We investigate a non-Hermitian model featuring non-reciprocal gradient
hoppings. Through an in-depth analysis of the Liouvillian spectrum and
dynamics, we confirm the emergence of the Liouvillian skin effect resulting
from the non-reciprocal nature of hoppings in this model. Furthermore, we
observe that the presence of gradient hopping strength leads to an accelerated
relaxation time for the system. Through numerical investigations of the
Liouvillian gap, relaxation time, and steady-state localization length, we
discover that the relaxation time in this model cannot be explained by the
currently established relationship associated with the Liouvillian skin effect.
This discrepancy highlights the need for further exploration and theoretical
advancements to fully comprehend the intricate mechanisms underlying quantum
relaxation processes. Motivated by these findings, we propose a theoretical
approach to realize this non-Hermitian model in an atomic system with a
sideband structure by employing adiabatic elimination technique. These results
contribute to our deeper comprehension of quantum relaxation dynamics and
provide theoretical backing for the development of techniques aimed at
controlling quantum relaxation processes.Comment: 9 pages, 6 figures, To be published in PR