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arXiv:1711.00263 · Physical review. B./Physical review. B

Tunable topological phases with fermionic atoms in a one-dimensional flux lattice

Yuangang Deng, Rong Lü, Li You

Published Oct 30, 2017• 5 citations
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Abstract

We present a simple scheme for implementing a one-dimensional (1D) magnetic-flux lattice of ultracold fermionic spin-1/2 atoms. The resulting tight-binding model supports gapped and gapless topological phases and chiral currents for Meissner and vortex phases. Its single-particle spectra exhibit topological flat bands at small flux, and the flatness sensitively depends on hopping strength. An effective $p$-wave interaction arises in a $s$-wave paired superfluid. Treating atomic internal states as forming a synthetic dimension and balancing the interplay of magnetic flux and Zeeman field, our model describes a tunable topological Fermi superfluid, which paves the way towards experimental explorations of non-Abelian topological matter in 1D atomic quantum gases.

DOI
10.1103/physrevb.96.144517

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We present a simple scheme for implementing a one-dimensional (1D) magnetic-flux lattice of ultracold fermionic spin-1/2 atoms. The resulting tight-binding model supports gapped and gapless topological phases and chiral currents for Meissner and vortex phases. Its single-particle spectra exhibit topological flat bands at small flux, and the flatness sensitively depends on hopping strength. An effective ppp-wave interaction arises in a sss-wave paired superfluid. Treating atomic internal states as forming a synthetic dimension and balancing the interplay of magnetic flux and Zeeman field, our model describes a tunable topological Fermi superfluid, which paves the way towards experimental explorations of non-Abelian topological matter in 1D atomic quantum gases.
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.
Abstract The manipulation of particle transport in synthetic quantum matter is an active research frontier for its theoretical importance and potential applications. Here we experimentally demonstrate an engineered topological transport in a synthetic flat-band lattice of ultracold 87 Rb atoms. We implement a quasi-one-dimensional rhombic chain with staggered flux in the momentum space of the atomic condensate and observe biased local oscillations that originate from the flat-band localization under the staggered synthetic flux. Based on these features, we design and experimentally confirm a state-dependent chiral transport under the periodic modulation of the synthetic flux. We show that the phenomenon is associated with the topology of the Floquet Bloch bands of a coarse-grained effective Hamiltonian. Our work opens the new avenue for exploring flat-band-assistant topological transport with ultracold atoms, and offers a new strategy for designing efficient quantum device with topological robustness.
We investigate the effects of attractive Hubbard interaction on two-component fermionic atoms in narrow two-dimensional (2D) energy bands that exhibit Rashba spin-orbit coupling (SOC) in the presence of an applied Zeeman field. This narrow-band 2D spin-orbit-coupled attractive Fermi-Hubbard model can potentially be realized in cold-atom systems in optical lattices with artificially engineered Rashba SOC and Zeeman field. Employing a self-consistent mean-field approximation for the pairing potential, we uncover a complex phase diagram featuring various topological superfluid (TS) phases, dependent on the chemical potential and the Zeeman field. We focus on the pairing potential and the corresponding quasiparticle gap characterizing the TS phases, which are notably small for a wide-band model with quadratic dispersion near the $\mathrm{\ensuremath{\Gamma}}$ point, as found in earlier work. We identify the parameter regimes that maximize the gap. We find that, while generally the value of the pairing potential increases with the reduction of the fermionic bandwidth, as expected for narrow- or flat-band systems, the magnitude of the topological gap characterizing the TS phases reaches a significantly improved maximum of about 10−−12.510--12.5%10−−12.5 of the interaction strength at finite values of the hopping amplitude, Rashba coupling, and Zeeman field. Our work establishes a robust operating regime for experimenting with topological superfluids in cold-atom optical lattices.
Higher-order topological states that possess gapped bulk energy bands and exotic topologically protected boundary states with at least two dimensions lower than the bulk have opened a significant and new perspective for understanding topological quantum matter. Here, we propose to generate two-dimensional (2D) topological boundary states for implementing a synthetic magnetic flux of ultracold atoms trapped in bilayer optical lattices. It is shown that a Chern insulator, Dirac semimetals, and a second-order topological phase (SOTP) are generated by the interplay of the two-photon detuning and effective Zeeman shift. These observed topological phases can be well characterized by the energy gap of the bulk, the Wilson loop spectra, and the spin textures at the high-symmetry points of the system. We show that the SOTP exhibits a pair of 0D0\mathrm{D}0D boundary states. Meanwhile, the phases of the Dirac semimetals and Chern insulator support the conventional 1D1\mathrm{D}1D boundary states due to the principle of bulk-boundary correspondence. Strikingly, the boundary states that emerge for Dirac semimetals and the SOTP are topologically protected by PT\mathcal{P}TPT symmetry and chiral-mirror symmetry (${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathcal{M}}}_{\ensuremath{\alpha}}$), respectively. In particular, the location of 0D0\mathrm{D}0D corner states for the SOTP which are associated with ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathcal{M}}}_{\ensuremath{\alpha}}$ symmetry are highly manipulable by tuning the magnetic flux. Our scheme herein provides a platform for emerging exotic topological boundary states, which may facilitate the study of higher-order topological phases in ultracold atomic gases.
Abstract The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid. In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines, which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.
We propose a simple experimental scheme to realize simultaneously the one-dimensional spin-orbit coupling and the staggered spin flip in ultracold pseudospin-1/21/21/2 atomic Fermi gases trapped in optical lattices. In the absence of interspecies interactions, the system supports type-I and II Weyl semimetals in three-dimensional and gapped Chern insulators and gapless topological semimetal states in two-dimensional lattices. By turning on the sss-wave interactions, a rich variety of gapped and gapless inhomogeneous topological superfluids can emerge. In particular, a gapped topological Fulde-Ferrell superfluid, which supports the chiral edge states at opposite boundaries with the same chirality, is predicted.