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Journal of Shangluo University

The Distance for coherent states and their superposition stetes

Gao Rong-fa

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

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.

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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.
Based on the Ludwig Knll s general definition of distance function of which is between two quantum states, the general distance function between the two coherent state |β1,|β2 , vacuum state and coherent state are studied. The relationships amount this distance and the parameters of states are discussed carefully. It is find that the similitude degrees of states |β1 and |β2 correlate with distance of every distance which is moved in complex space, and D(β1,β2) represents cyclically mutation with their initially phases differential Δ θ changing under some condition.If distance is displaced very small, coherent state is same as vacuum state.
In this paper we will study the statistical properties of a generalized superposition of two displaced number states of the form, [Formula: see text] with a phase difference of φ between them. A particular case of this state is obtained when we consider n1=n2=n and α1=-α2=α, which we will call even and odd displaced number state. It will be shown that they are the generalization of the even and odd coherent states. The generation of this states, based on the dispersive interaction with a two-level atom, will also be discussed.
We study the decoherence of even and odd superpositions of displaced number states in the frameworks of the standard master equation, describing phase insensitive attenuators and amplifiers. We compare different possible definitions of the ‘decoherence time’ and show that the frequently used approaches based on the time derivatives of some quantities (such as the ‘quantum purity’), taken at the initial moment, are not quite satisfactory for quantum states characterized by several parameters, due to the absence of the scaling laws. Defining the conditional decoherence time as the time necessary for diminishing the interference peak of the Wigner function to the given relative level, we study its dependence on the initial distance between peaks |α|, excitation number m and parameters of the reservoir. We show that highly excited states with can be more robust against decoherence than the coherent superpositions with m = 0.