Acceleration and deceleration of quantum dynamics based on inter-trajectory travel with fast-forward scaling theory

In this section, we show that ITT can be used to realize shortcuts to adiabaticity. As an example, we consider the case that (omega _1


where (E(omega _1)) is the eigenenergy, and again (m,lin {1,2}) and (lne m). When (omega _1


We assume that (phi _m^{text{FF}}) also satisfies Eq. (7). Using Eqs. (7), (13) and (14), we obtain

$$begin{aligned} frac{dphi _m(omega _1



$$begin{aligned} omega _m^{text{FF}}


where again, (m,lin {1,2}) and (lne m)we assume that (film) is real. Equation (15) is used to calculate the additional phase, (f_m


where (Delta omega _0) is constant, and (T_{text{F}}) is the final time of the control.

Figure 3 shows the intensity of (beta ^{text{FF}}_{text{STA}}) defined as

$$begin{aligned} beta ^{text{FF}}_{text{STA}}(t,f_2) = frac{dphi _1(omega _1


which is the difference of the left hand side and the right hand side of Eq. (15) for (f_1

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