Based on N different coherent states with equal weights and phase-space rotation symmetry, we introduce N-headed incoherent superposition states (NHICSSs) and N-headed coherent superposition states (NHCSSs). These N coherent states are associated wit
h N-order roots of the same complex number. We study and compare properties of NHICSSs and NHCSSs, including average photon number, Mandel Q parameter, quadrature squeezing, Fock matrix elements and Wigner function. Among all these states, only 2HCSS (i.e., Schrodinger cat state) presents quadrature-squeezing effect. Our theoretical results can be used as a reference for researchers in this field.
This paper focuses on changing Fock matrix elements of two-mode squeezed vacuum state (TMSVS) by employing three quantum operations in one-sided lossy channel. These three quantum operations include one-photon replacement (OPR), one-photon substracti
on (OPS) and one-photon addition (OPA). Indeed, three conditional quantum states have been generated from the original TMSVS. Using the characteristic function (CF) representation of quantum density operator, we derive the analytical expressions of their Fock matrix elements, which are dependent on the interaction parameters, including the squeezing parameter of the input TMSVS, the loss factor and the transmissivity of the variable beam splitter. For convenience of discussion, we only give the Fock matrices in the subspace span {|00>,|01>,|10>,|02>,|11>,|20>} for these two-mode states. Obviously, the TMSVS only has the populations in |00> and |11> in such subspace. By comparing the generated states with the TMSVS, we find that: (1) The generated state after OPR will remain the populations in |00> and |11>, and add the populations in |10> and |20>; (2) The generated state after OPS will lost the populations in |00> and |11>, but add the populations in |10> and |20>; (3) The generated state after OPA will remain the population only in |11> and add the population in |01>.
Evolution formulas of the density operator, the photon number distribution, and the Wigner function are derived for the problem on the optical fields propagation in realistic environments. The method of deriving these formulas is novel and the result
s are very useful for quantum optics and quantum statistics.
We theoretically generate nonclassical states from coherent state heralded by Knill-Laflamme-Milburn (KLM)-type SU(3) interference. Injecting a coherent state in signal mode and two single-photon sources in other two auxiliary modes of SU(3) interfer
ometry, a broad class of useful nonclassical states are obtained in the output signal port after making two single-photon-counting measurements in the two output auxiliary modes. The nonclassical properties, in terms of anti-bunching effect and squeezing effect as well as the negativity of the Wigner function, are studied in detail by adjusting the interaction parameters. The results show that the input coherent state can be transformed into non-Gaussian states with higher nonclassicality after measurement induction. The maximum squeezing of our generated states can be arrived at about 1.9 dB.
