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Wigner Distribution Function and Husimi Function of a Kind of Squeezed Coherent State

Fan Hong‐Yi, Liu Shu-Guang

We find a new κ-parameter squeezed coherent state | p , q ⟩ κ representation, which possesses well-behaved features, i.e., its Wigner function's marginal distribution in the `` q -direction'' and in the `` p -direction'' is the Gaussian form exp {−κ( q '− q ) 2 }, and exp {( p '− p ) 2 /κ}, respectively. Based on this, the Husimi function of | p , q ⟩ κ is also obtained, which is a Gaussian broaden version of the Wigner function. The | p , q ⟩ κ state provides a good representative space for studying various properties of the Husimi operator.We find a new κ-parameter squeezed coherent state | p , q ⟩ κ representation, which possesses well-behaved features, i.e., its Wigner function's marginal distribution in the `` q -direction'' and in the `` p -direction'' is the Gaussian form exp {−κ( q '− q ) 2 }, and exp {( p '− p ) 2 /κ}, respectively. Based on this, the Husimi function of | p , q ⟩ κ is also obtained, which is a Gaussian broaden version of the Wigner function. The | p , q ⟩ κ state provides a good representative space for studying various properties of the Husimi operator.

Communications in Theoretical PhysicsMar 1, 200712 citations

New Application of Weyl Correspondence in Studying Husimi Operator

Fan Hong‐Yi, Qin Guo, Ma Shan-Jun

In this paper, the so-called Husimi operator Δ h ( q , p ; κ), which is introduced by smoothing out the Wigner operator Δ w ( q , p ) by averaging over the "coarse graining" function exp[-κ( q '- q ) 2 - ( p ' - p ) 2 /κ], is now regarded as a Weyl correspondence connecting the Husimi operator Δ h ( q , p ; κ) with its classical correspondence, since the integration kernel is just the Wigner operator. In this way we can easily identify | p , q ;κ⟩ such that Δ h ( q , p ;κ) = | p , q ;κ⟩ ⟨ p , q ;κ|, where | p , q ; κ⟩ is a new kind of squeezed coherent states. The entangled Husimi operator is also treated in this way. Thus a simple way to find the Husimi operator is presented.In this paper, the so-called Husimi operator Δ h ( q , p ; κ), which is introduced by smoothing out the Wigner operator Δ w ( q , p ) by averaging over the "coarse graining" function exp[-κ( q '- q ) 2 - ( p ' - p ) 2 /κ], is now regarded as a Weyl correspondence connecting the Husimi operator Δ h ( q , p ; κ) with its classical correspondence, since the integration kernel is just the Wigner operator. In this way we can easily identify | p , q ;κ⟩ such that Δ h ( q , p ;κ) = | p , q ;κ⟩ ⟨ p , q ;κ|, where | p , q ; κ⟩ is a new kind of squeezed coherent states. The entangled Husimi operator is also treated in this way. Thus a simple way to find the Husimi operator is presented.

Communications in Theoretical PhysicsJan 1, 20080 citations

The Wigner Function and the Husimi Function of the One- and Two-Mode Combination Squeezed State

Qin Guo

International Journal of Theoretical PhysicsJun 5, 20075 citations

Husimi operator and Husimi function for describing electron's probability distribution in uniform magnetic field derived by virtue of the entangled state representation

Hong-Yi Fan, Qin Guo

For the first time we introduce the Husimi operator Delta_h(gamma,varepsilon;kappa) for studying Husimi distribution in phase space(gamma,varepsilon) for electron's states in uniform magnetic field, where kappa is the Gaussian spatial width parameter. Using the Wigner operator in the entangled state |lambda> representation [Hong-Yi Fan, Phys. Lett. A 301 (2002)153; A 126 (1987) 145) we find that Delta_h(gamma,varepsilon;kappa) is just a pure squeezed coherent state density operator |gamma,varepsilon>_kappa kappaFor the first time we introduce the Husimi operator Delta_h(gamma,varepsilon;kappa) for studying Husimi distribution in phase space(gamma,varepsilon) for electron's states in uniform magnetic field, where kappa is the Gaussian spatial width parameter. Using the Wigner operator in the entangled state |lambda> representation [Hong-Yi Fan, Phys. Lett. A 301 (2002)153; A 126 (1987) 145) we find that Delta_h(gamma,varepsilon;kappa) is just a pure squeezed coherent state density operator |gamma,varepsilon>_kappa kappa

arXiv:quant-ph/0611206Nov 20, 20061 citation

Quantum State Generated by Parity-Squeezing Combinatorial Operator and Its Wigner Function and Husimi Function

Jian-ming Du, Hai-jun Yu, Zhongquan Wang +1 more

International Journal of Theoretical PhysicsNov 19, 20100 citations

A Kind of Atomic Coherent State as a Two-Mode Squeezed State

Ma Shan-Jun, Wang Shu-Jing

We find that a kind of atomic coherent state, formed as exp[ξJ + – ξ*J − ] |00〉, when the SU(2) generators J± are taken as Fan's form, J + = (1/2)(a 1 – a 2 † )(a 1 † – a 2 ), J − = (1/2)(a † 1 + a 2 ) (a 1 + a 2 † ), and J 0 = (1/2)(a 1 † a 2 † – a 1 a 2 ), is simultaneously a two-mode squeezed state. We analyse this squeezed state's physical properites, such as the cross-correlation function, the Wigner function, and its marginal distribution as well as the Husimi function.We find that a kind of atomic coherent state, formed as exp[ξJ + – ξ*J − ] |00〉, when the SU(2) generators J± are taken as Fan's form, J + = (1/2)(a 1 – a 2 † )(a 1 † – a 2 ), J − = (1/2)(a † 1 + a 2 ) (a 1 + a 2 † ), and J 0 = (1/2)(a 1 † a 2 † – a 1 a 2 ), is simultaneously a two-mode squeezed state. We analyse this squeezed state's physical properites, such as the cross-correlation function, the Wigner function, and its marginal distribution as well as the Husimi function.

Communications in Theoretical PhysicsSep 1, 20090 citations

Wigner Distribution Function and Husimi Function of a Kind of Squeezed Coherent State

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Wigner Distribution Function and Husimi Function of a Kind of Squeezed Coherent State

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