Timescales for equilibration and adiabaticity in optical lattices

Stefan S. Natu, Erich J. Mueller, Kaden R. A. Hazzard

Takashi Hara, Tatsuhiko Koike

For a class of translation-invariant free-fermion systems including those with uniform nearest-neighbor hopping) on a d-dimensional L×⋯×L hypercubic lattice, we prove that, starting from an arbitrary pure initial state, the system equilibrates with respect to the coarse-grained density within a timescale of order L. This scaling is optimal, since there exist initial states whose equilibration requires time of order L. Our result establishes O(L) as the equilibration timescale, as is expected in normal macroscopic systems with a conserved quantity, such as total number of particles.

Terry Farrelly

Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes paradigmatic systems such as gases confined to boxes, but also Luttinger liquids and the free superfluid Hubbard model. To do this, we focus on two classes of measurements: (i) coarse-grained observables, such as the number of particles in a region of space, and (ii) few-mode measurements, such as phase correlators. We show that, in this setting, equilibration occurs quite generally despite the fact that the particles are not interacting. Furthermore, for coarse-grained measurements the timescale is generally at most polynomial in the number of particles N , which is much faster than previous general upper bounds, which were exponential in N . For local measurements on lattice systems, the timescale is typically linear in the number of lattice sites. In fact, for one-dimensional lattices, the scaling is generally linear in the length of the lattice, which is optimal. Additionally, we look at a few specific examples, one of which consists of N fermions initially confined on one side of a partition in a box. The partition is removed and the fermions equilibrate extremely quickly in time .

Georg A. Raithel, G. Birkl, William D. Phillips +1 more

Terry Farrelly

Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes paradigmatic systems such as gases confined to boxes, but also Luttinger liquids and the free superfluid Hubbard model. To do this, we focus on two classes of measurements: (i) coarse-grained observables, such as the number of particles in a region of space, and (ii) few-mode measurements, such as phase correlators.Weshow that, in this setting, equilibration occurs quite generally despite the fact that the particles are not interacting. Furthermore, for coarse-grained measurements the timescale is generally at most polynomial in the number of particles N, which is much faster than previous general upper bounds, which were exponential in N. For local measurements on lattice systems, the timescale is typically linear in the number of lattice sites. In fact, for one-dimensional lattices, the scaling is generally linear in the length of the lattice, which is optimal. Additionally, we look at a few specific examples, one of which consists ofNfermions initially confined on one side of a partition in a box. The partition is removed and the fermions equilibrate extremely quickly in time O(1 N).

Andrew J. Daley, Hannes Pichler, P. Zoller