Changing Fock matrix elements of two-mode squeezed vacuum state by employing three conditional operations in one-sided lossy channel

摘要

This paper focuses on changing Fock matrix elements of two-mode squeezed vacuum state (TMSVS) by employing three conditional operations in one-sided lossy channel. These three conditional operations include one-photon replacement (OPR), one-photon substraction (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 depend 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 {vertical bar 00 >, vertical bar 01 >, vertical bar 10 >, vertical bar 02 >, vertical bar 11 >, vertical bar 20 >} for these two-mode states. Obviously, the TMSVS only has the populations in vertical bar 00 > and vertical bar 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 vertical bar 00 > and vertical bar 11 >, and add the populations in vertical bar 10 > and vertical bar 20 >; (2) the generated state after OPS will lost the populations in vertical bar 00 > and vertical bar 11 >, but add the populations in vertical bar 10 > and vertical bar 20 >; (3) the generated state after OPA will remain the population only in vertical bar 11 > and add the population in vertical bar 01 >.