Photon-number and wait-time distributions are studied for superposed coherent states (SCS), and superposed squeezed-vacuum states (SSVS). The odd-cat (even-cat) states always show antibunching (bunching), generalized SCS show bunching and antibunching, and SSVS always show bunching.
We study the statistical properties in the superpositions of SU(1,1) coherent states |ζ,k〉and |ζ,k〉. The even SU(1,1) coherent state (|ζ,1/4〉) and odd SU(1,1) coherent state (|ζ,3/4〉) correspond to squeezed vacuum state and squeezed one photon number state, respectively. It is shown that the superposed states can exhibit much stronger squeezing and antibunching for the suitable phase of ζ and the relative phase in superposition. We also propose a method of generating such superposed states.
The generalized inverses of q -boson operators denoted by are introduced via their acting on the q -number states. The even and odd number eigenstates of two photon operators are constructed. It is shown that these states can show quantum-squeezing. However, their even number states always show quantum-antibunching, while their odd number states always show quantum-bunching. This result is different from that in recent paper (C.L. Mehta, A.K. Roy and G.M. Saxena, Phys. Rev. A46 (1992) 1565) where the odd number eigenstates of operators with q ≡ 1 show bunching for some parameter values and antibunching for other parameter values.
From the normally ordered form of the density operator of a squeezed coherent state(SCS),we directly derive the compact expression of the SCS’s photon-number distribution(PND).Besides the known oscillation characteristics,we find that the PND is a periodic function with a period of π and extremely sensitive to phase.If the squeezing is strong enough,and the compound phase which is relevant to the complex squeezing and displacement parameters are assigned appropriate values,different oscillation behaviours in PND for even and odd photon numbers appear,respectively.