Cost of counterdiabatic driving and work output

Abstract

Unitary processes allow for the transfer of work to and from Hamiltonian systems. However, to achieve non-zero power for the practical extraction of work, these processes must be performed within a finite-time, which inevitably induces excitations in the system. We show that depending on the time-scale of the process and the physical realization of the external driving employed, the use of counterdiabatic quantum driving to extract more work is not always effective. We also show that by virtue of the two-time energy measurement definition of quantum work, the cost of counterdiabatic driving can be significantly reduced by selecting a restricted form of the driving Hamiltonian that depends on the outcome of the first energy measurement. Lastly, we introduce a measure, the exigency, that quantifies the need for an external driving to preserve quantum adiabaticity which does not require knowledge of the explicit form of the counterdiabatic drivings, and can thus always be computed. We apply our analysis to systems ranging from a two-level Landau-Zener problem to many-body problems, namely the quantum Ising and Lipkin-Meshkov-Glick models.

Energy consumption for shortcuts to adiabaticity

“…It was soon clear that this quantity could not represent all relevant energy flows, which led to the consideration of alternative measures [7]. Several disparate definitions of energy cost have been proposed in the context of quantum thermodynamics to characterize quantum engines and refrigerators [8][9][10][11][12][13][14][15][16][17][18]. These definitions have been systematically formulated in terms of the cycling system (PS) alone.…”

Nearly optimal quantum control: an analytical approach

“…Many techniques to do this have been developed for spin-1/2 systems [6][7][8]. Here we will focus on the class of such solutions called shortcuts to adiabaticity [8,[11][12][13][14][15]. This class covers not only spin-1/2 but also many practically interesting multistate situations [16].…”

“…The Hamiltonian of a shortcut to adiabaticity is obtained by adding a countertermĤ ct (t) such that the evolution of the state vector with the HamiltonianĤ(t) = H 0 (t) +Ĥ ct (t) does follow the path of eigenstates |u(t) . It turns out that there is a formal expression for such a counterterm [8,14,15]:…”

Lipkin-Meshkov-Glick model in a quantum Otto cycle

“…Also, efficient techniques for the adiabatic evolution of the finite size chain LMG model have been given in Refs. [62,63,64,65]. In the isochoric stages of the cycle, the thermalization of the working substance with the hot and cold heat baths is assumed for fixed Hamiltonians.…”