Abstract
Motivated by ideal gradiometer °ux qubit (GFQ), which suppresses coupling strength asgradient form due to geometry symmetry, we study the eRect that qubit system seriouslycouples to one or a few modes of heat bath in decoherence analysis. We set up a simplemodel to analyze this coupling form dominated by several modes of heat bath so-called thelocal coordinates coupling. In experiment, special electrical circuit in localized space or lo-calized random electromagnetic �攏ed are more reasonable and reality to be described by localcoordinates coupling. Moreover, we analyze the problem by eRectively complementary meth-ods: time dependence SchrAodinger's equation for spin part of Hamiltonian, and imaginarypath-integral method for coordinate part. During analysis, the problem could be reduced as,how to calculate the dynamics of local coordinates part with non-local in time potential com-ing from heat bath. For single mode of local coordinates coupling (system seriously couplesto only one mode of heat bath), we �曝d the bath spectral density of symmetry correlation(or so-called noise spectrum) is Lorentzian form. When the coupling modes of local coordi-nate are increase, there would be not only multiple eRect, but also mixing eRect|echo andshifting eRect|in spectral density. More than that, the real quantum correction should betaken care by Keldysh non-equilibrium Green's function. In addition, we propose a way|canonical transformation to analyze the higher eigenstates correction during truncation bytaking GFQ system as an example. And we also observe that, without carefully choosing theinitial conditions and °ux integer n, the GFQ cannot behave as a qubit.