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arXiv:2201.05372 · Physical Review Research

Supersolid devil's staircases of spin-orbit-coupled bosons in optical lattices

Daisuke Yamamoto, Kotaro Bannai, Nobuo Furukawa, Carlos A. R. Sá de Melo

Published Aug 12, 2022• 1 citation
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Abstract

We study the emergence of supersolid devil's staircases of spin-orbit-coupled bosons loaded in optical lattices.We consider two-and three-dimensional systems of pseudo-spin-1/2 bosons interacting via local spin-dependent interactions.These interactions together with spin-orbit coupling produce length scales that are commensurate to the lattice spacing.This commensurability leads to devil's staircases of supersolids, with fractal Hausdorff dimensions, which arise from uniform superfluid phases.We show that umklapp processes are essential for the existence of commensurate supersolids, and that without them the devil's staircase does not exist.Lastly, we emphasize the generality of our results, suggest experiments that can unveil these unusual predictions, and discuss potential applications to the case of 87 Rb.

DOI
10.1103/physrevresearch.4.l032023

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We study the emergence of supersolid devil's staircases of spin-orbit-coupled bosons loaded in optical lattices.We consider two-and three-dimensional systems of pseudo-spin-1/2 bosons interacting via local spin-dependent interactions.These interactions together with spin-orbit coupling produce length scales that are commensurate to the lattice spacing.This commensurability leads to devil's staircases of supersolids, with fractal Hausdorff dimensions, which arise from uniform superfluid phases.We show that umklapp processes are essential for the existence of commensurate supersolids, and that without them the devil's staircase does not exist.Lastly, we emphasize the generality of our results, suggest experiments that can unveil these unusual predictions, and discuss potential applications to the case of 87 Rb.
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We consider a single-component gas of dipolar bosons confined in a one-dimensional optical lattice, where the dipoles are aligned such that the long-ranged dipolar interactions are maximally repulsive. In the limit of zero intersite hopping and sufficiently large on-site interaction, the phase diagram is a complete devil's staircase for filling fractions between 0 and 1, wherein every commensurate state at a rational filling is stable over a finite interval in chemical potential. We perturb away from this limit in two experimentally motivated directions involving the addition of hopping and a reduction in the on-site interaction. The addition of hopping alone yields a phase diagram, which we compute in perturbation theory in the hopping, where the commensurate Mott phases now compete with the superfluid. Further softening of the on-site interaction yields alternative commensurate states with double occupancies which can form a staircase of their own, as well as one-dimensional ``supersolids'' which simultaneously exhibit discrete broken symmetries and superfluidity.
In this advance, we study the system of strongly interacting spinor bosons in a square lattice subject to any of the linear combinations of the Rashba and Dresselhaus spin-orbit coupling (SOC). The SOC leads to novel and rich quantum and topological phenomena in a lattice system. They include masses generated from order from quantum disorder mechanism, collinear spin-bond correlated magnetic phase, quantum commensurate ( C ) and In-commensurate ( IC ) non-coplanar Skyrmion crystal phases, stripe co-planar ( spiral ) C and IC phases, quantum Lifshitz C-IC transitions, metastable states, hysteresis, topological rational and irrational winding numbers, incomplete and complete devil staircases, Cantor sets, multi-fractals, etc. Various perspectives and possible intimate connections with topological spin liquids due to geometric frustrations or quantum spin glass due to quenched disorders are discussed. Implications on current or near future cold atom systems and on 4d or 5d strongly correlated materials with SOC are discussed.
Ultracold bosons in optical lattices are one of the few systems where bosonic matter is known to exhibit strong correlations. Here we push the frontier of our understanding of interacting bosons in optical lattices by adding synthetic spin-orbit coupling, and show that new kinds of density- and chiral-orders develop. The competition between the optical lattice period and the spin-orbit coupling length - which can be made comparable in experiments - along with the spin hybridization induced by a transverse field (i.e., Rabi coupling) and interparticle interactions create a rich variety of quantum phases including uniform, non-uniform and phase-separated superfluids, as well as Mott insulators. The spontaneous symmetry breaking phenomena at the transitions between them are explained by a two-order-parameter Ginzburg-Landau model with multiparticle umklapp processes. Finally, in order to characterize each phase, we calculated their experimentally measurable crystal momentum distributions. PACS numbers: 67.85.-d,67.85.Hj,67.85.Fg.
We consider a mixture of ultracold bosonic atoms on a one-dimensional lattice described by the XXZ-Bose-Hubbard model, where the tunneling of one species depends on the spin state of a second deeply trapped species. We show how the inclusion of antiferromagnetic interactions among the spin degrees of freedom generates a Devil's staircase of symmetry-protected topological phases for a wide parameter regime via a bosonic analog of the Peierls mechanism in electron-phonon systems. These topological Peierls insulators are examples of symmetry-breaking topological phases, where long-range order due to spontaneous symmetry breaking coexists with topological properties such as fractionalized edge states. Moreover, we identify a region of supersolid phases that do not require long-range interactions. They appear instead due to a Peierls incommensurability mechanism, where competing orders modify the underlying crystalline structure of Peierls insulators, becoming superfluid. Our work show the possibilities that ultracold atomic systems offer to investigate strongly-correlated topological phenomena beyond those found in natural materials.
We study the ground-state phases of a spin-orbit-coupled Bose-Einstein condensate loaded in a two-dimensional optical lattice. We find three types of helical supersolid phases, which are dependent on the anisotropy of the spin-orbit coupling with respect to the relative strength of the yyy and xxx directions. The period of density modulation increases with the strength of the spin-orbit coupling.