In this paper, we introduce the space-fractional Poisson process whose state probabilities pkα(t), t≥0, α∈(0,1], are governed by the equations (d/dt)pkα(t)=−λα(1−B)αpkα(t), where (1−B)α is the fractional difference operator found in the time series analysis. We explicitly...

Maximum simultaneous squeezing and antibunching in the superposition states, |ψ〉=Z1|α〉+Z2|β〉, of two coherent states |α〉 and |β〉, where Z1,Z2,α,β are complex numbers, is studied for the case |α+β|⪢|α−β|. We show that the maximum squeezing for the operator...

We study squeezing in the most general case of superposition of two coherent states by considering 〈ψ|(ΔXθ)2|ψ〉 where Xθ=X1cosθ+X2sinθ,X1+iX2=a is annihilation operator, θ is real, |ψ〉=Z1|α〉+Z2|β〉, |α〉 and |β〉 are coherent states and Z1,Z2,α,β are complex numbers. We...