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arXiv:1112.5662 · Physical Review B

Clustered Wigner-crystal phases of cold polar molecules in arrays of one-dimensional tubes

Michael Knap, Erez Berg, Martin Ganahl, Eugene Demler

Published Aug 1, 2012• 37 citations
arXivHTMLPDF

Abstract

We analyze theoretically polar molecules confined in planar arrays of one-dimensional tubes. In the classical limit, if the number of tubes is finite, new types of ``clustered Wigner crystals'' with increasingly many molecules per unit cell can be stabilized by tuning the in-plane angle between the dipolar moments and the tube direction. Quantum mechanically these phases melt into distinct ``clustered Luttinger liquids.'' We calculate the phase diagram of the system and study the quantum melting of the clustered phases. We find that the requirements for exploring these phases are reachable in current experiments and discuss possible experimental signatures.

DOI
10.1103/physrevb.86.064501

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We analyze theoretically polar molecules confined in planar arrays of one-dimensional tubes. In the classical limit, if the number of tubes is finite, new types of clustered Wigner crystals'' with increasingly many molecules per unit cell can be stabilized by tuning the in-plane angle between the dipolar moments and the tube direction. Quantum mechanically these phases melt into distinct clustered Luttinger liquids.'' We calculate the phase diagram of the system and study the quantum melting of the clustered phases. We find that the requirements for exploring these phases are reachable in current experiments and discuss possible experimental signatures.
We systematically study ground-state properties of fermionic dipolar gases in a planar array of one-dimensional potential tubes for arbitrary orientation of dipole moments. Using the Luttinger liquid theory with the generalized Bogoliubov transformation, we calculate the elementary excitations and the Luttinger scaling exponents for various relevant quantum orders. The complete quantum phase diagrams for arbitrary polar angle of the dipole moment are obtained including charge-density wave, ppp-wave superfluid, intertube gauge-phase density wave, and intertube sss-wave superfluid, where the last two break the U(1) gauge symmetry of the system (conservation of particle number in each tube) and occur only when the intertube interaction is larger than the intratube interaction. We then discuss the physical properties and experimental features of these many-body phases.
We investigate the finite-temperature phase diagram of polar molecules confined in a quasi-two-dimensional geometry by a harmonic potential along the polarization axis. We employ quantum Monte Carlo simulations to explore the strongly correlated regime accessible with current experimental setups. By tuning temperature and confinement strength, we identify a rich set of phases, including normal fluid, superfluid, supersolid, cluster crystal, and bilayer crystal states. Our results reveal the emergence of crystallization upon increasing temperature, highlighting the nontrivial role of thermal fluctuations in dipolar systems. In particular, we show that a bilayer crystal with one molecule per lattice site can be stabilized by varying the confinement strength at fixed interaction. Moreover, we show evidence of layering of superfluid states with phase coherence between the two layers. These findings provide insight into the interplay between interactions, confinement, and temperature in low-dimensional dipolar systems, and suggest new directions for engineering quantum phases with ultracold polar molecules.
We investigate bosonic atoms or molecules interacting via dipolar interactions in a planar array of one-dimensional tubes. We consider the situation in which the dipoles are oriented perpendicular to the tubes by an external field. We find various quantum phases reaching from a "sliding Luttinger liquid" phase to a two-dimensional charge density wave ordered phase. Two different kinds of charge density wave order occur: a stripe phase in which the bosons in different tubes are aligned and a checkerboard phase. We further point out how to distinguish the occurring phases experimentally.
We discuss the realization of mesoscopic phases of dipolar gases relevant to current experiments with cold polar molecules and Rydberg atoms confined to two dimensions. We predict the existence of superfluid clusters, mesoscopic supersolids, and crystals for a small number of trapped particles, with no counterpart in the homogeneous situation. For certain strengths of the dipole-dipole interactions, the stabilization of purely {\it non-classical crystals} by quantum fluctuations is possible. We propose a magnification scheme to detect the spatial structure of these crystalline phases.
The exploration of cold polar molecules in different geometries is a rapidly developing experimental and theoretical pursuit. Recently, the implementation of optical lattices has enabled confinement in stacks of planes, the number of which is also controllable. Here we consider the bound state structure of two polar molecules confined in two adjacent planes as function of the polarization angle of the dipole moment of the molecules. We prove analytically and present numerical evidence for the existence of bound states for arbitrary dipole moments and polarization directions in this two-dimensional geometry. The spatial structure of the bound states is dominated by two-dimensional s- and p-waves, where the latter exceeds 40 percent over a large range of polarization angles for intermediate or strong dipole strength. Finally, we consider the influence of the dimer bound states on the potential many-body ground-state of the system.
Following the recent proposal to create quadrupolar gases [Bhongale et al., Phys. Rev. Lett. 110, 155301 (2013)], we investigate what quantum phases can be created in these systems in one dimension. We consider a geometry of two coupled one-dimensional (1D) systems, and derive the quantum phase diagram of ultracold fermionic atoms interacting via quadrupole-quadrupole interactions within a Tomonaga-Luttinger-liquid framework. We map out the phase diagram as a function of the distance between the two tubes and the angle between the direction of the tubes and the quadrupolar moments. The latter can be controlled by an external field. We show that there are two magic angles ${\ensuremath{\theta}}_{B,1}^{c}$ and ${\ensuremath{\theta}}_{B,2}^{c}$ between 0 and $\ensuremath{\pi}/2$, where the intratube quadrupolar interactions vanish and change signs. Adopting a pseudospin language with regard to the two 1D systems, the system undergoes a spin-gap transition and displays a zigzag density pattern, above ${\ensuremath{\theta}}_{B,2}^{c}$ and below ${\ensuremath{\theta}}_{B,1}^{c}$. Between the two magic angles, we show that polarized triplet superfluidity and a planar spin-density-wave order compete with each other. The latter corresponds to a bond-order solid in higher dimensions. We demonstrate that this order can be further stabilized by applying a commensurate periodic potential along the tubes.