A new approach to developing the series expansion of the density operator of quantum optics is given, and the result is applied to finding the second-order polarization vector. Coherent, number, and squeezed states are each investigated and the results compared.
An analytic expression is obtained for the expansion coefficients of a single-mode squeezed coherent state in the number state (or Fock) basis. This is done by deriving a set of coupled recursion relations for the coefficients that are solved in closed form. The result coincides with that of Stoler and Yuen but the present method has the advantage (for neophytes) that it does not involve any sophisticated operator ordering techniques. Thus the present approach is suitable for inclusion in a course on quantum mechanics dealing with squeezed states.
Two “amplified” quantum states, that is, amplified coherent state (ACS) and amplified squeezed vacuum (ASV), are considered in this paper by applying operator [Formula: see text] on coherent state (CS) and squeezed vacuum (SV), respectively. Here [Formula: see text] [Formula: see text] denotes a amplification factor and [Formula: see text]) denote the creation (annihilation) operator. Along these two lines, we make a comparative analysis of properties for ACS and ASV. The considered properties include density matrix elements, Wigner function, mean photon number, second-order autocorrelation function, and quadrature squeezing. We derive analytical expressions and make numerical simulations for all the properties. The noteworthy results include: (1) the ACS has antibunching and squeezing characters; (2) the ASV will have the bunching and antibunching effect in small initial squeezing.