Generation of dipolar supersolids through a barrier sweep in droplet lattices

Abstract

We propose a dynamical protocol to generate supersolids in dipolar quantum gases by sweeping a repulsive Gaussian barrier through an incoherent quasi-one-dimensional droplet array. Supersolidity is inferred by monitoring the ensuing dynamics of the density, momentum distribution, center-of-mass motion, and superfluid fraction within the framework of the extended Gross-Pitaevskii equation with quantum corrections. A persistent superfluid background arises, atop which the crystals oscillate in unison, indicating the establishment of phase coherence. This process is accompanied by energy redistribution and the gradual transfer of higher-lying momenta toward the zero momentum mode. The dependence of the superfluid fraction on the barrier velocity and height is also elucidated evincing the parametric regions which facilitate the rise of a superfluid background. Our results pave the way for engineering supersolid generation using experimentally accessible protocols.

Figures (8)

• Figure 1: (a) Schematic illustration of the driving protocol. A Gaussian barrier (red shaded region) located at $x_0$ and being characterized by height $V_0$ and waist $w$, is swept towards a quasi-1D array of $^{164}$Dy droplets (blue shaded area). (b) The barrier sweep results in the dynamical generation of a supersolid, exhibiting an excited superfluid background, denoted by the green shading, on top of which crystalline structures persist.
• Figure 2: Spatiotemporal 1D integrated density, $n(x,t)$, evolution of the droplet lattice consisting of four crystals after being perturbed by a Gaussian barrier. The latter travels with different velocities (see legends) toward the droplet array. The barrier trajectory is illustrated by the red dashed line. At long evolution times, following the crystal collisions, atom redistribution gives rise to a superfluid background atop which the post-collision crystals oscillate in-sync, thereby manifesting the emergence of supersolidity. The vertical dash-dotted lines designate the three distinct dynamical regimes corresponding to the unperturbed crystal lattice (I), the droplet collisions (II), and the superfluid background nucleation (III). In all cases, the characteristics of the Gaussian barrier correspond to $V_0=10~\hbar \omega_x$, and $w=0.31~\mu m$, while the system consists of $N=8\times 10^4$$^{164}$Dy atoms with $a=86~a_0$ and $a_\text{dd} = 131~a_0$.
• Figure 3: Droplet inelastic collisions induced by the barrier sweep at selected time instants of the density evolution (see legends) yielding the appearance of a superfluid background. The integrated 1D density profiles, $n(x,t)$, have been rescaled and shifted appropriately to ensure a proper visualization. The barrier velocity refers to (a1)-(a5) $v_0 \approx 1.46 ~ \mu m/ ms$, and (b1)-(b6) $v_0 \approx 3.01 ~ \mu m/ms$, see also Fig. \ref{['fig:Density_dynamics']}(a), (c). All other parameters are the same as in Fig. \ref{['fig:Density_dynamics']}.
• Figure 4: Time-evolution of the 1D momentum distribution for two different barrier velocities (see legends). The gradual formation of a superfluid background at long evolution times becomes evident from the underlying momentum transfer toward the zero momentum peak. This process is associated with the dynamical generation of the supersolid. The vertical dashed lines delineate the same dynamical regimes, i.e. I, II and III, identified in Fig. \ref{['fig:Density_dynamics']}. The remaining system parameters are the same as in Fig. \ref{['fig:Density_dynamics']}.
• Figure 5: (a) Dynamics of the center-of-mass of the dipolar gas, $\braket{x}$, for different barrier velocities (see legend) capturing the collective motion triggered by the barrier sweep. This collective motion, in particular, occurs at evolution times where the barrier is long past the dipolar gas (regime III). (b) The time-evolution of the associated chemical potential exhibits an increase (regime II) and a subsequent oscillatory behavior (regime III) unveiling underlying energy redistribution induced by the barrier drag. Afterwards, the chemical potential shows a saturation tendency toward a value larger than the respective $\mu$ of the initial droplet ground-state but in the ballpark of the supersolid ground-state phase marked by the shaded area. This occurs in the dynamical stage III, where the superfluid background has been established and remains persistent. The parameters for the potential barrier and the dipolar gas are the same as in Fig. \ref{['fig:Density_dynamics']}.