Atomic Regional Superfluids in two-dimensional Moiré Time Crystals

Abstract

Moiré physics has transcended spatial dimensions, extending into synthetic domains and enabling novel quantum phenomena. We propose a theoretical model for a two-dimensional (2D) Moiré time crystal formed by ultracold atoms, induced by periodic perturbations applied to a non-lattice trap. Our analysis reveals the emergence of regional superfluid states exhibiting moiré-scale quantum coherence across temporal, spatial, and spatiotemporal domains. This work provides fundamental insights into temporal moiré phenomena and presents an alternative pathway to engineer spatial moiré phases without requiring twisted multilayer lattices.

Figures (7)

• Figure 1: (a) A schematic diagram of the model depicts ultracold atoms moving within a 2D square potential well (blue) and experiencing perturbation from an additional laser beam (light blue) featuring multifrequency intensity modulation. (b) 2D FPS effective potential $\mathcal{V}_{n=16,m=12}(\bar{\theta}_x, \bar{\theta}_y)$, with the depth indicated by color, at twist angle $\alpha\approx16.26^\circ$ and primary cell periodicity $a_0=\pi/10$ denoted by the white shorter arrows. Two distinct morié patterns, $A$ and $B$, are observed (bordered by white dashed lines), corresponding to a quadrilateral unit cell with equal-length morié vectors $|\mathbf{a_{M}^{1}}|=|\mathbf{a_{M}^{2}}|=5a_0$.
• Figure 2: The atomic probability density $|\psi(x,y,t)|^2$ at three moments is accompanied by the inset showing (a) the real part of spatial autocorrelation $C_{t_0}(\delta r)$ at $t_0=98T_y$ within a spatial moiré period $a_M^r$ (dashed lines mark spatial primary cell period $a_0^r$) and (b) the real part of temporal autocorrelation $C_{x_0,y_0}(\tau)$ at position $(x_0,y_0)$ (red dot) within a temporal moiré period $T_M^x=T_x/4$ (dashed lines mark the temporal primary cell period $T_0^x=T_x/20$), using parameters $\Omega_{x}=\pi\times10^{3}E_{r}/\hbar$, $\Omega_x/\Omega_{y}=64\pi$, $\mathcal{V}_{16,12}=0.35E_{r}$, $E_{r}=\frac{\hbar^{2}}{m_{a}}(\frac{2\pi}{a_0^r})^2$, and $\eta gN=10^2\hbar^{2}/m_{a}$.
• Figure 3: (a) $|\psi(x_0,y_0,t)|^2$ in $(j,k)$ temporal coordinates ($t=\Delta t_x j+\Delta t_y k+98T_y$) shows temporal Moiré superfluidity. (b) Evolution versus $\tau=t-98T_y$ reveals Moiré patterns $A/B$ at $T_y$ scale. (c,d) Higher-resolution views show nested Moiré structures at $T_x$ scale. Parameters as in Fig. \ref{['fig2']}.
• Figure 4: (a) Slices of probability density in the coordinate $(x,k)$ reveal a 2D spatiotemporal moiré lattice, and the two moiré patterns are denoted with different shading colors. (b) Spatiotemporal autocorrelation $C(\delta x,\delta k)$ in the 2D coordinate $(x,k)$ possesses a spatiotemporal coherent length up moiré scale. Parameters as in Fig. \ref{['fig2']}.
• Figure S1: Heating rates $\Gamma_\alpha$ (blue dots) for the lowest $32$ single Floquet states, whose superposition forms the Moiré time crystal state with heating rate $\Gamma_0$ (dashed line). Parameters are the same as in the main text.