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arXiv:2312.01716 · Physical Review A

Density-wave-type supersolid of two-dimensional tilted dipolar bosons

A. N. Aleksandrova, I. L. Kurbakov, Aleksey K. Fedorov, Yu. E. Lozovik

Published Jun 24, 2024• 8 citations
arXivHTMLPDF

Abstract

We predict a stable density-wave-type supersolid phase of a dilute gas of tilted dipolar bosons in a two-dimensional (2D) geometry. This many-body phase is manifested by the formation of the stripe pattern and elasticity coexisting together with the Bose-Einstein condensation and superfluidity at zero temperature. With the increasing of the tilting angle the type of the gas-supersolid transition changes from the first order to the second-order one despite the 2D character of the system, whereas the anisotropy and many-body stabilizing interactions play crucial roles. Our approach is based on the numerical analysis of the phase diagram using the simulated annealing method for a free-energy functional. The predicted supersolid effect can be realized in a variety of experimental setups ranging from excitons in heterostructures to cold atoms and polar molecules in optical potentials.

DOI
10.1103/physreva.109.063326

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We predict a stable density-wave-type supersolid phase of a dilute gas of tilted dipolar bosons in a two-dimensional (2D) geometry. This many-body phase is manifested by the formation of the stripe pattern and elasticity coexisting together with the Bose-Einstein condensation and superfluidity at zero temperature. With the increasing of the tilting angle the type of the gas-supersolid transition changes from the first order to the second-order one despite the 2D character of the system, whereas the anisotropy and many-body stabilizing interactions play crucial roles. Our approach is based on the numerical analysis of the phase diagram using the simulated annealing method for a free-energy functional. The predicted supersolid effect can be realized in a variety of experimental setups ranging from excitons in heterostructures to cold atoms and polar molecules in optical potentials.
We analyze the ground state of a system of dipolar bosons moving in the XYXYXY plane and such that their dipolar moments are all aligned in a fixed direction in space. We focus on the general case where the polarization field forms a generic angle $\ensuremath{\alpha}$ with respect to the ZZZ axis. We use the path-integral ground-state method to analyze the static properties of the system as both $\ensuremath{\alpha}$ and the density nnn vary over a wide range where the system is stable. We use the maximum of the static structure function as an order parameter to characterize the different phases and the transition lines among them. We find that, in addition to a superfluid gas and a solid phase, the system reaches a stripe phase at large tilting angles that is entirely induced by the anisotropic character of the interaction. We also show that the quantum phase transition from the gas to the stripe phase is of second order and report approximate values for the critical exponents.
Experiments on quantum degenerate Fermi gases of magnetic atoms and dipolar molecules begin to probe their broken-symmetry phases dominated by the long-range, anisotropic dipole-dipole interaction. Several candidate phases including the ppp-wave superfluid, the stripe density wave, and a supersolid have been proposed theoretically for two-dimensional spinless dipolar Fermi gases. Yet the phase boundaries predicted by different approximations vary greatly and a definitive phase diagram is still lacking. Here we present a theory that treats all competing many-body instabilities in the particle-particle and particle-hole channel on equal footing. We obtain the low-temperature phase diagram by numerically solving the functional renormalization-group flow equations and find a nontrivial density wave phase at small dipolar tilting angles and strong interactions, but no evidence of the supersolid phase. We also estimate the critical temperatures of the ordered phases.
By means of quantum Monte Carlo simulations we study phase diagrams of dipolar bosons in a square optical lattice. The dipoles in the system are parallel to each other and their orientation can be fixed in any direction in the three-dimensional space. Starting from experimentally tunable parameters like scattering length and dipolar interaction strength, we derive the parameters entering the effective Hamiltonian. Depending on the direction of the dipoles, various types of supersolids (e.g., checkerboard, stripe) and solids (checkerboard, stripe, diagonal stripe, and an incompressible phase) can be stabilized. Remarkably, we find a cluster supersolid characterized by the formation of horizontal clusters of particles. These clusters order along a direction at an angle with the horizontal. Moreover, we find what we call a grain-boundary superfluid. In this phase, regions with solid order are separated by extended defects---grain boundaries---which support superfluidity. We also investigate the robustness of the stripe supersolid against thermal fluctuations. Finally, we comment on the experimental realization of the phases found.
We study the superfluid properties of a system of fully polarized dipolar bosons moving in the XY plane. We focus on the general case where the polarization field forms an arbitrary angle α with respect to the Z axis, while the system is still stable. We use the diffusion Monte Carlo and the path integral ground state methods to evaluate the one-body density matrix and the superfluid fractions in the region of the phase diagram where the system forms stripes. Despite its oscillatory behavior, the presence of a finite large-distance asymptotic value in the s-wave component of the one-body density matrix indicates the existence of a Bose condensate. The superfluid fraction along the stripes direction is always close to 1, while in the Y direction decreases to a small value that is nevertheless different from zero. These two facts confirm that the stripe phase of the dipolar Bose system is a clear candidate for an intrinsic supersolid without the presence of defects as described by the Andreev-Lifshitz mechanism.
We investigate the phases of a Bose-Einstein condensate of dipolar atoms restricted to move in a two-dimensional plane. The dipole moments are all aligned in a direction tilted with respect to the plane normal. As a result of the attractive and repulsive components of the dipole-dipole interaction, the dipolar gas has a self-bound phase, which is stabilized by quantum fluctuations. Tilting the dipoles tunes the anisotropy of the dipole-dipole interaction, which can trigger a spatial density modulation. In this work we study these two aspects and investigate the conditions for the formation of a self-bound and striped phase, which has been realized in experiments with dipolar droplets. We use a variational method based on the hypernetted-chain Euler-Lagrange optimization of a Jastrow-Feenberg ansatz for the many-body wave function to study the ground-state properties. This method takes into account quantum fluctuations in a nonperturbative way and thus can be used also for strongly correlated systems.
Fluctuations typically destroy long-range order in two-dimensional (2D) systems, posing a fundamental challenge to the existence of exotic states like supersolids, which paradoxically combine solid-like structure with frictionless superfluid flow. While long-predicted, the definitive observation of a 2D supersolid has remained an outstanding experimental goal. Here, we report the observation of a supersolid stripe phase in a strongly dipolar quantum gas of erbium atoms confined to 2D. We directly image the periodic density modulation, confirming its global phase coherence through matter-wave interference and demonstrating its phase rigidity relevant to the low-energy Goldstone mode, consistent with numerical calculations. Through collective excitation measurements, we demonstrate the hydrodynamic behavior of the supersolid. This work highlights a novel mechanism for supersolid formation in low dimensions, and opens the door for future research on the intricate interplay between temperature, supersolidity, and dimensionality.