + are annihilation and creation operator of a and b mode of dual mode radiation field, respectively.They satisfy with If the inequality is right . With the view of description degree of squeeze, In order to get values of ( 8) and ( 9), according to (1), the below expressions are obtained After ( 10)-( 13) are put into (8) and ( 9), the sum squeezing properties of entangle coherent state are investigated by means of numerical calculation technique.Under μ , ν and r given certain value, some of graphs are obtained, which show squeeze degree varying with parameter δ and φ .V .In addition, 1 S and 2 S vary with ϕ and φ periodically.[ , ] 2 If the inequality is right then there is squeeze effect in optical field component i W .With the view of description degree of squeeze, From the expression (17), the squeezing degrees i S can read In order to obtain value of ( 19) and ( 20), according to (1), the below expressions are got After ( 13), ( 21)-( 24) are put into ( 19) and ( 20), the difference squeezing properties of entangle coherent state are investigated by means of numerical calculation technique.Under μ , ν and r given certain value, some of graphs are obtained, which show squeeze degree varying with parameter δ and φ .S vary with ϕ and φ periodically.

Conclusions
In the paper, a kind of entangle coherent states is introduced.According to the concepts of sum and difference operator introduced by Mark Hillery about two mode radiation field, by means of using numerical theology, non-classical properties of entangle coherent states are investigated.Results show that the entangle coherent states may appear sum and different squeezing effect under given conditions.

Figure 1 .SS
Figure 1.The sum squeezing degree S 1 vary with ϕ andφ when

Figure 4 .SSS
Figure 3.The sum squeezing degree S 3 vary with ϕ andφ when