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arXiv:1402.4335 · Journal of Physics B Atomic Molecular and Optical Physics

Formation of classical crystals of dipolar particles in a helical geometry

J K Pedersen, D V Fedorov, A S Jensen, Nikolaj Thomas Zinner

Published Aug 8, 2014• 15 citations

Abstract

We consider crystal formation of particles with dipole-dipole interactions that are confined to move in a one-dimensional helical geometry with their dipole moments oriented along the symmetry axis of the confining helix. The stable classical lowest energy configurations are found to be chain structures for a large range of pitch-to-radius ratios for relatively low density of dipoles and a moderate total number of particles. The classical normal mode spectra support the chain interpretation both through structure and the distinct degeneracies depending discretely on the number of dipoles per revolution. A larger total number of dipoles leads to a clusterization where the dipolar chains move closer to each other. This implies a change in the local density and the emergence of two length scales, one for the cluster size and one for the inter-cluster distance along the helix. Starting from three dipoles per revolution, this implies a breaking of the initial periodicity to form a cluster of two chains close together and a third chain removed from the cluster. This is driven by the competition between in-chain and out-of-chain interactions, or alternatively the side-by-side repulsion and the head-to-tail attraction in the system. The speed of sound propagates along the chains. It is independent of the number of chains although depending on geometry.

DOI: 10.1088/0953-4075/47/16/165103

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We consider crystal formation of particles with dipole-dipole interactions that are confined to move in a one-dimensional helical geometry with their dipole moments oriented along the symmetry axis of the confining helix. The stable classical lowest energy configurations are found to be chain structures for a large range of pitch-to-radius ratios for relatively low density of dipoles and a moderate total number of particles. The classical normal mode spectra support the chain interpretation both through structure and the distinct degeneracies depending discretely on the number of dipoles per revolution. A larger total number of dipoles leads to a clusterization where the dipolar chains move closer to each other. This implies a change in the local density and the emergence of two length scales, one for the cluster size and one for the inter-cluster distance along the helix. Starting from three dipoles per revolution, this implies a breaking of the initial periodicity to form a cluster of two chains close together and a third chain removed from the cluster. This is driven by the competition between in-chain and out-of-chain interactions, or alternatively the side-by-side repulsion and the head-to-tail attraction in the system. The speed of sound propagates along the chains. It is independent of the number of chains although depending on geometry.

Abstract We study a quantum mechanical system consisting of up to three identical dipoles confined to move along a helical shaped trap. The long-range interactions between particles confined to move in this one dimension leads to an interesting effective two-particle potential with an oscillating behavior. For this system we calculate the spectrum and the wave functions of the bound states. The full quantum solutions show clear imprints of the tendency for the system to form chains of dipoles along the helix, i.e. a configuration in which the dipoles are sitting approximately one winding of the helix apart so that they can take maximal advantage of the strong head-to-tail attraction that is a generic feature of the dipole–dipole interaction.

Constraining long-range interacting particles to move on a curved manifold can drastically alter their effective interactions. As a prototype we explore the structure and vibrational dynamics of crystalline configurations formed on a closed helix. We show that the ground state undergoes a pitchfork bifurcation from a symmetric polygonic to a zigzag-like configuration with increasing radius of the helix. Remarkably, we find that, for a specific value of the helix radius, below the bifurcation point, the vibrational frequency spectrum collapses to a single frequency. This allows for an essentially independent small-amplitude motion of the individual particles and, consequently, localized excitations can propagate in time without significant spreading. Upon increasing the radius beyond the degeneracy point, the band structure is inverted, with the out-of-phase oscillation mode becoming lower in frequency than the mode corresponding to the center-of-mass motion.

We explore the helical quantum two-body problem i.e. two repulsively Coulomb interacting particles confined to move along a helix. The effective potential possesses a tunable number of potential wells superimposed on the repulsive Coulomb interaction that can be varied by changing the ratio of the pitch and radius of the helix. The anharmonicity of these wells depends crucially on this ratio and on the order of the well which can be seen also by analyzing the individual wells energy eigenvalue spacing. Our main focus is the investigation of the quantum dynamics of differently prepared wave packets that scatter from the multi-well potential landscape. We show that there exists a rich pattern forming transient evolution which depends also on the number of bound states of the individual wells. We demonstrate how the multiple wells leave their fingerprints in the dynamics leading, among others, to oscillatory structures on different spatial scales, the formation of beats and pulsed emission from single well localized wave packets due to their intrawell dynamics.

Dipolar interactions support the formation of intersite soliton molecules in a stack of quasi-one-dimensional (quasi-1D) traps. We show that the stability and properties of individual solitons and soliton molecules in such a geometry crucially depend on the interplay between contact and dipolar interactions. In particular, two different quasi-1D soliton regimes are possible: a one-dimensional (1D) soliton characterized by purely repulsive dipole-dipole interactions (DDI) and a three-dimensional (3D) soliton for which a sufficiently large dipole moment renders the DDI attractive. Furthermore, we find that in contrast to the dimers of polar molecules the soliton dimers exhibit a nontrivial behavior of the elementary excitations that stems from the competition between onsite and intersite DDI. Finally, we prove the existence of soliton trimers in a regime where molecular trimers do not occur. We demonstrate that the soliton molecules that we report are well feasible under realistic experimental conditions.

We study the ground-state phase diagram of ultracold dipolar gases in highly anisotropic traps. Starting from a one-dimensional geometry, by ramping down the transverse confinement along one direction, the gas reaches various planar distributions of dipoles. At large linear densities, when the dipolar gas exhibits a crystal-like phase, critical values of the transverse frequency exist below which the configuration exhibits transverse patterns. These critical values are found by means of a classical theory, and are in full agreement with classical Monte Carlo simulations. The study of the quantum system is performed numerically with Monte Carlo techniques and shows that the quantum fluctuations smoothen the transition and make it completely disappear in a gas phase. These predictions could be experimentally tested and would allow one to reveal the effect of zero-point motion on self-organized mesoscopic structures of matter waves, such as the transverse pattern of the zigzag chain.

We predict that ultracold bosonic dipolar gases, confined within a multilayer geometry, may undergo self-assembling processes, leading to the formation of chain gases and solids. These dipolar chains, with dipoles aligned across different layers, emerge at low densities and resemble phases observed in liquid crystals, such as nematic and smectic phases. We calculate the phase diagram using quantum Monte Carlo methods, introducing a newly devised trial wave function designed for describing the chain gas, where dipoles from different layers form chains without in-plane long-range order. We find gas, solid, and chain phases, along with quantum phase transitions between these states. Specifically, we predict the existence of quantum phase transitions from gaseous to self-ordered phases, as the interlayer distance is decreased. Remarkably, in the self-organized phases, the mean interparticle distance can significantly exceed the characteristic length of the interaction potential, yielding solids and chain gases with densities several orders of magnitude lower than those of conventional quantum solids.