Transitionless Quantum Driving (Shortcut to Adiabaticity) via Judicious Coupling to Suitably Fluctuating External Fields

For a quantum system driven by a time-dependent Hamiltonian $H_0(t)$, Berry has shown that complete suppression of transitions between its instantaneous eigenstates is always possible via the addition of an auxiliary term to the Hamiltonian, $H_1(t)$, determined by $H_0(t)$. The resulting quantum evolution (driven by $H_0+H_1$), referred to as transitionless quantum driving (TQD), is then exactly adiabatic with respect to the instantaneous eigenstates of $H_0(t)$. We report an alternative way of achieving TQD, via the coupling of the quantum system to an external fluctuating field, with coupling parameter $J(t)$ and external field correlators (EFC) properly chosen. Averaging over the external field yields TQD with respect to the original quantum system. To illustrate this result, we explore the suppression of the Schwinger pair-creation effect in a (1+1)D gas of Dirac fermions coupled to a time-dependent electric field $E(t)$. We show that to completely suppress the Schwinger effect requires $J\propto\sqrt{E}$, and the EFCs to mimic the correlators of a 'partner' system of the original system. This partner shares properties with the SUSY partner of the Dirac fermions, suggesting a possible connection between TQD and a modified SUSY that needs to be explored further.