$T_2^{(\rm s)}$: the relaxation time constant of the signal in the selective-decoupling case, and $T_1$(HSs): the longitudinal relaxation time constant of HSs’ spins.

In the full-decoupling case, small but not negligible direct influence of the Markovian environment on CC should be observed. $T_1$’s of CC in Table \[FID\_tc\] are inversely proportional to the magnetic impurity concentration $C_{\rm m}$ which implies that this $T_1$ is determined by the impurity [@Iwakura2017]. On the other hand, in the selective-decoupling case, the interaction between CC and the Markovian environment through HSs (system II) should be added although it is expected to be small. Therefore, we obtain the engineered environment which consists of 6 spins + Markovian Environment and that it causes a non-exponential decay of CC [@Binho2019]. We note, however, that the large interactions between CC and CSs ($J^{\rm (CC, CSs)}=2\pi \cdot 34$ rad/s) compared with those between CC and HSs ($J^{\rm (CC, HSs)}=2\pi \cdot 4.4$ rad/s) prevent from observing the above subtle non-exponential dynamics.

![(Color online) FID signals of Sample 1, 2, 3, and 4 in Table \[FID\_tc\]. The initial states were $\displaystyle |+\rangle \langle + | \otimes
\left( |01\rangle \langle 01 |
    +  |10\rangle \langle 10 | \right).
$ The real parts 