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A new kind of quantum optical state, photon-added and -subtracted displaced Fock states, is introduced by applying the inverse of bosonic creation and annihilation operators to displaced Fock states. The quantum statistical properties of these states are investigated by numerical methods. Numerical results indicate that these states reveal some interesting non-classical properties, such as anti-bunching effects, sub-Poisson distributions and negativities of their Wigner functions.

The fidelity of the generated Schrodinger Cat state (SCS) of a single trapped ion in the Lamb–Dicke approximation is discussed. The results show that the fidelity significantly decreases with the values of Lamb–Dicke parameter η and coherent state amplitude α increasing. For η = 0.20 and α = 3, the typical values of experimental parameters, the fidelity is rather low (30%). A scheme for generating the SCS is proposed without making the Lamb–Dike approximation in laser–ion interaction, and the fidelity of the generated SCS is about 99% for the typical values of experimental Lamb–Dicke parameters.

Using a new set of nucleon coupling constants CZ11 the properties of a proto neutron star are examined within the framework of the relativistic mean-field theory for the baryon octet system. It is found that the relative number density of Λ, Ξ−, and Ξ0 for CZ11 are all smaller than those for GL97 and for both CZ11 and GL97, Σ−, Σ0, and Σ+ do not appear. It is also found that the pressure and the maximum mass for CZ11 are all smaller than those for GL97. The maximum mass for CZ11 decreases by approximately 9 percent compared with that for GL97.

By applying the bosonic creation operator to squeezed vacuum states, this paper introduces a new kind of quantum states: photon-added squeezed vacuum states. It also presents an experimental approach to prepare these states, and investigates their quantum statistical properties by the numerical method. The results indicate that these states reveal some interesting non-classical properties, such as anti-bunching effects, squeezing effects and negativities of the relevant Wigner functions.