Controlled dynamics of qubits in the presence of decoherence

TL;DR

This paper presents an exactly solvable model for qubit decoherence under a time-dependent magnetic field, revealing how bath size, coupling, and field tuning influence decoherence, entanglement, and purity decay.

Contribution

It introduces a novel exactly solvable model for qubit decoherence with a dynamic magnetic field, analyzing entanglement loss and decay rates in various interaction scenarios.

Findings

Qubit polarization exhibits oscillatory power-law decay over long times.

Entanglement loss can be controlled by adjusting the rotating field's frequency.

Decay rates of entanglement and purity are identical for non-interacting qubits but differ when they interact.

Abstract

An exactly solvable model for the decoherence of one and two-qubit states interacting with a spin-bath, in the presence of a time-dependent magnetic field is studied. The magnetic field is static along $\hat{z}$ direction and oscillatory in the transverse plane. The transition probability and Rabi oscillations between the spin-states of a single qubit is shown to depend on the size of bath, the distribution of qubit-bath couplings and the initial bath polarization. In contrast to the fast Gaussian decay for short times, the polarization of the qubit shows an oscillatory power-law decay for long times. The loss of entanglement for the maximally entangled two-qubit states, can be controlled by tuning the frequency of the rotating field. The decay rates of entanglement and purity for all the Bell-states are same when the qubits are non-interacting, and different when they are interacting.