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arXiv:1707.01241 · New Journal of Physics

Topological orbital superfluid with chirald-wave order in a rotating optical lattice

Ningning Hao, Huaiming Guo, Ping Zhang

Published Aug 21, 2017• 4 citations
arXivHTMLPDF

Abstract

Topological superfluid is an exotic state of quantum matter that possesses a nodeless superfluid gap in the bulk and Andreev edge modes at the boundary of a finite system. Here, we study a multi-orbital superfluid driven by an attractive s -wave interaction in a rotating optical lattice. Interestingly, we find that the rotation induces the inter-orbital hybridization and drives the system into topological orbital superfluid in accordance with intrinsically chiral d -wave pairing characteristics. Thanks to the conservation of spin, the topological orbital superfluid supports four rather than two chiral Andreev edge modes at the boundary of the lattice. Moreover, we find that the intrinsic harmonic confining potential forms a circular spatial barrier which accumulates atoms and supports a mass current under the injection of small angular momentum as an external driving force. This feature provides an experimentally detectable phenomenon to verify the topological orbital superfluid with chiral d -wave order in a rotating optical lattice.

DOI
10.1088/1367-2630/aa7cea

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Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for exploring quantum many-body states of matter that had not been accessible previously. Here we report that a topological fermionic superfluid with higher Chern number emerges spontaneously from sss-wave spin-singlet pairing in an orbital optical lattice when its geometry is tuned to explicitly break reflection symmetry. Qualitatively distinct from the conventional scheme that relies on higher partial-wave pairing, the crucial ingredient of our model is topology originating from mixing higher Wannier orbitals. It leads to unexpected changes in the topological band structure at the single-particle level, i.e., the bands are transformed from possessing two flux-$\ensuremath{\pi}$ Dirac points into a single quadratic touching point with flux $2\ensuremath{\pi}$. Based on such engineered single-particle bands, spin-singlet pairing of ultracold fermions arising from standard sss-wave attractive interaction is found to induce higher Chern number (Chern number of 2) and topologically protected chiral edge modes, all occurring at a higher critical temperatures in relative scales, potentially circumventing one of the major obstacle for its realization in ultracold gases.
Recent advanced experimental implementations of optical lattices with highly tunable geometry open up new regimes for quantum many-body states of matter that previously had not been accessible. Here we introduce a symmetry-based method of utilizing the geometry of optical lattice to systematically control topologically non-trivial orbital hybridization. Such an orbital mixing leads to an unexpected and yet robust topological semimetal at single-particle level for a gas of fermionic atoms. When considering s-wave attractive interaction between atoms as for instance tuned by Feshbach resonance, topological superfluid state with high Chern number is unveiled in the presence of on-site rotation. This state supports chiral edge excitations, manifesting its topological nature. An experimental realization scheme is designed, which introduces a systematic way of achieving a new universality class (such as Chern number of 2) of orbital-hybridized topological phases beyond geometrically standard optical lattices.
Spin and orbital are two basic degrees of freedom that play significant roles in exploring exotic quantum phases in optical lattices with synthetic spin-orbit coupling (SOC) and high orbital bands, respectively. Here, we combine these two crucial ingredients for the first time by proposing a completely new orbital optical Raman lattice scheme to explore exotic high-orbital Bose condensates with Raman-induced SOC in a square lattice. We find that both the SOC and p-orbital interactions influence the condensed state of bosons. Their interplay results in two novel high-orbital many-body quantum phases: the uniform angular momentum superfluid phase, which exhibits a global topological chiral orbital current characterized by a uniform Chern number, and the two-dimensional topological spin-orbital supersolid phase, which is characterized by the spin and orbital angular momentum density wave patterns and topological excitations with opposite Chern numbers, respectively protecting the chiral and antichiral edge modes in the neighboring supersolid clusters. Our scheme may open a new avenue for exploring exotic SOC and high-orbital physics in optical lattices, and is expected to advance the experimental realization of novel supersolids in higher dimensions.
We propose a symmetry-based method of using noncentrosymmetric optical lattices to systematically control topological nontrivial orbital hybridization. A crucial difference from the previous studies is the role of inversion symmetry breaking, which is applied to induce an exotic orbital-changing hopping perpendicular to the direction without inversion symmetry and opens a band gap, instead of reducing the codimension and producing gapless points. The orbital mixing here is reminiscent of the spin-orbit physics based on hyperfine states but differs in symmetry and origin. This nontrivial orbital hybridization produces a topological band structure. Attractively interacting fermionic atoms loaded in such a lattice are found to show an orbital topological Fulde-Ferrell superfluid state in the presence of onsite rotation. This state supports Majorana fermions on its edges. Our mechanism should pave an alternative way to achieve orbital topological phases in optical lattices of nonstandard geometry.
A Majorana zero bound mode exists in the vortex core of a chiral p+ipp+ipp+ip superconductor or superfluid, which can be driven from an sss-wave pairing state by two-dimensional spin-orbit coupling. We propose here a novel scheme based on realistic cold atom platforms to generate two-dimensional spin-orbit interactions in a blue-detuned square optical lattice, and predict both the quantum anomalous Hall effect and chiral topological superfluid phase in the experimentally accessible parameter regimes. This work may open a new direction with experimental feasibility to observe non-Abelian topological orders in cold atom systems.
Abstract Topological superfluidity is an important concept in electronic materials as well as ultracold atomic gases1. However, although progress has been made by hybridizing superconductors with topological substrates, the search for a material—natural or artificial—that intrinsically exhibits topological superfluidity has been ongoing since the discovery of the superfluid 3He-A phase2. Here we report evidence for a globally chiral atomic superfluid, induced by interaction-driven time-reversal symmetry breaking in the second Bloch band of an optical lattice with hexagonal boron nitride geometry. This realizes a long-lived Bose–Einstein condensate of 87Rb atoms beyond present limits to orbitally featureless scenarios in the lowest Bloch band. Time-of-flight and band mapping measurements reveal that the local phases and orbital rotations of atoms are spontaneously ordered into a vortex array, showing evidence of the emergence of global angular momentum across the entire lattice. A phenomenological effective model is used to capture the dynamics of Bogoliubov quasi-particle excitations above the ground state, which are shown to exhibit a topological band structure. The observed bosonic phase is expected to exhibit phenomena that are conceptually distinct from, but related to, the quantum anomalous Hall effect3–7 in electronic condensed matter.