Polarization-controlled pattern formation in antiparallel dipolar binary condensates

TL;DR

This work analyzes non-equilibrium pattern formation in a two-component antiparallel-dipole Bose-Einstein condensate by tuning the polarization angle $\alpha$ and the trap aspect ratio $\lambda$, revealing stripe order at finite $\alpha$ and roton-assisted mushroom corrugations leading to labyrinths when $\alpha$ is reduced to zero. A slow linear ramp preserves metastable curved-stripe textures before eventual labyrinth formation, while population imbalance biases the minority component toward robust droplet arrays and induces elastic, reversible hysteresis without lattice topology changes. The dynamics are captured by coupled nonlocal Gross-Pitaevskii equations in a quasi-two-dimensional regime with negligible beyond-mean-field corrections, and the initial pattern wavelength and instability timescales are controllable via $\lambda$. The observed textures mirror nuclear 'pasta' morphologies, highlighting a common organizing principle of frustrated pattern formation across disparate physical systems and offering practical routes to steer patterns in dipolar mixtures.

Abstract

We investigate non-equilibrium pattern formation in an antiparallel two-component dipolar Bose-Einstein condensate by varying the polarization angle and the trap aspect ratio. At finite tilt, the condensate supports stripe order. Quenching the angle to zero triggers a roton-assisted, mushroom-like corrugation that destroys translational order and drives the system into labyrinthine textures, whereas a slow linear ramp produces long-lived curved stripes that ultimately converge to labyrinths. Population imbalance strongly biases the evolution: the minority component preferentially fragments into a stable droplet array while the majority remains comparatively diffuse; once formed, the droplet crystal is robust under polarization hysteresis with largely reversible shape changes and unchanged lattice topology. The trap aspect ratio controls both the initial stripe number and the instability timescale, with tighter axial confinement accelerating corrugation and yielding denser labyrinths at late times. All behaviors arise within a quasi-two-dimensional mean-field regime where beyond-mean-field corrections are negligible; accordingly, the droplets reported here are not self-bound in free space. The observed textures (such as stripes, curved stripes, and labyrinths) mirror the taxonomy and instability pathways of nuclear "pasta" morphologies (rods and slabs) known from neutron-star and supernova matter, highlighting polarization angle, trap geometry, and population imbalance as practical, experimentally accessible controls for selecting and steering patterns in dipolar mixtures.

Figures (8)

• Figure 1: Column-density profiles of the two components during real-time evolution. (a) With zero polarization angle ($\alpha = 0$), both components display a labyrinthine pattern. (b)--(d) For a finite angle $\alpha = \pi/3$, the textures evolve toward stripes. Parameters: $a_{11} = a_{22} = a_{12} = 100 a_B$, $N_1 = N_2 = 2 \times 10^{6}$, $(\omega_{\perp}, \omega_{z}) = 2 \pi \times (100, 800)$ Hz, and $\mu_1 = -\mu_2 = 6\mu_B$.
• Figure 2: Column-density profiles $|\psi_{1}|^{2}$ and $|\psi_{2}|^{2}$ during real-time dynamics for $N_1/N_2=1$. (a) At $\alpha=\pi/3$, both components realize a stripe phase. At $t=0$ ms the polarization angle is quenched to $\alpha=0$ and then held fixed; the two-component stripe order destabilizes, developing mushroom-like protrusions and complex labyrinthine textures [panels (b)–(g)]. Parameters: $N_{1}=N_{2}=2\times10^{6}$, $a_{11}=a_{22}=a_{12}=100 a_B$, $(\omega_{\perp}, \omega_z)=2\pi\times(100, 800)$ Hz, $\mu_{1}=6\mu_{B}$, and $\mu_{2}=-6\mu_{B}$.
• Figure 3: Column-density profiles $|\psi_{1}|^{2}$ and $|\psi_{2}|^{2}$ during real-time dynamics for a population-imbalanced mixture with $N_1/N_2=6$ ($N_1=2 \times 10^{6}$). (a) Initial state at $\alpha=\pi/3$. At $t=0$ ms, the angle is quenched to $\alpha=0$ and held thereafter. Following the quench, the stripe order rapidly fragments into discrete, droplet-like density peaks that subsequently stabilize [panels (b)–(g)]. Other parameters as in Fig. \ref{['fig:quench_pi3']}.
• Figure 4: Column-density profiles $|\psi_{1}|^{2}$ and $|\psi_{2}|^{2}$ for a linear ramp of the polarization angle. (a) The system is initialized at $\alpha=\pi/3$. The angle is then reduced linearly to $\alpha=0$ over $100$ ms and held at zero thereafter. During the ramp, the stripe-axis symmetry breaks and the stripes bend from their centers, generating progressively intricate patterns [panels (a)–(e)]. Once $\alpha=0$ [panels (e)–(g)], the textures evolve toward a labyrinthine state. Parameters: $N_{1}=N_{2}=2 \times 10^{6}$, $a_{11}=a_{22}=a_{12}=100 a_B$, $(\omega_{\perp}, \omega_z)=2 \pi \times(100,800)$ Hz, $\mu_{1}=6\mu_{B}$, and $\mu_{2}=-6\mu_{B}$.
• Figure 5: Column-density profiles $|\psi_{1}|^{2}$ and $|\psi_{2}|^{2}$ for a linear ramp with population imbalance $N_1/N_2=6$ ($N_1=2 \times 10^{6}$). (a) Initial configuration at $\alpha=\pi/3$; (a)–(e) $\alpha$ is ramped linearly to $0$ over $100$ ms; (e)–(g) $\alpha=0$ is then held constant. Other parameters are as in Fig. \ref{['fig:linear_pi3']}.