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Journal of Physics Conference Series

Roton Instability and Phonon Collapse of Two-dimensional Tilted Dipoles

Aleksey K. Fedorov, I. L. Kurbakov, Yu. E. Lozovik

Published Feb 8, 2013• 4 citations
Publisher

Abstract

Bose-Einstein condensed gas of two-dimensional tilted dipoles in a thin layer is under consideration. The problem of stability is resolved. Phase diagram for system of two-dimensional dipole atoms in a thin layer is obtained. A formation of density waves and their orientation control possibility via polarizing field are considered. These effects can be experimentally observed for magnetically dipolar atoms at the Feshbach resonance or polar molecules in one-dimensional optical lattices.

DOI
10.1088/1742-6596/414/1/012036

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Journal of Physics Conference Series•Jun 1, 2018•4 citations
Bose-Einstein condensed gas of two-dimensional tilted dipoles in a thin layer is under consideration. The problem of stability is resolved. Phase diagram for system of two-dimensional dipole atoms in a thin layer is obtained. A formation of density waves and their orientation control possibility via polarizing field are considered. These effects can be experimentally observed for magnetically dipolar atoms at the Feshbach resonance or polar molecules in one-dimensional optical lattices.
We predict the effect of the roton instability for a two-dimensional weakly interacting gas of tilted dipoles in a single homogeneous quantum layer. Being typical for strongly correlated systems, the roton phenomena appear to occur in a weakly interacting gas. It is important that in contrast to a system of normal to the layer dipoles, breaking of the rotational symmetry for a system of tilted dipoles leads to the convergence of the condensate depletion even up to the threshold of the roton instability, with mean-field approach being valid. Predicted effects can be observed in a wide class of dipolar systems. We suggest observing predicted phenomena for systems of ultracold atoms and polar molecules in optical lattices, and estimate optimal experimental parameters.
The effect of dipolar orientation with respect to the condensate plane on the mean-field dynamics of dipolar Bose-Einstein condensates in a pancake-shaped confinement is discussed. The stability of a quasi-two-dimensional condensate, with respect to the tilting angle, is found to be different from a two-dimensional layer of dipoles, indicating the relevance of the transverse extension while characterizing two-dimensional dipolar systems. An anisotropic excitation spectrum exhibiting a highly tunable, rotonlike minimum can arise entirely from the dipole-dipole interactions, by tilting the dipoles. At the magic angle and in the absence of contact interactions, the long-wavelength excitations are not phononlike and always unstable. The post-roton-instability dynamics, in contrast to phonon instability, in a uniform condensate, is featured by a transient, defect-free, stripe pattern, which eventually undergoes local collapses, and driving the condensate back into the stable regime can make them sustained for longer. Hopping between stripes has been observed before it melts into a uniform state in the presence of dissipation. Finally, we discuss a class of solutions, in which a quasi-two-dimensional condensate is self-trapped in one direction, as well as a regime of interaction parameters, including attractive short-range interactions, at which a two-dimensional anisotropic soliton can be stabilized, and we show that a chromium condensate with a relatively small number of atoms is well suited for this.
The effect of dipolar orientation with respect to the soliton plane on the physics of two-dimensional bright solitons in dipolar Bose-Einstein condensates is discussed. Previous studies on such a soliton involved dipoles either perpendicular or parallel to the condensate plane. The tilting angle constitutes an additional tuning parameter, which helps us to control the in-plane anisotropy of the soliton as well as provides access to previously disregarded regimes of interaction parameters for soliton stability. In addition, it can be used to drive the condensate into phonon instability without changing its interaction parameters or trap geometry. The phonon instability in a homogeneous two-dimensional condensate of tilted dipoles always features a transient stripe pattern, which eventually breaks into a metastable soliton gas. Finally, we demonstrate how a dipolar BEC in a shallow trap can eventually be turned into a self-trapped matter wave by an adiabatic approach involving the tuning of the tilting angle.
We examine the stability of quasi-two-dimensional dipolar Bose-Einstein condensates in the presence of weak optical lattices of various geometries. We find that when the condensate possesses a roton-maxon quasiparticle dispersion, the conditions for stability exhibit a strong dependence both on the lattice geometry and the polarization tilt. This results in rich structures in the system's stability diagram akin to spectroscopic signatures. We show how these structures originate from the mode matching of rotons to the perturbing lattice. In the case of a one-dimensional lattice, some of the features emerge only when the polarization axis is tilted into the plane of the condensate. Our results suggest that the stability diagram may be used as a novel means to spectroscopically measure rotons in dipolar condensates.
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.
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.