Shortcuts to Adiabaticity by Counterdiabatic Driving

The evolution of a system induced by counterdiabatic driving mimics the adiabatic dynamics without the requirement of slow driving. Engineering it involves diagonalizing the instantaneous Hamiltonian of the system and results in the need of auxiliary nonlocal interactions for matter waves. Here, experimentally realizable driving protocols are found for a large class of single-particle, many-body, and nonlinear systems without demanding the spectral properties as an input. The method is applied to the fast decompression of Bose-Einstein condensates in different trapping potentials.

Figure 1

Shortcut to adiabaticity by counterdiabatic driving. The time-dependent frequency $\omega (t)$ (solid line) in Eq. (25) does not suffice to fulfill adiabaticity in a finite time $t_F$. The necessary counterdiabatic driving of the trap frequency $\Omega (t)$ for a shortcut to an adiabatic expansion is given by Eq. (22) and is displayed here for three different values of $t_F$ (symbols), for an expansion factor $\gamma (t_F)=2$. The values of the product ${\omega }_0{t}_F$ correspond to the onset of the adiabatic limit (open circle), a moderate speedup (open square), and an ultrafast expansion (diamond).