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arXiv:1112.5082 · Physical Review B

Exploring spin-orbital models with dipolar fermions in zigzag optical lattices

Gaoyong Sun, George Jackeli, Luis Santos, T. Vekua

Published Oct 31, 2012• 13 citations
arXivHTMLPDF

Abstract

Ultracold dipolar spinor fermions in zig-zag--type optical lattices can mimic spin-orbital models relevant in solid-state systems, as transition-metal oxides with partially filled $d$ levels, with the interesting advantage of reviving the quantum nature of orbital fluctuations. We discuss two different physical systems in which these models may be simulated, showing that the interplay between lattice geometry and spin-orbital quantum dynamics produces a wealth of novel quantum phases.

DOI
10.1103/physrevb.86.155159

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Ultracold dipolar spinor fermions in zig-zag--type optical lattices can mimic spin-orbital models relevant in solid-state systems, as transition-metal oxides with partially filled ddd levels, with the interesting advantage of reviving the quantum nature of orbital fluctuations. We discuss two different physical systems in which these models may be simulated, showing that the interplay between lattice geometry and spin-orbital quantum dynamics produces a wealth of novel quantum phases.
Two-component dipolar fermions in zigzag optical lattices allow for the engineering of spin-orbital models. We show that dipolar lattice fermions permit the exploration of a regime typically unavailable in solid-state compounds that is characterized by a spin-liquid phase with a finite magnetization and spontaneously broken SU(2) symmetry. This peculiar spin liquid may be understood as the Luttinger liquid of composite particles consisting of bound states of spin waves and orbital domain walls moving in an unsaturated ferromagnetic background. In addition, we show that the system exhibits a boundary phase transitions involving nonlocal entanglement of edge spins.
Motivated by the experiment [St-Jean et al., Nat. Photonics 11, 651 (2017)] on topological phases with collective photon modes in a zigzag chain of polariton micropillars, we study spinless ppp-orbital fermions with local interorbital hoppings and repulsive interactions between px{p}_{x}px​ and py{p}_{y}py​ bands in zigzag optical lattices. We show that spinless ppp-band fermions in zigzag optical lattices can mimic the interacting Su-Schrieffer-Heeger model and the effective transverse field Ising model in the presence of local hoppings. We analytically and numerically discuss the ground-state phases and quantum phase transitions of the model. This work provides a simple scheme to simulate topological phases and the quench dynamics of many-body systems in optical lattices.
In this dissertation we focus on many-body phenomena on a quantum level. In particular fermionic quantum gases in a temperature regime approaching absolute zero. Ultracold quantum gases have proven to be a versatile framework for Theorists and Experimentalists to probe many-body quantum mechanics. They also serve to quantum simulate solid state problems in a clean and controllable environment. The use of optical lattices include the advantage of tuning the required lattice structure nearly at will and lack the experimental shortcomings compared to the solid state, like the presence of lattice dislocations. The relevant lattice parameters can be easily tuned without changing the setup. In recent years many goals within theory and experiments of ultracold quantum gases in optical lattices were achieved. This emphasizes the significance of ongoing research with ultracold quantum gases on optical lattices. We present two aspects of modern theory of ultracold quantum gases in optical lattices. On the one hand, we implement orbital physics in a setup of optical lattices and on the other, we find elusive Majorana fermions in a setup with ultracold fermionic gases. Both aspects are well-known in solid state systems, but did not make the step towards ultracold quantum gases so far. We propose and investigate setups to quantum simulate these challenges in the framework of optical lattices. The first part of this work concerns the implementation of orbital physics in optical lattices. The orbital structure of atoms reveals novel phenomena in solid state systems. This raises the interest in creating optical lattice systems exhibiting analog behavior, as dictated by the orbitals in the solid state. We derive the microscopic Hamiltonian for a p-orbital system and investigate it in detail. For this Hamiltonian we perform a mean-field treatment and discover novel phase transitions including a possible tricritical point. In the analysis of the strong coupling regime we find an additional phase transition towards an antiferromagnet and then extend the mean-field phase diagram. Concluding the investigations is a proposal of an experimental setup to achieve orbital physics with state-of-the-art experimental tools. The second part of this work considers Majorana modes and p-wave superfluids. Majorana modes are not only present in high-energy physics, but also in condensed matter systems. Here we demonstrate a setup in order to simulate Majorana modes and p-wave superfluids in optical lattices. We derive an effective Hamiltonian and investigate it on a mean-field level as well as give the mean-field phase diagram. It contains a rich manifold of different p-wave phases. In addition, we extend our investigations to topological properties of our system and provide the topological phase diagram. We discover the special phenomena that the mean-field and topological phase transitions are decoupled in our system. The proposed system is suited to have Majorana modes at vortices and dislocations, which are injected into the system in controllable experimental manner. We conclude the considerations by giving a protocol for braiding in order to demonstrate non-Abelian statistics of Majorana modes.
Spinor bosons offer a conceptually simple picture of macroscopic quantum behavior of topological order-by-disorder: The paramagnetic state of two-component dipolar bosons in an orbitally degenerate zigzag lattice is unstable against infinitesimal quantum fluctuations of orbitals, $\ensuremath{\lambda}$, towards developing nonlocal hidden order. Adjacent to the topological state a locally correlated exact ground state with spontaneously a quadrupoled lattice constant is realized for the broad parameter regime. The topological order is extremely robust surviving the $\ensuremath{\lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit where the ground state evolves into the Majumdar-Ghosh state of a frustrated spin-12\frac{1}{2}21​ chain.
In this review, we discuss the physics of spin-orbit coupled quantum gases in optical lattices. After reviewing some relevant experimental techniques, we introduce the basic theoretical model and discuss some of its generic features. In particular, we concentrate on the interplay between spin-orbit coupling and strong interactions and show how it leads to various exotic quantum phases in both the Mott insulating and superfluid regimes. Phase transitions between the Mott and superfluid states are also discussed.