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arXiv:0908.0072 · Physical Review A

Quantum phase diagrams of fermionic dipolar gases in a planar array of one-dimensional tubes

Yi-Ping Huang, Daw-Wei Wang

Published Nov 12, 2009• 23 citations
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Abstract

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, $p$-wave superfluid, intertube gauge-phase density wave, and intertube $s$-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.

DOI
10.1103/physreva.80.053610

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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 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.
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.
We present a theory for a lattice array of weakly coupled one-dimensional ultracold attractive Fermi gases (1D tubes) with spin imbalance, where strong intratube quantum fluctuations invalidate mean-field theory. We first construct an effective field theory, which treats spin-charge mixing exactly, based on the Bethe ansatz solution of the 1D single tube problem. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a two-component Luttinger liquid, and its elementary excitations are fractional states carrying both charge and spin. We analyze the instability of the 1D FFLO state against intertube tunneling by renormalization group analysis, and find that it flows into either a polarized Fermi liquid or a FFLO superfluid, depending on the magnitude of interaction strength and spin imbalance. We obtain the phase diagram of the quasi-1D system and further determine the scaling of the superfluid transition temperature with intertube coupling.
The rapid progress in the production and cooling of molecular gases indicates that experimental studies of quantum gases with a strong dipolar interaction is soon within reach. Dipolar gases are predicted to exhibit very rich physics including quantum liquid crystal phases such as density waves as well as superfluid phases, both of which play an important role for our understanding of strongly correlated systems. Here, we investigate the zero temperature properties of the density-wave phase of a two-dimensional (2D) system of fermionic dipoles using a conserving Hartree-Fock theory. We calculate the amplitude of the density waves as a function of the dipole moment and orientation with respect to the 2D plane. The stripes give rise to a 1D Brillouin zone structure, and the corresponding quasiparticle spectrum is shown to have gapped as well as gapless regions around the Fermi surface. As a result, the system remains compressible in the density-wave phase, and it collapses for strong attraction. We show that the density waves have clear signatures in the momentum distribution and in the momentum correlations. Both can be measured in time-of-flight experiments. Finally, we discuss how the striped phase can be realized with experimentally available systems.
We investigate the ground-state properties of the quasi-one-dimensional dipolar gases using continuous matrix product states techniques. Making use of the first- and second-order correlation functions, we find that the system supports the superfluid, super-Tonks-Girardeau, and quasicrystal phases according to the Luttinger liquid theory. We also map out the phase diagram on the parameter plane consisting the contact and dipolar interaction strengths. Furthermore, we compute the Luttinger parameter, the structure factor, and the momentum distribution of the system. Finally, we show that the predicted dipolar effect can potentially be observed in quasi-one-dimensional gases of polar molecules.
We investigate the ground-state properties of the quasi-one-dimensional dipolar gases using continuous matrix product states techniques. Making use of the first- and second-order correlation functions, we find that the system supports the superfluid, super-Tonks-Girardeau, and quasicrystal phases according to the Luttinger liquid theory. We also map out the phase diagram on the parameter plane consisting the contact and dipolar interaction strengths. Furthermore, we compute the Luttinger parameter, the structure factor, and the momentum distribution of the system. Finally, we show that the predicted dipolar effect can potentially be observed in quasi-one-dimensional gases of polar molecules.