Breaking of scale invariance in a strongly dipolar 2D Bose gas

Abstract

Two-dimensional (2D) dipolar atomic gases present unique opportunities for exploring novel quantum phases due to their anisotropic and long-range interactions. However, the behavior of strongly dipolar Bose gases in 2D remains unclear, especially when dipoles are tilted. Here, we demonstrate the creation and characterization of strongly dipolar 2D condensates in a quasi-2D harmonic trap with tunable dipole orientation. By investigating scale invariance properties through breathing collective mode measurements, we observe significant breaking of scale invariance when dipoles are tilted in-plane indicating the dominance of the nonlocal dipole-dipole interactions (DDIs) in this regime. Interestingly, the breaking of the scale invariant dynamics is accompanied by an increase in quantum fluctuations, as shown by comparison with mean-field and beyond mean-field theoretical studies. Our experiments also reveal that at critical tilt angles around 70°, stripe-type density modulations emerge, suggesting the presence of a roton spectrum in 2D, while the system still shows hydrodynamic nature with the phase-locking breathing behavior. This observation elucidates the many-body effect induced by DDIs in 2D, thus marking a crucial step toward realizing 2D supersolids and other exotic quantum phases.

Figures (4)

• Figure 1: Scale-invariance theory and the breathing mode in a quasi-2D dipolar gas.a, Breaking of scale invariance (SI) in a quasi-2D dipolar gas. At the classical field level, isotropic contact interactions preserve SI due to their short-range nature. When dipoles are aligned perpendicular to the 2D plane, DDIs (shown in yellow) are largely isotropic and short-range, resulting a quasi-scale-invariance (quasi-SI). In contrast, SI is broken when dipoles lie parallel to the 2D plane, where local interactions are suppressed and the anisotropic nonlocal part of the DDIs become significant. b, Energy contributions from local contact interactions and nonlocal DDIs as a function of dipole angle $\theta$ with $\epsilon_{dd}=0.98$. The black and orange solid lines represent the local and nonlocal interaction energies, respectively, computed from a simulated ground-state profile (see text). Dots indicate the ratio $E_{\text{nonlocal}}/E_{\text{local}}$. Shaded regions and the dashed line serve as visual guides. c, Experimental setup. A sheet beam tightly confines atoms along the z-axis, with an oscillator length $l_z\sim 0.24\mu m$. An external magnetic field $\vec{B}$, rotating in the $y$-$z$ plane, controls the dipole orientation. A quench of the radial trap excites the breathing mode in the $x$-$y$ plane.
• Figure 2: Breaking of scale invariance in coherent dipolar samples with tilted dipole orientation $\theta$.a, Example measurements of the breathing mode dynamics. Top and bottom panels show in-situ images for $\theta=0^{\circ}$ and $90^{\circ}$ samples, respectively, at $\epsilon_{dd}=0.98$, displayed as the optical density. Central panels depict oscillations in the average radial width $\sigma_r$, plotted relative to its mean value over all hold times, $\overline{\sigma_r}$. The holdtime $t_n$ is normalized by the trap period $T_{\text{trap}}$. Dashed lines are damped sinusoidal fits supplementary. The shades representing one trap period are guides to eyes. b, The breathing frequency of a quasi-2D dipolar gas with $\epsilon_{dd}=0.98$ and different dipole orientations. The blue (white) points correspond to the breathing mode frequencies of condensates (normal gas). As dipoles rotate into the 2D plane, the breathing mode frequency of the condensates gradually deviates from the $SO(2,1)$ symmetry value $\omega_B=2\omega_t$, represented by the grey dashed line. The mean-field GPE simulation is shown as triangles, and the blue dashed lines are direct connection of the symbols. The results of the MCTDHB simulation with $M=2$ are shown as green open diamonds. Incorporating quantum fluctuations does not significantly alter the GPE predictions, except at large $\theta$, where quantum effects shift the frequency upward, in agreement with experimental observations. The blue shade represents the calibration uncertainty on $a_s$patscheider2022determination. The inset compares the breathing mode frequency to the relative strength of nonlocal DDIs. Error bars represent the 95$\%$ confidence interval.
• Figure 3: The signatures of nonlocal DDIs in the strongly dipolar regime.a, The breathing mode frequency of samples in the strongly dipolar regime with highly tilted dipoles. With larger $\epsilon_{dd}$, $\omega_B$ deviates more from the standard value. While the mean-field GPE simulation, plotted as solid lines (and the dash-dot line as extension in the mean-field unstable regime), captures the trend of this strong scaling anomaly, the MCTDHB simulation, shown as green labels, matches the measurements better by including the effect of quantum fluctuations. Error bars represent the 95$\%$ confidence interval. b, The in-situ profiles of samples with $\theta=70^{\circ}$ and $\epsilon_{dd}=0.98,1.20, 1.38$. Three example single images $\text{OD}_i(x,y)$ are shown in the left column, plotted in the optical density (OD). The corresponding averaged profiles $\overline{\text{OD}}(x,y)$ are shown in the middle column. The right column shows the contrast between $\text{OD}_i(x,y)$ and $\overline{\text{OD}}(x,y)$, visualizing the emergence of the stripe-like density modulation in the roton-instable regime.
• Figure 4: Anisotropy of the breathing mode in the hydrodynamics and collisionless regime. The anisotropy of breathing mode $\delta_B$ and the trap frequency anisotropy $\delta_T$ of samples with $\epsilon_{dd}=0.98$ and different dipole angles are shown in orange and blue points. The left (right) panel demonstrates the condensate (normal gas) sample. The blue (orange) solid lines and shades represent the mean and the standard deviation of the trap (breathing) anisotropy. The dashed line is a guide to eyes. Error bars represent the 95$\%$ confidence interval. The inset shows the data of samples with $\epsilon_{dd}>1$ and dipole angles at 70$^{\circ}$ (circles), 80$^{\circ}$ (squares) and 90$^{\circ}$ (triangles).