Agradecimentos: M.F.C. would like to thank Rodrigo G. Pereira for useful comments about the manuscript and Isaac M. Carvalho for providing some preliminary numerical calculations related to this work. This work is supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil, through Grant No. 200267/2023-0. M.V.S.B. acknowledges the support of CNPq under Grant No. 304120/2022-7 and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) under Grant No. 2020/02170-4. E.M. acknowledges the support of CNPq (Grant No. 309584/2021-3) and FAPESP (Grant No. 22/15453-0). S.D. acknowledges support from the U.S. National Science Foundation under Grant No. DMR-2010127 and the John Templeton Foundation under Grant No. 62422 Ver menos

Abstract: We consider the optimal control of switching on a coupling term between two quantum many-body systems. Specifically, we (i) quantify the energetic cost of establishing a weak junction between two quantum spin-1/2 chains in finite time r and (ii) identify the energetically optimal protocol to realize it. For linear driving protocols, we find that for long times the excess (irreversible) work scales as tau(-n), where n = 1, 2 or a nonuniversal number depending on the phase of the chains. Interestingly, increasing a J(z) anisotropy in the chains suppresses the excess work, thus promoting quasiadiabaticity. The general optimal control problem is solved, employing a Chebyshev Ansatz. We find that the optimal control protocol is intimately sensitive to the chain phases Ver menos