We demonstrate a supersolid-like spatially periodic square- and honeycomb-lattice crystallization of droplets in addition to the commonly studied triangular-lattice crystallization in a cylindrically symmetric quasi-two-dimensional trapped dipolar condensate, using a beyond-mean-field model including a quantum-fluctuation Lee-Huang-Yang-type interaction. These three types of crystallization of droplets may appear for the same atomic interaction and the same trap frequencies. The energies $E$ of all three crystallizations as a function of the number $N$ of atoms satisfy the universal scaling relation $E\ensuremath{\sim}{N}^{0.4}$, indicating that all three arrangements of the droplets should be energetically probable processes of phenomenological interest. The state of square-lattice crystallization may have the central site occupied or unoccupied, corresponding to a parity-symmetric or parity-antisymmetric state, respectively. The state of square-lattice crystallization with the occupied central site and the state of triangular-lattice crystallization, for a fixed $N$ , constitute two quasidegenerate ground states, while the other states are low-lying excited states. This makes the square-lattice crystallization with the occupied central site an ideal candidate for future experimental observation.We demonstrate a supersolid-like spatially periodic square- and honeycomb-lattice crystallization of droplets in addition to the commonly studied triangular-lattice crystallization in a cylindrically symmetric quasi-two-dimensional trapped dipolar condensate, using a beyond-mean-field model including a quantum-fluctuation Lee-Huang-Yang-type interaction. These three types of crystallization of droplets may appear for the same atomic interaction and the same trap frequencies. The energies $E$ of all three crystallizations as a function of the number $N$ of atoms satisfy the universal scaling relation $E\ensuremath{\sim}{N}^{0.4}$, indicating that all three arrangements of the droplets should be energetically probable processes of phenomenological interest. The state of square-lattice crystallization may have the central site occupied or unoccupied, corresponding to a parity-symmetric or parity-antisymmetric state, respectively. The state of square-lattice crystallization with the occupied central site and the state of triangular-lattice crystallization, for a fixed $N$, constitute two quasidegenerate ground states, while the other states are low-lying excited states. This makes the square-lattice crystallization with the occupied central site an ideal candidate for future experimental observation.

arXiv:2202.13264Physical Review AMar 21, 202228 citations

Moiré and frustration physics of dipolar supersolids under periodic confinement

Ze-Hong Guo, Kai Gan, and Qizhong Zhu

We study the ground-state phases of a two-dimensional dipolar supersolid subjected to external periodic confinement by numerically solving the extended Gross--Pitaevskii equation. Focusing on a regime in which the unconfined system forms an intrinsic triangular droplet crystal, we consider triangular, honeycomb, and square optical lattices and classify them into isostructural and heterostructural settings relative to the spontaneous supersolid order. We map out the stationary states as functions of the lattice depth $V_0$ and the commensurability ratio between the intrinsic droplet spacing and the external lattice period. For triangular and honeycomb confinements, the competition between the soft self-organized supersolid lattice and the rigid external potential can generate long-wavelength moiré superstructures in the weak- to intermediate-lattice regime, together with a sequence of reconstructed states including ring-like clusters and stripe-segment configurations. By contrast, the square lattice introduces strong symmetry mismatch between the intrinsic $C_6$ order and the imposed $C_4$ geometry, leading to frustration-induced anisotropic states and symmetry-reduced cluster arrangements. Our results establish dipolar supersolids under periodic confinement as an unconventional route to exploring moiré physics, where moiré superstructures arise from the competition between a self-organized soft lattice and an externally imposed rigid one.We study the ground-state phases of a two-dimensional dipolar supersolid subjected to external periodic confinement by numerically solving the extended Gross--Pitaevskii equation. Focusing on a regime in which the unconfined system forms an intrinsic triangular droplet crystal, we consider triangular, honeycomb, and square optical lattices and classify them into isostructural and heterostructural settings relative to the spontaneous supersolid order. We map out the stationary states as functions of the lattice depth $V_0$ and the commensurability ratio between the intrinsic droplet spacing and the external lattice period. For triangular and honeycomb confinements, the competition between the soft self-organized supersolid lattice and the rigid external potential can generate long-wavelength moiré superstructures in the weak- to intermediate-lattice regime, together with a sequence of reconstructed states including ring-like clusters and stripe-segment configurations. By contrast, the square lattice introduces strong symmetry mismatch between the intrinsic $C_6$ order and the imposed $C_4$ geometry, leading to frustration-induced anisotropic states and symmetry-reduced cluster arrangements. Our results establish dipolar supersolids under periodic confinement as an unconventional route to exploring moiré physics, where moiré superstructures arise from the competition between a self-organized soft lattice and an externally imposed rigid one.

arXiv:2603.27983Mar 30, 20260 citations

Crystallization of a dilute atomic dipolar condensate

R. N. Bisset, Blair Blakie

Bulletin of the American Physical SocietyMay 26, 20160 citations

Competing scenarios for dipolar hard-core bosons within square and triangular lattices

Wei-Lin Tu, Huan-Kuang Wu, Takafumi Suzuki +2 more

Bulletin of the American Physical SocietyMar 15, 20210 citations

E

of all three crystallizations as a function of the number

N

of atoms satisfy the universal scaling relation $E\ensuremath{\sim}{N}^{0.4}$, indicating that all three arrangements of the droplets should be energetically probable processes of phenomenological interest. The state of square-lattice crystallization may have the central site occupied or unoccupied, corresponding to a parity-symmetric or parity-antisymmetric state, respectively. The state of square-lattice crystallization with the occupied central site and the state of triangular-lattice crystallization, for a fixed

N

, constitute two quasidegenerate ground states, while the other states are low-lying excited states. This makes the square-lattice crystallization with the occupied central site an ideal candidate for future experimental observation.

V_0

and the commensurability ratio between the intrinsic droplet spacing and the external lattice period. For triangular and honeycomb confinements, the competition between the soft self-organized supersolid lattice and the rigid external potential can generate long-wavelength moiré superstructures in the weak- to intermediate-lattice regime, together with a sequence of reconstructed states including ring-like clusters and stripe-segment configurations. By contrast, the square lattice introduces strong symmetry mismatch between the intrinsic

C_6

order and the imposed

C_4

geometry, leading to frustration-induced anisotropic states and symmetry-reduced cluster arrangements. Our results establish dipolar supersolids under periodic confinement as an unconventional route to exploring moiré physics, where moiré superstructures arise from the competition between a self-organized soft lattice and an externally imposed rigid one.