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arXiv:2605.18546 · Physical Review A

Bilayer crystals in a polar-molecule system

Vinicius Zampronio, Matteo Ciardi, Fabio Cinti

Published Sep 8, 2026• 0 citations
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Abstract

We investigate the finite-temperature phase diagram of polar molecules confined in a quasi-two-dimensional geometry by a harmonic potential along the polarization axis. We employ quantum Monte Carlo simulations to explore the strongly correlated regime accessible with current experimental setups. By tuning temperature and confinement strength, we identify a rich set of phases, including normal fluid, superfluid, supersolid, cluster crystal, and bilayer crystal states. Our results reveal the emergence of crystallization upon increasing temperature, highlighting the nontrivial role of thermal fluctuations in dipolar systems. In particular, we show that a bilayer crystal with one molecule per lattice site can be stabilized by varying the confinement strength at fixed interaction. Moreover, we show evidence of layering of superfluid states with phase coherence between the two layers. These findings provide insight into the interplay between interactions, confinement, and temperature in low-dimensional dipolar systems, and suggest new directions for engineering quantum phases with ultracold polar molecules.

DOI
10.1103/64fx-rnc1

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We investigate the finite-temperature phase diagram of polar molecules confined in a quasi-two-dimensional geometry by a harmonic potential along the polarization axis. We employ quantum Monte Carlo simulations to explore the strongly correlated regime accessible with current experimental setups. By tuning temperature and confinement strength, we identify a rich set of phases, including normal fluid, superfluid, supersolid, cluster crystal, and bilayer crystal states. Our results reveal the emergence of crystallization upon increasing temperature, highlighting the nontrivial role of thermal fluctuations in dipolar systems. In particular, we show that a bilayer crystal with one molecule per lattice site can be stabilized by varying the confinement strength at fixed interaction. Moreover, we show evidence of layering of superfluid states with phase coherence between the two layers. These findings provide insight into the interplay between interactions, confinement, and temperature in low-dimensional dipolar systems, and suggest new directions for engineering quantum phases with ultracold polar molecules.
The ground state of a two-dimensional, harmonically confined mesoscopic assembly of up to 30 polar molecules is studied by computer simulations. As the strength of the confining trap is increased, clusters evolve from superfluid, to supersolid, to insulating crystals. For strong confinement, the crystalline structure can be predicted based on classical energetics. However, clusters of specific numbers of particles (i.e., N=12N=12N=12 and N=19N=19N=19) display a nonclassical crystalline structure, stabilized by quantum effects, in an intermediate range of confinement strength. In these cases, coexistence of quantum and classical crystalline configurations is observed at finite temperature.
It is well-known that the liquid properties in a strongly confined system can be very different from their ordinary behaviors in an extended system, due to the competition between the thermal energy and the interaction energy. Here we show that, in a low-dimensional self-assembled dipolar crystal, the parabolic optical confinement potential can also strongly affect the quantum many-body properties in the low temperature regime. For example, by changing the confinement aspect ratio, the bulk of the system can undergo a quantum phase transition between a liquid state and a solid state via a nonmonotonic pattern formation of the domain wall. Furthermore, the entropy of a trapped dipolar crystal can be much larger than the liquid state in the weak dipole limit, indicating an intrinsic polarization cooling mechanism via increasing the external field. These highly correlated confinement effects are very important to the experimental preparation of a self-assembled dipolar crystal using ultracold polar molecules.
We explore the phase diagram of ultracold bosonic polar molecules confined to a planar optical lattice of triangular geometry. External static electric and microwave fields can be employed to tune the effective interactions between the polar molecules into a regime of extended two- and three-body repulsions of comparable strength, leading to a rich quantum phase diagram. In addition to various solid phases, an extended supersolid phase is found to persist deep into the three-body dominated regime. While three-body interactions break particle-hole symmetry explicitly, a characteristic supersolid-supersolid quantum phase transition is observed, which indicates the restoration of particle-hole symmetry at half-filling. We revisit the spatial structure of the supersolid at this filling, regarding the existence of a further supersolid phase with three inequivalent sublattices, and provide evidence that this state is excluded also at finite temperatures.
We investigate the physics of ultracold dipolar molecules using path-integral quantum Monte Carlo simulations, and construct the complete phase diagram extending from weak to strong interactions and from small to mesoscopic particle numbers. Our calculations predict the formation of self-bound quantum droplets at interaction strengths lower than previous estimates for molecular condensates. Strikingly, we observe that, for stronger interactions, the oblate quantum droplet transitions to a two-dimensional sheet or superfluid membrane with a thickness of a single molecule. As interactions are increased further the system continually loses superfluidity while correlations develop, and is eventually found to undergo a transition to a crystalline monolayer that remains self-bound without external confinement. The spontaneous formation of such two-dimensional phases from a three-dimensional quantum gas is traced back to the peculiar anisotropic form of the dipole-dipole interaction generated by microwave dressing of rotational molecular states. For sufficiently large particle numbers, crystallization takes place for comparably low interaction strengths that do not promote two-body bound states and should thus be observable in ongoing experiments without limitations from three-body recombination.
We investigate the confinement effects on a two-dimensional mesoscopic (particle number N >200) self-assembled dipolar crystal trapped in a harmonic potential. The ground-state wave function and energy are calculated by diagonalizing the position fluctuations to the quadratic order within the strong-interaction limit. We further investigate the crystal-liquid domain wall boundary as well as the system temperature by changing the confinement aspect ratio and/or dipole moment strength. We find that the entropy of a trapped dipolar crystal can be much larger than the entropy in the liquid state at zero dipole moment, indicating a polarization cooling mechanism during the formation of dipolar crystal when the external field is increased adiabatically. Our results therefore have significant application to the experimental preparation of a self-assembled dipolar crystal using ultracold polar molecules.
We study the phase diagram of a system of soft-core dipolar bosons confined to a two-dimensional optical lattice layer. We assume that dipoles are aligned perpendicular to the layer such that the dipolar interactions are purely repulsive and isotropic. We consider the full dipolar interaction and perform Path Integral Quantum Monte Carlo simulations using the Worm Algorithm. Besides a superfluid phase, we find various solid and supersolid phases. We show that, unlike what was found previously for the case of nearest-neighboring interaction, supersolid phases are stabilized not only by doping the solids with particles but with holes as well. We further study the stability of these quantum phases against thermal fluctuations. Finally, we discuss pair formation and the stability of the pair checkerboard phase formed in a bilayer geometry, and suggest experimental conditions under which the pair checkerboard phase can be observed.