Schematics of a TLS (blue, central spin) coupled to a spin bath and a boson bath. The spin bath, which has no intrabath interactions, interacts uniformly via Ising-like coupling to the TLS. Both the TLS and the spin bath are coupled to the boson bath via conventional linear spin-boson coupling.
Steady-state probability of finding the TLS in its up state as a function of the T-S coupling strength γ after prepared in the down state initially. Parameters used are ɛ = J = α = 1, T = 0.5, N = 10, and ω c = 2.
The TLS polarization ⟨σ z ⟩(t) as a function of time t and the T-S coupling strength γ for two values of κ2: κ2 = 0 (upper) and κ2 = 0.02 (lower). κ1 = 0.05 and other parameters are the same as those in Fig. 2 .
Time-dependent magnitudes of matrix elements |Θ++| (red), |Θ+−| = |Θ−+| (green), and |Θ−−| (blue). Parameters chosen: N = 10, J = 0.1, α = 0, ω c = 1, β = 100, and κ3 = 0.5. The dotted lines are calculated in the absence of the TLS 16 and τMQS = 1.685.
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