Exact Decay and Control Dynamics of a Qubit
Engineered environments with tunable coupling strengths show great potential for fast and accurate qubit initialization. However, the estimates for speed and fidelity for the existing initialization protocols have been made under the assumption of weak coupling. We use exact numerical methods to study the strong bath-coupling effects to the qubit decay that affect these figures of merit and are typically neglected in the conventional Born-Markov master equations. We find that there exists a fundamental trade-off between fast and accurate qubit initialization which has to be taken into account in the initialization-protocol design. This is caused by the unavoidable entanglement between the qubit and the bath which generates a steady state that can deviate significantly from the Boltzmann distribution of the bare and even the Lamb shifted qubit. We also show that the qubit decay is superexponential at a short time scale, contrary to the perturbative and coarse-grained master equations. Our results can be used in the development of quantum devices with engineered environments and steer the future experiments towards probing the properties of the reservoir.