Nano ölçekli spin hamamları için en altyapı ve dörtkutup etkileşimleri altında Loschmidt yankısı

Environmental dynamics in solid state matrix is of much importance for quantum information processing and storage purposes. Here, we first give a basic recipe to get Loschmidt echo (LE) which is a measure of decoherence (loss of information from the qubit) in heterogeneously interacting nuclear spin bath (NSB) in the presence of Fermi-contact hyperfine and nuclear spin dipole-dipole interactions. Then, by dropping the latter we discuss the basic dependencies of pure-dephasing regime on size, initial polarization, hyperfine coupling inhomogeneity, spin quantum number in nuclear spin environments, and arrive at a phenomenological expression that governs all these attributes. For NSBs consisting of spin-$I\geq 1$, the effect of nuclear electric quadrupole interaction is also considered where its biaxiality term has an influence on the decoherence process. Furthermore, a general decoherence channel is also employed to see how phase-flip rate affects LE. After insights gained from these models, we consider two generic realistic systems, namely, donor center and quantum dot and explain the power spectral density of LE in these cases.