3.4.2. Frequency Dependence

We show in Figure 3 the frequency dependence of the pumped quantity ˆ *<sup>I</sup>*energy = 1 T *h*¯ *ω*0 (<sup>Δ</sup>*q<sup>R</sup>* − <sup>Δ</sup>*q<sup>L</sup>*). For comparison, we also exhibit the frequency dependence of the quantity under the adiabatic approximation presented as a geometric phase in Reference [28]. We find that the nonadiabatic term decreases the pumped quantity in the higher frequency region. We also find that the pumped quantity depends on the initial condition of the two-level system. The feature shown in Figure 3 is universal for different settings of these parameters. For example, when we increase *τr* by decreasing the coupling strength with keeping the value of *ω*0, we find the similar feature of the frequency dependence ranging up to ∼10 GHz which corresponds to the maximum driving frequency of electronic voltage due to the limitation of experimental bandwidth at the present time. The parameter setting of *λ* in this study is chosen to expect the further acceleration of the recent rapid development of Tera Hz technology in a future.

**Figure 3.** (Color online) Frequency dependence of pumped quantity *<sup>I</sup>*energy with *λ* = 0.01, *ωc* = 3*<sup>ω</sup>*0, and *h*¯ *ω*0 = 25 meV with changing initial conditions of the two-level system *β* ¯ *s* values: (1) the black line corresponds to *β* ¯ *s* = *β* ¯(0)(≈1.07) which is the effective inverse temperature of the stationary state for the initial temperature setting, (2) the blue dotted line to *β* ¯ *s* = 5; (3) the red dottdashed line represents the frequency dependence of the net geometrical phase [28].
