Effects of intertube dipole-dipole interactions in nearly integrable one-dimensional $^{162}$Dy gases

TL;DR

The paper addresses how intertube dipole-dipole interactions (DDI) affect arrays of nearly integrable 1D dipolar Bose gases. By modeling the leading intertube DDI as a self-consistent mean-field correction to the 1D trapping potential and propagating it through state preparation and $t_{ m ev}$-scaled expansion with thermodynamic Bethe Ansatz (TBA), LDA, and generalized hydrodynamics (GHD), the authors show that these corrections are small and, crucially, largely cancel between the initial state and expansion dynamics. Consequently, the measured rapidity distributions remain very close to the predictions without intertube DDI, suggesting that DDI is not the source of discrepancies with prior experiments; nonthermal effects tied to near-integrability are more likely responsible. The work highlights a delicate balance between confinement-modification cooling and DDI-induced antitrapping, with cooling more pronounced in low-filling tubes, and sets a framework for including weak long-range interactions in studies of quantum integrability and thermalization in 1D gases.

Abstract

We study the effects of the intertube dipole-dipole interactions (DDI) in recent experiments with arrays of nearly integrable one-dimensional (1D) dipolar Bose gases of $^{162}$Dy atoms. An earlier theoretical modeling ignored those interactions, which we include here via a modification of the 1D confining potentials. We investigate the effects of the intertube DDI both during the state preparation and during the measurements of the rapidity distributions. We explore how the strength of the contact interactions and the magnetic field angles modify the intertube DDI corrections. We find that those corrections slightly change both the properties of the equilibrium state and the rapidity measurements. Remarkably, however, the changes nearly cancel each other, resulting in measured rapidity distributions that are very close to those predicted in the absence of the intertube DDI.

Figures (11)

• Figure 1: (a) Spatial depiction of the dipolar 1D gases. The 2D array (in the $y$-$z$ plane) of 1D gases (along the $x$ direction) is created using a deep 2D optical lattice with wavelength $\lambda$. The atomic dipoles align with the magnetic field $\bf B$ producing the intertube and intratube DDIs. (b) Sequence used to measure the rapidity distributions. After preparing the equilibrium 1D gases (tubes), the trapping potential $V_{1D}$ is turned off and the atoms are allowed to expand in one dimension in the presence of interactions. The momentum distribution of the 1D gases becomes equal to the rapidity distribution after a long-enough expansion time $t_\text{ev}$. (c) Theoretical modeling of the experimentally created equilibrium state. Starting from a BEC (left), the 2D optical lattice potential $U_{2D}$ is ramped up to create the array of tubes (right). We assume that at $U_{2D}^*$ all the tubes decouple from each other, and that they are all at the same temperature $T_{2D}^*$ (center). The ramping of 2D lattice is assumed to be adiabatic for $U_{2D}>U_{2D}^*$.
• Figure 2: Atom distribution at decoupling. (a) [(b)] Distribution of atoms $N_\text{atom}(y_l,z_l)$ in the tubes when we neglect (account for) the intertube DDI. Each dot indicates a tube "$l$" at position $(y_l,z_l)$. (c) Distribution of atoms along the $y$ direction, $N_{y}=\sum_{z_l}N_\text{atom}(y_l,z_l)$ (blue lines), and along the $z$ direction, $N_{z}=\sum_{y_l}N_\text{atom}(y_l,z_l)$ (green lines), in calculations with (dashed) and without (solid) the intertube DDI correction. (d) The number of tubes $N_\text{tube}$ with $N_\text{atom}$ atoms versus $N_\text{atom}$.
• Figure 3: Density and rapidity distributions at decoupling. (a) Average density distribution of the 1D gases with (dashed lines) and without (solid lines) including the intertube DDI correction at decoupling. The green solid line in the top panel shows the difference $\Delta n(x)=n(x;{\rm with\,} U^{\rm intra}_{\rm DDI})-n(x;{\rm without\,} U^{\rm intra}_{\rm DDI})$. (b) Same as (a) but for rapidity distribution $f(\theta)$, with $\Delta f(\theta)=f(\theta; {\rm with\,} U^{\rm intra}_{\rm DDI})-f(\theta;{\rm without\,} U^{\rm intra}_{\rm DDI})$.
• Figure 4: Temperature distribution at the end of the loading process. (a) [(b)] Temperature for tubes without (with) intertube DDI after the state preparation. Each dot indicates a 1D tube at position $(y,z)$. (c) [(d)] The ratio between atoms at temperature $T$ ($N_T$) and the total number of atom ($N_\text{total}$), after the state preparation without (with) intertube DDI correction. The temperature is binned in $0.5$ nK intervals. We show results for tubes with $N_{l}\geq 2$ atoms.
• Figure 5: Density and rapidity distributions at the end of the loading process. (a) Density distributions $n(x)$ at the end of the loading process without (red dotted line) and with (blue dashed dotted line) the intertube DDI correction. (b) Rapidity distributions $f(\theta)$ at the end of the loading process without (red dotted line) and with (blue dashed dotted line) the intertube DDI correction. We also show the rapidity distribution obtained after a 15 ms expansion in the tubes (green dashed line, overlapping with the red dotted line), and the experimental results (orange solid line) from Ref. li_zhang_23.