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arXiv:1311.1947 · Physical Review A

Quantum phases of quadrupolar Fermi gases in coupled one-dimensional systems

Wen-Min Huang, M. Lahrz, Ludwig Mathey

Published Jan 6, 2014• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.89.013604

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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 \ensuremathθB,1c{\ensuremath{\theta}}_{B,1}^{c}\ensuremathθB,1c​ and \ensuremathθB,2c{\ensuremath{\theta}}_{B,2}^{c}\ensuremathθB,2c​ between 0 and \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/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 \ensuremathθB,2c{\ensuremath{\theta}}_{B,2}^{c}\ensuremathθB,2c​ and below \ensuremathθB,1c{\ensuremath{\theta}}_{B,1}^{c}\ensuremathθB,1c​. 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 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.
The formation of bound states of fermions in one dimension has always been one of the key topics in condensed matter physics. Motivated by recent experimental progresses in Prof. Jeremy Levy's group, we study the interplay of both species (spin and transverse band index) and mass imbalance in a mixture of two or more species of fermions with attractive interactions in one dimension. Previous theoretical and experimental efforts have shown the existence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase for the case of two species with equal mass, in addition to the fully paired and fully polarized phases. For the unequal mass case, there are signatures of trion phases as well. We use DMRG to explore the rich possibilities of quantum phases and their transport signatures for the cases of two and more species of Fermions as we vary the interaction strengths and mass imbalances. With this we can gain insights into ongoing experiments with sketched nanowires in LAO/STO and ultracold atoms confined to one-dimensional tubes. We also study the formation of bound states in a single component Fermi chain with attractive interactions. The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of fermion triplets (trion phase), but also a phase with two gapless modes. We show that the latter phase is described by a 2-component Tomonaga-Luttinger liquid (TLL) theory, consisting of one charged and one emergent neutral mode. We argue based on our numerical data, that the single, pair, and trion phases are descendants of the 2-component TLL theory. We speculate on the nature of the phase transitions amongst these phases.
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.
We introduce a new platform for quantum simulation of many-body systems based on nonspherical atoms or molecules with zero dipole moments but possessing a significant value of electric quadrupole moments. We consider a quadrupolar Fermi gas trapped in a 2D square optical lattice, and show that the peculiar symmetry and broad tunability of the quadrupole-quadrupole interaction results in a rich phase diagram encompassing unconventional BCS and charge density wave phases, and opens up a perspective to create a topological superfluid. Quadrupolar species, such as metastable alkaline-earth atoms and homonuclear molecules, are stable against chemical reactions and collapse and are readily available in experiment at high densities.
We calculate the zero-temperature (T=0) phase diagram of a polarized two-component Fermi gas in an array of weakly coupled parallel one-dimensional (1D) "tubes" produced by a two-dimensional optical lattice. Increasing the lattice strength drives a crossover from three-dimensional (3D) to 1D behavior, stabilizing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulated superfluid phase. We argue that the most promising regime for observing the FFLO phase is in the quasi-1D regime, where the atomic motion is largely 1D but there is weak tunneling in the other directions that stabilizes long-range order. In the FFLO phase, we describe a phase transition where the quasiparticle spectrum changes from gapless near the 3D regime to gapped in quasi-1D.
Spinor ultracold gases in one dimension (1D) represent an interesting example of strongly correlated quantum fluids. They have a rich phase diagram and exhibit a variety of quantum phase transitions. We consider a 1D spinor gas of bosons with a large spin S . A particular example is the gas of chromium atoms ( S =3), where the dipolar collisions efficiently change the magnetization and make the system sensitive to the linear Zeeman effect. We argue that in 1D the most interesting effects come from the pairing interaction. If this interaction is negative, it gives rise to a (quasi)condensate of singlet bosonic pairs with an algebraic order at zero temperature, and for (2 S +1)≫1 the saddle point approximation leads to physically transparent results. Since in 1D one needs a finite energy to destroy a pair, the spectrum of spin excitations has a gap. Hence, in the absence of a magnetic field, there is only one gapless mode corresponding to phase fluctuations of the pair quasicondensate. Once the magnetic field exceeds the gap, another condensate emerges, namely the quasicondensate of unpaired bosons with spins aligned along the magnetic field. The spectrum then contains two gapless modes corresponding to the singlet-paired and spin-aligned unpaired Bose condensed particles, respectively. At T =0, the corresponding phase transition is of the commensurate–incommensurate type.