Disorderless Quasi-localization of Polar Gases in One-Dimensional Lattices

W. Li, A. Dhar, X. Deng, K. Kasamatsu, L. Barbiero, and L. Santos

Phys. Rev. Lett. 124, 010404 – Published 10 January 2020

Abstract

One-dimensional polar gases in deep optical lattices present a severely constrained dynamics due to the interplay between dipolar interactions, energy conservation, and finite bandwidth. The appearance of dynamically bound nearest-neighbor dimers enhances the role of the $1 / r^{3}$ dipolar tail, resulting in the absence of external disorder, in quasi-localization via dimer clustering for very low densities and moderate dipole strengths. Furthermore, even weak dipoles allow for the formation of self-bound superfluid lattice droplets with a finite doping of mobile, but confined, holons. Our results, which can be extrapolated to other power-law interactions, are directly relevant for current and future lattice experiments with magnetic atoms and polar molecules.

Received 5 February 2019

DOI:https://doi.org/10.1103/PhysRevLett.124.010404

Physics Subject Headings (PhySH)

Cold gases in optical lattices Dipolar gases

Atomic, Molecular & Optical

Authors & Affiliations

W. Li¹, A. Dhar ¹, X. Deng¹, K. Kasamatsu², L. Barbiero³, and L. Santos¹

¹Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany
²Department of Physics, Kindai University, Higashi-Osaka 577-8502, Japan
³Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 124, Iss. 1 — 10 January 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Squares (circles) indicate $L_{cr}$ (see text) for two dimers with (without) a singlon in between, such that for an initial interdimer distance $L_{0} < L_{cr}$ the dimers remain at a fixed distance [39]. In both cases $L_{cr} \propto (V / J)^{2 / 3}$ (dotted curves). (b) $⟨ {\hat{n}}_{j} ⟩ (t)$ evaluated by means of time-dependent density-matrix renormalization group ( $t$ -DMRG) calculations [40] using Eq. (1) for $V / J = 50$ , for two dimers initially 15 sites apart and an intermediate singlon. The singlon quickly delocalizes in the interdimer space, but the dimers remain at fixed distance for $J_{D} t ≫ 1$ .
Reuse & Permissions
Figure 2
(a) Shannon entropy $S (t)$ , evaluated using exact evolution of Eq. (1) for 25 sites and periodic boundary conditions for two dimers initially 5 sites apart, for $V / J = 12$ (blue) and 42 (orange). Horizontal lines indicate $S_{\max}$ for unbound (dashed-dotted) and bound (dashed) dimer clusters [42]. (b) Inhomogeneity $η (t) / η (0)$ as a function of $J_{D} t$ evaluated using exact evolution of Eq. (2) for $V / J = 40$ for $N_{D} = 2$ (triangles), 3 (circles), and 4 (squares) dimers, initially with 3 sites between each dimer in a lattice with $5 (N_{D} + 1)$ sites and periodic boundary conditions (particle filling $≃ 0.3$ ). (c) Same as (a) but for two dimers initially 7 sites apart and a singlon in between for $V / J = 12$ (blue), 37 (orange), and 50 (green). Horizontal lines indicate $S_{\max}$ for dimers with an unbound relative distance (dashed-dotted), for dimers at a fixed distance with a singlon freely moving between them (dotted), and when the dimer-dimer and the dimer-singlon distance are fixed (dashed) [42].
Reuse & Permissions
Figure 3
(a) $(V / J)_{cr} (ρ)$ for self-bound droplets obtained using exact evolution of Eq. (1) for 16 sites. The particles are initially in the ground state (with $V = 0$ ) of a box trap in the central 8 sites. We determine $F (V / J, ρ) = ξ (t_{f}) / ξ (0)$ , where $ξ (t) = ρ_{c} (t) - ρ_{av}$ , with $ρ_{av}$ the density for an homogeneous lattice gas, $ρ_{c} (t)$ the central density, and $t_{f} = 100 t_{D}$ , with $t_{D}$ the homogenization time for $V = 0$ . We determine $(V / J)_{cr}$ as that for which $F [(V / J)_{cr}, ρ] = 0.1$ . (b) Density distribution, obtained using $t$ -DMRG simulations of Eq. (1) [40], for a gas initially confined with $ρ = 1$ (red triangles) $J t = 30$ after release, for $V / J = 1$ (unbound, green circles) and $V / J = 2.5$ (droplet, blue squares).
Reuse & Permissions
Figure 4
(a) Droplet with a holon initially at the center (red triangles) after $J t = 6$ (blue circles), for $V / J = 30$ . Partial holon evaporation results in particle ejection (left inset), but is inefficient, as shown by the particle-hole entropy averaged over the 5 central sites (right inset). (b) Initial droplet with $ρ = 1$ and two singlons outside (red triangles) after $J t = 55$ (blue circles). The shadowed region is that of the droplet. Note singlon aggregation at the droplet edge. Figures obtained by $t$ -DMRG calculations using Hamiltonian (1) [40].
Reuse & Permissions

Physical Review Letters