Chiral phases and dynamics of dipoles in triangular optical ladders

TL;DR

This work shows how geometric frustration on a triangular ladder combined with anisotropic long-range dipolar interactions yields chiral quantum phases in both itinerant dipolar bosons and pinned spin-1/2 dipoles. Using an extended Bose-Hubbard model for itinerant particles and a long-range dipolar XXZ model for spins, it demonstrates a dipole-induced transition between a chiral superfluid and a two-component superfluid at experimentally accessible temperatures, with the transition tunable by dipole orientation and interaction strength. The authors map rich phase diagrams including CSF, 2SF, magnon-TLLs, and nematic (bound bi-magnon) states, and they show dynamic formation of chirality in non-equilibrium protocols. The results provide practical routes to realize and detect chiral order in ultracold dipolar systems across platforms such as magnetic atoms, polar molecules, and Rydberg arrays, leveraging tunable dipolar interactions and lattice geometries.

Abstract

Dipoles in triangular optical ladders constitute a flexible platform for the study of the interplay between geometric frustration and long-range anisotropic interactions, and in particular for the observation of the spontaneous onset of chirality. Frustration magnifies the effect of the dipolar interactions in itinerant polarized dipolar bosons. As a result, the dipole-induced transition between a chiral superfluid and a non-chiral two-component superfluid may be observed for current state-of-the-art temperatures even for the weak inter-site interaction characterizing magnetic atoms in standard optical lattices. On the other hand, pinned spin-$1/2$ dipoles, which we discuss in the context of polar molecules in two rotational states, realize frustrated dipolar XXZ spin models. By controlling the external electric field strength and orientation, these systems can explore a rich ground-state landscape including chiral and nematic phases, as well as intriguing chiral dynamics.

Figures (8)

• Figure 1: Scheme of dipolar bosons on a triangular ladder.
• Figure 2: (a) Phase diagram for the EBHM \ref{['eq1']} with $U/t=1$, $\theta=0$, and lattice filling $\rho=0.2$ on a ladder with $120$ sites, obtained using DMRG, employing the TeNPy library Hauschild2018, with a maximum bond-dimension of $300$, applying open boundary conditions, and considering up to $3$ particles per site. (b) $\kappa^2$ as a function of $\theta$ and $V/t$ for the same system at fixed $U/t=1$, and $\eta=0.75$. (c) $\kappa^2$ as a function of $V/t$ and $k_BT/t$ for $U/t=1$, $\eta=0.6$, and $\rho=1$ for a ladder with $30$ sites. (d) Momentum distribution $n(q)$ in the 2SF at (i) $k_B T=0$, $V=0.7t$, (ii) $k_B T=0.6t$, $V=0.4t$, and (iii) $k_B T=1.8t$, $V=0.2t$.
• Figure 3: (a) Anisotropy $\Delta$ as a function of the electric-field for KRb molecules Carroll2025. (b) Phase diagram of the dipolar XXZ model as a function of $\Delta$ and $\theta$ for dipoles on the $yz$ plane. (c) Same for dipoles on the $xz$ plane. Results obtained for a magnetization $\langle S^z \rangle = -0.4$ using DMRG, employing TeNPy Hauschild2018, with a maximum bond-dimension of $200$, and considering interactions up to $10$ neighbors on a system of $120$ sites with open boundary conditions.
• Figure 4: Local chirality $\langle \hat{\kappa}_i\rangle$ as a function of time $\tau$ (in units of $1/V$) for dipoles on the $yz$ plane at an angle $\theta=0.15\pi$ with the $z$-axis, $\langle \hat{S}^z \rangle = -0.4$, and $\Delta=0.05$ (a) and $1.5$ (b). The initial state is that of two independent magnon TLLs in each leg. The calculations were performed using TDVP, employing TeNPy Hauschild2018, for $60$ sites with open-boundary conditions, keeping a maximum bond-dimension of $300$.
• Figure S1: Long-range chirality-chirality correlation $\kappa^2$ for the case of itinerant dipolar bosons. The white dashed line is the contour line $\left.d^2 n(q)/dq^2\right|_{q=0} = 0$, separating the SF phase from the other superfluid phases.