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arXiv:2208.05028 · Physical Review A

Striped dilute liquid of dipolar bosons in two dimensions

Clemens Staudinger, Diana Hufnagl, Ferran Mazzanti, Robert E. Zillich

Published Sep 5, 2023• 10 citations
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Abstract

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.

DOI
10.1103/physreva.108.033303

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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.
Bose-Einstein condensation of dipolar molecules can be achieved by shielding loss channels with microwave fields. The microwave coupling can be approximated by effective dipole-dipole interactions with a short-range repulsion. We study properties and stability of these molecular Bose gases with a many-body variational method, the hypernetted-chain Euler-Lagrange method for a wide range of densities and repulsion strengths of the microwave shield. We find a homogeneous gas-like phase which, however, is unstable at low density against density waves: at a critical density, which depends on the repulsion strength, the dipolar fluid undergoes a phase transition to a layer phase. Thus, if the molecular condensate is expanded adiabatically by decreasing the confinement strength, it will spontaneously form layers at the critical density. These quasi-two-dimensional layers can be self-bound, hence form two-dimensional liquids. By varying the microwave shield, the predicted equilibrium densities span more than an order of magnitude.
We characterize a system of tilted dipoles in a quasi two-dimensional (flattened) geometry and in the thermodynamic limit. We consider a finite trapping in the z-axis achievable in current experiments. We compute the phase diagram of the system at its equilibrium density for high tilting angles, where it becomes self-bound, and a striped liquid state emerges. To characterize the system, we perform a variational calculation, which is benchmarked with the solution of the extended Gross-Pitaevskii equation. We connect the phenomenology in the thermodynamic limit to the physics of the finite-size system, provide parameters for the realization of potentially supersolid striped states and study the critical number for dipolar droplet formation. Our results are helpful to guide potential experiments in the study of dipolar atoms in quasi two-dimensional geometries in the dipole-dominated regime.
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.
Ground-state properties of a two-dimensional fluid of bosons with repulsive dipole-dipole interactions are studied by means of the Euler-Lagrange hypernetted-chain approximation. We present a self-consistent semianalytical theory of the pair distribution function g(r)g(r)g(r) and ground-state energy of this system. Our approach is based on the solution of a zero-energy scattering Schr\"odinger equation for the ``pair amplitude'' g(r)\sqrt{g(r)}g(r)​ with an effective potential from Jastrow-Feenberg correlations. We find excellent agreement with quantum Monte Carlo results over a wide range of coupling strength, nearly up to the critical coupling for the liquid-to-crystal quantum phase transition. We also calculate the one-body density matrix and related quantities, such as the momentum distribution function and the condensate fraction.
Abstract We calculate analytically the quantum and thermal fluctuations corrections of a dilute quasi-two-dimensional Bose-condensed dipolar gas. We show that these fluctuations may change their character from repulsion to attraction in the density-temperature plane owing to the striking momentum dependence of the dipole–dipole interactions. The dipolar instability is halted by such unconventional beyond mean field corrections leading to the formation of a droplet phase. The equilibrium features and coherence properties exhibited by such droplets are deeply discussed. At finite temperature, we find that the equilibrium density crucially depends on the temperature and on the confinement strength and thus, a stable droplet can exist only at ultralow temperature due to the strong thermal fluctuations.