Observation of a Dipolar Quantum Gas with Metastable Supersolid Properties

The competition of dipole-dipole and contact interactions leads to exciting new physics in dipolar gases, well illustrated by the recent observation of quantum droplets and rotons in dipolar condensates. We show that the combination of the roton instability and quantum stabilization leads under proper conditions to a novel regime that presents supersolid properties due to the coexistence of stripe modulation and phase coherence. In a combined experimental and theoretical analysis, we determine the parameter regime for the formation of coherent stripes, whose lifetime of a few tens of milliseconds is limited by the eventual destruction of the stripe pattern due to three-body losses. Our results open intriguing prospects for the development of long-lived dipolar supersolids.

Figure 1

(a) Typical momentum distribution $n(k_x,k_y)$ for different evolution times in three regimes: (top row) $B=5.305\mathrm{G}$ ($a\simeq 108a_0$, BEC regime); (middle row) $B=5.279\mathrm{G}$ ($a\simeq 94a_0$, stripe regime); (bottom row) $B=5.272\mathrm{G}$ ($a\simeq 88a_0$, incoherent regime). (b) Mean squared deviation (MSD) of $n(k_x,k_y)$ from a Gaussian, distinguishing BEC and stripe or incoherent regions in the $B\text{−}N$ plane [32]. The black line represents the theoretical prediction for the roton instability [11, 32]. (Inset) Trap geometry.

Figure 2

(a) Time evolution of the atom number for stripes ($B=5.279\mathrm{G}$, blue circles) and incoherent ($B=5.272\mathrm{G}$, red squares) regimes. Blue and red shaded areas represent the atom loss predicted by our dynamical simulations at $a_s\simeq 94a_0$ and $a_s\simeq 88a_0$, respectively. (b) Time evolution of the interference amplitude $A$ in the stripe regime ($B=5.279\mathrm{G}$). The dashed line is an exponential fit to the initial ($t\le 10\mathrm{ms}$) growth. The error bars represent the standard deviation of about 40 measurements.

Figure 3

(a) Time evolution of the interference phase variance $\mathrm{\Delta }{\varphi }^2$ in the stripe regime ($a\simeq 94a_0$). The error bars correspond to $\mathrm{\Delta }{\varphi }^{2}2/(2N-2)$, with $N\simeq 40$ being the number of measurements for each dataset. The red-dashed line is the expected variance for a uniformly distributed phase. (b) Averaged momentum distribution $\overline{n}(k_x,k_y)$ over 40 absorption images (top panel) in the stripe regime and (bottom panel) in the incoherent regime at different evolution times. The profiles are obtained by integrating $\overline{n}(k_x,k_y)$ along $k_y$ in the region between dashed lines.

Figure 4

Simulations of stripe formation and evolution. (a) Snapshots for a simulation with coherent stripes after a ramp to $a_s/a_0=94$ are shown at times $(t_1,t_2,t_3)=(13.7,30.9,55)\mathrm{ms}$, while the incoherent regime can be seen in another simulation after a ramp to $a_s/a_0=88$ for $(t_1^{\prime },t_2^{\prime },t_3^{\prime })=(2.7,7.9,28.5)\mathrm{ms}$. Density cuts $n(x,0,0)$—with color representing the wave function phase—and column densities $\int dzn(x,y,z)$ are shown. (b) Stripe contrast $\mathcal{C}$ for stable stripes with $a_s/a_0=94$ (blue circles) and unstable stripes with $a_s/a_0=88$ (red squares). The error bars represent standard deviations for six simulations, each with different initial noise. (c) Phase incoherence, ${\alpha }^I={\int }^{\tau }dxdyn|\alpha -⟨\alpha ⟩|/{\int }^{\tau }dxdyn$, where $\alpha (x,y,0)$ is the wave function phase, $⟨\alpha ⟩$ is its average over $\tau$, defined as the region between the dashed lines in (a) [32]. The limit ${\alpha }^I=0$ indicates global phase coherence, while ${\alpha }^I=\pi /2$ signals incoherence.