Slow interaction ramps in trapped many-particle systems: Universal deviations from adiabaticity

Abstract

For harmonic-trapped atomic systems, we report system-independent non-adiabatic features in the response to interaction ramps. We provide results for several different systems in one, two, and three dimensions: bosonic and fermionic Hubbard models realized through optical lattices, a Bose-Einstein condensate, a fermionic superfluid and a fermi liquid. The deviation from adiabaticity is characterized through the heating or excitation energy produced during the ramp. We find that the dependence of the heat on the ramp time is sensitive to the ramp protocol but has aspects common to all systems considered. We explain these common features in terms of universal dynamics of the system size or cloud radius.

Time evolution during and after finite-time quantum quenches in Luttinger liquids

“…This may even be more severe in the case of finite-time quenches since the quench time τ will introduce an additional energy scale in the problem, which may increase the importance of marginal and irrelevant perturbations to the TLM. Nevertheless, various numerical studies 13,14,17,20,26,28,29,33 of observables in onedimensional lattice models after sudden quenches showed a surprisingly good agreement with the results obtained in the TLM; a finding also obtained for the time evolution during finite-time interaction quenches 39,41,45 in the Bose-Hubbard model. Still, from a practical point of view the study of the time evolution after finite-time quenches is complicated by the restriction of the achievable times in numerical simulations due to the finite quench time and the unknown effects of perturbations to the TLM as well as the energy (and thus time) scales involved.…”

“…Several aspects of finite-time quenches and the interpolation between the sudden and adiabatic limit have been studied. [34][35][36][37][38][39][40][41][42] For the Luttinger liquid Dora et al 43 first considered linear quench protocols. They obtained perturbative results for the total energy and fermionic chiral Green function, which were later extended to spinspin correlation functions and compared with numerical simulations of the time evolution during the quench in the XXZ Heisenberg chain.…”

Quantum crystal growing: adiabatic preparation of a bosonic antiferromagnet in the presence of a parabolic inhomogeneity

“…In this paper, we study the influence of a static parabolic inhomogeneity, while the transition from one quantum phase to the other is induced by varying the terms that themselves do not break translational symmetry. Similar scenarios have recently been investigated for temperature-driven phase transitions [31][32][33] or for ramps not passing a phase transition [34]. We are not considering a quench of the inhomogeneity itself, as has been studied, for example, in [35].…”

Modulated trapping of interacting bosons in one dimension

“…The situation is similar to Ref. [30], where the dominant dynamics in interaction ramps was extracted through consideration of size dynamics, even though the full dynamics includes shape distortions, as seen through the time evolution of the kurtosis of the density profile.…”