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New Journal of Physics

Few trapped quantum dipoles: quantum versus classical structures

Juan Sánchez-Baena, Ferran Mazzanti, Jordi Boronat

Published Jan 8, 2018• 1 citation
Publisher

Abstract

We analyze the ground state of a two-dimensional quantum system of a few strongly confined dipolar bosons. Dipoles arrange in different stable structures that depend on the tilting polarization angle and the anisotropy of the confining trap. To this end, we use the exact diffusion Monte Carlo method and the quantum results are compared with classical ones obtained by stochastic optimization using simulated annealing. We establish the stability domains for the different patterns and estimate the transition boundaries delimiting them. Our results show significant differences between the classical and quantum regimes which are mainly due to the quantum kinetic energy.

DOI
10.1088/1367-2630/aaa5f9

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We analyze the ground state of a two-dimensional quantum system of a few strongly confined dipolar bosons. Dipoles arrange in different stable structures that depend on the tilting polarization angle and the anisotropy of the confining trap. To this end, we use the exact diffusion Monte Carlo method and the quantum results are compared with classical ones obtained by stochastic optimization using simulated annealing. We establish the stability domains for the different patterns and estimate the transition boundaries delimiting them. Our results show significant differences between the classical and quantum regimes which are mainly due to the quantum kinetic energy.
Strongly interacting systems of dipolar bosons in three dimensions confined by harmonic traps are analyzed using the exact path integral ground-state Monte Carlo method. By adding a repulsive two-body potential, we find a narrow window of interaction parameters leading to stable ground-state configurations of droplets in a crystalline arrangement. We find that this effect is entirely due to the interaction present in the Hamiltonian without resorting to additional stabilizing mechanisms or specific three-body forces. We analyze the number of droplets formed in terms of the Hamiltonian parameters, relate them to the corresponding s-wave scattering length, and discuss a simple scaling model for the density profiles. Our results are in qualitative agreement with recent experiments showing a quantum Rosensweig instability in trapped Dy atoms.
We present a Quantum Monte Carlo study of the ground state properties of a two dimensional system of Bose particle with dipole moment in a harmonic trap. The direction of the dipoles is assumed to be fixed by an external field. We study how the system behaves when the direction of the dipole moments is changed. Our analysis is made using Path Integral Monte Carlo simulations in the Grand Canonical ensemble, using the Worm Algorithm. We study systems of increasing size, focusing on the spatial distribution of the atoms inside the trap and on the superfluid fraction of the sample. We find that vertical dipoles form a crystal, characterized by a shell structure, while tilting the dipoles has the effect of inducing a striped structure. We find that similar behaviour can be found in the analogue classical system. Vertical dipoles display nonclassical inertia while a strong tilting decreases superfluidity.
In this Thesis, we report a detailed study of the ground-state properties of a set of quantum few- and many-body systems in one and two dimensions with different types of interactions by using Quantum Monte Carlo methods. Nevertheless, the main focus of this work is the study of the ground-state properties of an ultracold Bose system with dipole-dipole interaction between the particles. We consider the cases where the bosons are confined to a bilayer and multilayer geometries, that consist of equally spaced two-dimensional layers. These layers can be experimentally realized by imposing tight confinement in one direction. We specifically address the study of new quantum phases, their properties, and transitions between them. One expects these systems to have a rich collection of few- and many-body phases because the dipole-dipole interaction is anisotropic and quasi long-range.
A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.
Recent experimental advances in creating stable dipolar systems, including polar molecules with large electric dipole moments, have led to vigorous theoretical activities. Here we discuss our work on homogeneous 2D dipolar bosons with dipoles oriented at an angle to the direction perpendicular to the confining 2D plane, i.e. for non-zero tilt angles. Using Bogoliubov-de Gennes equations, we obtain T=0 excitation spectrum of the dipolar Bose gas, and explore instabilities at varying tilt angle, density and dipolar coupling. We map out a phase diagram a function of tilt angle, dipole strength and density. We find the development of maxon-roton behavior leading to roton instabilities at large densities for small tilt angles, and at low densities for large tilt angles. The behavior is anisotropic in k-space; accordingly the roton instabilities occur in the k y direction, suggestive of inhomogeneity and stripe phase, with density mode becoming soft in the y direction. Our results compare favorably with existing Quantum Monte Carlo calculations for non-zero tilt angles.
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.