Not-quite-free shortcuts to adiabaticity

Abstract

Given the increasing use of shotcuts to adiabaticity (STA) to optimize power and efficiency of quantum heat engines, it becomes a relevant question if there are any theoretical limits to their application. We argue that quantum fluctuations in the control device which implements the shortcut deflect the system from the adiabatic path. This not only induces transitions to unwanted final states but also changes the system energy, so that using the STA has a definite cost in terms of conventional work definitions. This may be the ultimate cost of an adiabatic shortcut, in the sense that it is present even for a frictionless, zero temperature driving. We estimate the effect, to lowest nontrivial order in the derivatives of the time-dependent frequency, on a parametric harmonic oscillator, thus providing a consistency condition for the validity of the classical approximation. * calzetta@df.uba.ar arXiv:1807.00926v2 [quant-ph]

Shortcuts to adiabaticity: Concepts, methods, and applications

“…Several papers analyze the effect of a control system (CS) (also termed driving or auxiliary system) coupled to the primary system (PS) of interest to set the STA driving and its influence on the energy cost. Calzetta (2018) points out that the time-dependent driving Hamiltonians in STA processes are typically semiclassical and thus approximate. For a simplified model with a particle in a harmonic oscillator whose frequency depends on a coordinate of a driving system and is subjected to quantum fluctuations, Calzetta estimates the excitation when the STA process is implemented on average.…”

Energetic cost of quantum control protocols

“…Our aim is to both qualitatively and quantitatively assess the cost of implementing these protocols, which is a topic that has ignited significant interest recently [5,[8][9][10][11][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Indeed as discussed in [2] the notion of the cost has been somewhat loosely employed and therefore different quantifiers probe different aspects of the systemʼs energy or its interactions.…”

“…The question of how to quantify the necessary resources to control a quantum system using a particular protocol has recently become a topic of intense research activity (indeed, in the context of thermodynamic cycles the issue becomes more subtle since any additional energy which is not dissipated can in principle be recycled and act as a catalyst [20]). The variety of ways in which a particular set-up can be coherently controlled has led to a plethora of definitions [5,[8][9][10][11][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Nevertheless, since many of these quantifiers invariably share some common traits, it leads to a natural question: which control protocols are the most resource intensive?…”

Focus on Shortcuts to Adiabaticity

“…See, e.g. [6,[28][29][30][31][32][33][34][35][36][37]. It should be emphasized that STA designed by counterdiabatic driving can be formulated as time-optimal processes [29] that satisfy the quantum brachistochrone equation [38].…”