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arXiv:2002.01679 · Physical Review A

Effective Hamiltonian with tunable mixed pairing in driven optical lattices

Yu‐Biao Wu, Guang‐Can Guo, Zhen Zheng, Xu‐Bo Zou

Published Jan 21, 2020• 8 citations
arXivHTMLPDF

Abstract

Mixed pairing in ultracold Fermi gases can give rise to interesting many-body phases, such as topological nontrivial superfluids that support Majorana zero modes (MZMs) with various spatial configurations. Unfortunately, in ordinary lattice systems, the topological phase and the associated MZMs are suppressed by the dominant $s$-wave pairing. Here we present a proposal for engineering effective Hamiltonians with tunable mixed on- and off-site pairing based on driven optical lattices. The on- and off-site pairing can be changed independently by means of a periodical driving field rather than magnetic Feshbach resonances. It paves the way for suppressing the dominant on-site interaction that frustrates the emergence of topological superfluids and for synthesizing MZMs localized in edges or corners.

DOI
10.1103/physreva.101.013622

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Mixed pairing in ultracold Fermi gases can give rise to interesting many-body phases, such as topological nontrivial superfluids that support Majorana zero modes (MZMs) with various spatial configurations. Unfortunately, in ordinary lattice systems, the topological phase and the associated MZMs are suppressed by the dominant sss-wave pairing. Here we present a proposal for engineering effective Hamiltonians with tunable mixed on- and off-site pairing based on driven optical lattices. The on- and off-site pairing can be changed independently by means of a periodical driving field rather than magnetic Feshbach resonances. It paves the way for suppressing the dominant on-site interaction that frustrates the emergence of topological superfluids and for synthesizing MZMs localized in edges or corners.
Nonlocal interaction between ultracold atoms trapped in optical lattices can give rise to interesting quantum many-body phenomena. However, its realization usually demands unconventional techniques, for example, the artificial gauge fields or higher-orbit Feshbach resonances, and is not highly controllable. Here, we propose a valid and feasible scheme for realizing a tunable finite-range interaction for spinless fermions immersed into the bath of bosons. The strength of the effective interaction for the fermionic subsystem is artificially tunable by manipulating bosons, ranging from the repulsive to the attractive regime. In addition, the interaction distance is locked to the hopping of bosons, making the finite-range interaction perfectly clean for the fermionic subsystem. Specifically, we find that, by introducing an additional staggered hopping of bosons, the proposal is readily applied to search the Majorana corner modes in such a spinless system, without the implementation of complex artificial gauge fields, which is totally distinct from existing results reported in spinful systems. Therefore, this scheme provides a potential platform for exploring the unconventional topological superfluids and other nontrivial phases induced by long-range interactions in ultracold atoms.
I analyze the emergence of Majorana zero modes (MZM) in a one dimensional ultracold fermionic system confined by an optical lattice inside a high-Q cavity. This forms a quantum optical lattice due to the cavity backaction, with emergent long range interactions controlled by the light pumped into the system and thus long range pairing. I investigate the possibility of formation and emergence of edge modes using exact diagonalization and singular value decomposition of the Hamiltonian in the Majorana representation, while computing the mass gap of the MZM and its spectral properties. The interplay of cavity induced interactions and effective ppp-wave short range interactions controls the emergence of the signatures of MZM. I find that under certain conditions MZM distinctively emerge leading to a superradiant topological phase of matter. These MZM have potential applications for quantum information as they are topologically protected analogous to the behaviour of the Kitaev chain. The techniques employed lead to a scheme based on the Majorana representation and exact diagonalization with self consistent conditions that can be applied to other fermionic and analog systems termed Light-Matter-Majorana.
We investigate long-range pairing interactions between ultracold fermionic atoms confined in an optical lattice which are mediated by the coupling to a cavity. In the absence of other perturbations, we find three degenerate pairing symmetries for a two-dimensional square lattice. By tuning a weak local atomic interaction via a Feshbach resonance or by tuning a weak magnetic field, the superfluid system can be driven from a topologically trivial s wave to topologically ordered, chiral superfluids containing Majorana edge states. Our work points out a novel path towards the creation of exotic superfluid states by exploiting the competition between long-range and short-range interactions.
We demonstrate that an exotically chiral fff-wave topological superfluid can be induced in cold-fermionic-atom triangular optical lattices through a laser-field-generated effective non-Abelian gauge field, controllable Zeeman fields, and sss-wave Feshbach resonance. We find that the chiral fff-wave topological superfluid is characterized by three gapless Majorana edge states located on the boundary of the system. More interestingly, these Majorana edge states degenerate into one Majorana fermion bound to each vortex in the superfluid. Our proposal enlarges the topological superfluid family and specifies a unique experimentally controllable system to study Majorana fermion physics.
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.
Abstract We here present an experimentally feasible proposal for manipulating Cooper pairs in degenerate Fermi gases trapped by an optical lattice. Upon introducing an in situ periodically driven field, the system may be described by an effective time-independent Hamiltonian, in which the Cooper pairs, generated by the bound molecule state in Feshbach resonance, host a nonzero center-of-mass momentum. The system thus processes a crossover from a Bardeen–Cooper–Schrieffer superfluid phase to a Fulde–Ferrell (FF) one. Furthermore, the magnitude and direction of the Cooper pairs in the synthetic FF superfluids are both directly controllable via the periodically driven field. Our proposal offers a reliable and feasible scenario for manipulating the Cooper pairs in cold atoms, serving as a tunable as well as powerful platform for quantum-emulating and exploring the FF superfluid phase.