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arXiv:2211.07169 · Physical Review A

Tunable boson-assisted finite-range interaction and engineering Majorana corner modes in optical lattices

Yu‐Biao Wu, Zhen Zheng, Xianggang Qiu, Lin Zhuang, Guang‐Can Guo, Xu‐Bo Zou, Wu‐Ming Liu

Published Apr 5, 2023• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.107.043304

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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.
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.
Advances in experiments on dilute ultracold atomic gases have given us access to highly tunable quantum systems. In particular, there have been substantial improvements in achieving different kinds of interaction between atoms. As a result, utracold atomic gases oer an ideal platform to simulate many-body phenomena in condensed matter physics, and engineer other novel phenomena that are a result of the exotic interactions produced between atoms. In this dissertation, I present a series of studies that explore the physics of dilute ultracold atomic gases in different settings. In each setting, I explore a different form of the inter-particle interaction. Motivated by experiments which induce artificial spin-orbit coupling for cold fermions, I explore this system in my first project. In this project, I propose a method to perform universal quantum computation using the excitations of interacting spin-orbit coupled fermions, in which effective p-wave interactions lead to the formation of a topological superfluid. Motivated by experiments which explore the physics of exotic interactions between atoms trapped inside optical cavities, I explore this system in a second project. I calculate the phase diagram of lattice bosons trapped in an optical cavity, where the cavity modes mediates effective global range checkerboard interactions between the atoms. I compare this phase diagram with one that was recently measured experimentally. In two other projects, I explore quantum simulation of condensed matter phenomena due to spin-dependent interactions between particles. I propose a method to produce tunable spin-dependent interactions between atoms, using an optical Feshbach resonance. In one project, I use these spin-dependent interactions in an ultracold Bose-Fermi system, and propose a method to produce the Kondo model. I propose an experiment to directly observe the Kondo effect in this system. In another project, I propose using lattice bosons with a large hyperfine spin, which have Feshbach-induced spin-dependent interactions, to produce a quantum dimer model. I propose an experiment to detect the ground state in this system. In a final project, I develop tools to simulate the dynamics of fermionic superfluids in which fermions interact via a short-range interaction.
We investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with sss-, ppp-, and ddd-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.
Engineering long-range interactions in cold-atom quantum simulators can lead to exotic quantum many-body behavior. Fermionic atoms in ultracold atomic mixtures can act as mediators, giving rise to long-range Ruderman-Kittel-Kasuya-Yosida-type interactions characterized by the dimensionality and density of the fermionic gas. Here, we propose several tuning knobs, accessible in current experimental platforms, that allow one to further control the range and shape of the mediated interactions, extending the existing quantum simulation toolbox. In particular, we include an additional optical lattice for the fermionic mediator, as well as anisotropic traps to change its dimensionality in a continuous manner. This allows us to interpolate between power-law and exponential decays, introducing an effective cutoff for the interaction range, as well as to tune the relative interaction strengths at different distances. Finally, we show how our approach allows one to investigate frustrated regimes that were not previously accessible, where symmetry-protected topological phases as well as chiral spin liquids emerge.
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.
Attractive interaction between spinless fermions in a two-dimensional lattice drives the formation of a topological superfluid. But the topological phase is dynamically unstable towards phase separation when the system has a high density of states and large interaction strength. This limits the critical temperature to an experimentally challenging regime where, for example, even ultracold atoms and molecules in optical lattices would struggle to realize the topological superfluid. We propose that the introduction of a weaker longer-range repulsion, in addition to the short-range attraction between lattice fermions, will suppress the phase separation instability. Taking the honeycomb lattice as an example, we use the unrestricted Hartree-Fock approximation to show that our proposal significantly enlarges the stable portion of the topological superfluid phase and increases the critical temperature by an order of magnitude. Our work opens a route to enhance the stability of topological superfluids by engineering interparticle interactions.