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arXiv:1305.6007

Quantum Monte Carlo study of a two dimensional dipolar Bose gas in a harmonic trap

Michele Ruggeri

Published May 26, 2013• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1305.6007

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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.
We present extensive ab initio path-integral Monte Carlo (PIMC) simulations of two-dimensional quantum dipole few-body systems ($2\ensuremath{\le}N\ensuremath{\le}7$) in a harmonic confinement, taking into account both Bose- and Fermi-statistics. This allows us to study the nonclassical rotational inertia, which can lead to a negative superfluid fraction in the case of fermions [Phys. Rev. Lett. 112, 235301 (2014)]. Moreover, we study in detail the structural characteristics of such systems and are able to clearly resolve the impact of quantum statistics on density profiles and the respective shell structure. Further, we present results for a more advanced center-two-particle correlation function [Phys. Rev. E 91, 043104 (2015)], which allows detection of differences between Fermi and Bose systems even when they are almost absent in other observables like the density. Overall, we find that bosonic systems sensitively react to even small values of the dipole-dipole coupling strength, whereas such a weak interaction is effectively masked for fermions by the Pauli exclusion principle. In addition, the abnormal superfluid fraction for fermions is not reflected by the structural properties of the system, which are equal to the bosonic case even though the moments of inertia diverge from each other. Lastly, we have explored the possibility of fermionic PIMC simulations of quantum dipole systems despite the notorious fermion sign problem, which can be further extended in future investigations in this field.
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.
We study, by quantum Monte Carlo simulations, the ground state of a harmonically confined dipolar Bose gas with aligned dipole moments and with the inclusion of a repulsive two-body potential of varying range. Two different limits can clearly be identified, namely, a classical one in which the attractive part of the dipolar interaction dominates and the system forms an ordered array of parallel filaments and a quantum-mechanical one, wherein filaments are destabilized by zero-point motion, and eventually the ground state becomes a uniform cloud. The physical character of the system smoothly evolves from classical to quantum mechanical as the range of the repulsive two-body potential increases. An intermediate regime is observed in which ordered filaments are still present, albeit forming different structures from the ones predicted classically; quantum-mechanical exchanges of indistinguishable particles across different filaments allow phase coherence to be established, underlying a global superfluid response.
The ground-state phase properties of a two-dimensional Bose system with dipole-dipole interactions is studied by means of quantum Monte Carlo techniques. Limitations of mean-field theory in a two-dimensional geometry are discussed. A quantum phase transition from gas to solid is found. Crystal is tested for existence of a supersolid in the vicinity of the phase transition. Existence of mesoscopic analogue of the off-diagonal long-range order is shown in the one-body density matrix in a finite-size crystal. Non-zero superfluid fraction is found in a finite-size crystal, the signal being dramatically increased in presence of vacancies.
Two-dimensional (2D) dipolar atomic gases present unique opportunities for exploring novel quantum phases due to their anisotropic and long-range interactions. However, the behavior of strongly dipolar Bose gases in 2D remains unclear, especially when dipoles are tilted. Here, we demonstrate the creation and characterization of strongly dipolar 2D condensates in a quasi-2D harmonic trap with tunable dipole orientation. By investigating scale invariance properties through breathing collective mode measurements, we observe significant breaking of scale invariance when dipoles are tilted in-plane indicating the dominance of the nonlocal dipole-dipole interactions (DDIs) in this regime. Interestingly, the breaking of the scale invariant dynamics is accompanied by an increase in quantum fluctuations, as shown by comparison with mean-field and beyond mean-field theoretical studies. Our experiments also reveal that at critical tilt angles around 70°, stripe-type density modulations emerge, suggesting the presence of a roton spectrum in 2D, while the system still shows hydrodynamic nature with the phase-locking breathing behavior. This observation elucidates the many-body effect induced by DDIs in 2D, thus marking a crucial step toward realizing 2D supersolids and other exotic quantum phases.
The path-integral Monte Carlo method is used to simulate dilute trapped Bose gases and to investigate the equilibrium properties at finite temperatures. The quantum particles have a long-range dipole-dipole interaction and a short-range sss-wave interaction. Using an anisotropic pseudopotential for the long-range dipolar interaction and a hard-sphere potential for the short-range sss-wave interaction, we calculate the energetics and structural properties as a function of temperature and the number of particles. Also, in order to determine the effects of dipole-dipole forces and the influence of the trapping field on the dipolar condensate, we use two cylindrically symmetric harmonic confinements (a cigar-shaped trap and a disk-shaped trap). We find that the net effect of dipole-dipole interactions is governed by the trapping geometry. For a cigar-shaped trap, the net contribution of dipolar interactions is attractive and the shrinking of the density profiles is observed. For a disk-shaped trap, the net effect of long-range dipolar forces is repulsive and the density profiles expand.