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 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.
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.
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=12 and N=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.
A mesoscopic system of dipolar bosons trapped by a harmonic potential is considered. The system has a number of physical realizations including dipole excitons, atoms with large dipolar moment, polar molecules, and Rydberg atoms in inhomogeneous electric field. We carry out a diffusion Monte Carlo simulation to define the quantum properties of a two-dimensional system of trapped dipoles at zero temperature. In dimensionless units the system is described by two control parameters, namely, the number of particles and the strength of the interparticle interaction. We have shown that when the interparticle interaction is strong enough a mesoscopic crystal is formed. As the strength of interactions is decreased a multistage melting takes place. Off-diagonal order in the system is tested using natural-orbitals analysis. We have found that the system might be Bose condensed even in the case of strong interparticle interactions. There is a set of parameters for which a spatially ordered structure is formed while simultaneously the fraction of Bose-condensed particles is nonzero. This might be considered as a realization of a mesoscopic supersolid.
Motivated by the recent experimental observation of dipolar supersolid stripes in a quasi two-dimensional geometry [arXiv:2512.13280 (2025)], we study a trapped system of fully polarized dipoles in a strongly axially confined geometry, both at zero and finite temperatures, by means of Bogoliubov theory. The dipoles are strongly harmonically trapped along the z axis and subjected to a box trap in the x-y plane. We characterize the physics of the trapped system at zero and finite temperatures as a function of the tilting angle of the dipoles, the number of particles and the scattering length, restricting ourselves to the experimentally relevant regime of large condensate fractions. We also illustrate the influence of the aspect ratio of the box trap in the liquid character of the system and its structure. We observe a remarkable promotion of spatial modulations when temperature is increased while keeping the total particle number constant for specific configurations, in qualitative agreement with previous Monte Carlo results in a 3D geometry. Our results are useful to understand the zero temperature physics of the trapped dipolar system in the quasi-2D limit and in the strongly dipolar regime. In addition, they allow to assess the effect of temperature in its equilibrium properties in experimentally relevant conditions, which may be useful for thermometry applications.
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 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.