Detection of Physics in Environment by a Central Qubit

A weak noise can be detected by monitoring decoherence of a central spin under many-pulse dynamical decoupling control. We present the method to detect a low frequency noise that has a broadened noise spectrum instead of a delta one, which is much more common to occur in realistic systems. We study both the classical and quantum cases, and give the parameters range that is optimal for the detection. The sensitivity is calculated to determine the optimal pulse number of dynamical decoupling in experiments.;Quantum criticality is a very important critical phenomenon which accompany quantum phase transition. Quantum criticality is usually observed only at a very low temperature because the thermal fluctuation is much larger than the quantum part due to the weak quantum interaction. But with the help of dynamical decoupling technique, we may be able to observe the quantum criticality at a high temperature. We employ the exactly-solvable one-dimension transverse-field Ising model as the bath and couple it with a probe spin to illustrate the idea. We show the advantages of CPMG method in the application of revealing the quantum criticality at high temperature.;We also attempt to use the Landau-Zener tunneling of a qubit as a probe to the quantum criticality at high temperature due to the fact that the tunneling probability is insensitive to the static noise. In order to realize the idea, we study the Landau-Zener tunneling model and its standard solution. Then a Hamiltonian designed for illustrating the idea is given and a corresponding solution is provided, which gives the possibility of using the Landau-Zener tunneling as a probe.