Time-Rescaling of Dirac Dynamics: Shortcuts to Adiabaticity in Ion Traps and Weyl Semimetals

Abstract

Only very recently, rescaling time has been recognized as a way to achieve adiabatic dynamics in fast processes. The advantage of time-rescaling over other shortcuts to adiabaticity is that it does not depend on the eigenspectrum and eigenstates of the Hamiltonian. However, time-rescaling requires that the original dynamics are adiabatic, and in the rescaled time frame, the Hamiltonian exhibits non-trivial time-dependence. In this work, we show how time-rescaling can be applied to Dirac dynamics, and we show that all time-dependence can be absorbed into the effective potentials through a judiciously chosen unitary transformation. This is demonstrated for two experimentally relevant scenarios, namely for ion traps and adiabatic creation of Weyl points.

Shortcuts in stochastic systems and control of biophysical processes

“…To keep the system on target, we need to use one of the CD concentration protocols given by Eq. (43). For example, consider the one associated with tree 1, which means setting Φ 1 (t) = 0 at all t, so that from Eq.…”

“…In recent years a great deal of theoretical and experimental work has been dedicated to mathematical tools and practical schemes to suppress nonequilibrium excitations in finite-time, nonequilibrium processes. To this end, a variety of techniques have been developed: the use of dynamical invariants [20], the inversion of scaling laws [21], the fast-forward technique [22][23][24][25][26][27][28][29], optimal protocols from optimal control theory [30][31][32][33], optimal driving from properties of quantum work statistics [34], "environment" assisted methods [35], using the properties of Lie algebras [36], and approximate methods such as linear response theory [37][38][39][40], fast quasistatic dynamics [41], or time-rescaling [42,43], to name just a few. See Refs.…”

Environment-Assisted Shortcuts to Adiabaticity

“…Recent years have seen an explosion of work on, for instance, counterdiabatic driving [12][13][14][15][16][17][18][19], the fast-forward method [20][21][22][23], time-rescaling [24,25], methods based on identifying the adiabatic invariant [26][27][28][29], and even generalizations to classical dynamics [30][31][32]. For comprehensive reviews of the various techniques, we refer to the recent literature [9][10][11].…”

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

“…Fast-forward scaling theory (FFST) provides a systematic way for optimally designing control parameters which accelerate, decelerate, or reverse the dynamics of a quantum system [1,2]. The formalism of FFST has previously been extended with great effect to many-body [3] and discrete systems [4][5][6], systems of charged particles [7,8], tunneling dynamics [9,10], Dirac dynamics [11,12] and for the acceleration of adiabatic dynamics [13][14][15].…”

“…The virtual trajectory satisfies f 2 (0) = f 2 (T F ) = 0 and β FF (t, f 2 ) ≃ 0 for all times throughout the system's evolution. ω FF m can then be calculated for any given virtual trajectory by substituting the corresponding f 2 (t) and f 1 (t) = 0 into equation (12). While both ω FF 1 and ω FF 2 may be time-dependent in general, only the difference between the angular frequencies, ∆ω FF = ω FF 1 − ω FF 2 , is of physical importance in this subspace.…”