A study of excess energy and decoherence factor of a qubit coupled to a one dimensional periodically driven spin chain

Abstract

We take a central spin model (CSM), consisting of a one dimensional environmental Ising spin chain and a single qubit connected globally to all the spins of the environment, to study numerically the excess energy (EE) of the environment and the logarithm of decoherence factor namely, dynamical fidelity susceptibility per site (DFSS), associated with the qubit under a periodic driving of the transverse field term of environment across its critical point using the Floquet technique. The coupling to the qubit, prepared in a pure state, with the transverse field of the spin chain yields two sets of EE corresponding to the two species of Floquet operators. In the limit of weak coupling, we derive an approximated expression of DFSS after an infinite number of driving period which can successfully estimate the low and intermediate frequency behavior of numerically obtained DFSS. Our main focus is to analytically investigate the effect of system-environment coupling strength on the EEs and DFSS and relate the behavior of DFSS to EEs as a function of frequency by plausible analytical arguments. We explicitly show that the low-frequency beating like pattern of DFSS is an outcome of two frequencies, causing the oscillations in the two branches of EEs, that are dependent on the coupling strength. In the intermediate frequency regime, dip structure observed in DFSS can be justified by the resonance peaks of EEs at those coupling parameter dependent frequencies; high frequency saturation value of EEs and DFSS are also connected to each other by the coupling strength.

12 pages, 10 figures

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• Periodic and aperiodic dynamics of flat bands in diamond-octagon lattice
• Dynamics of decoherence of an entangled pair of qubits locally connected to a one-dimensional disordered spin chain
• Generation of concurrence between two qubits locally coupled to a one dimensional spin chain
• Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary
• Generation of concurrence in a generalized central spin model with a three-spin interacting environment