Kitaev honeycomb and other exotic spin models with polar molecules

Abstract

We show that ultracold polar molecules pinned in an optical lattice can be used to access a variety of exotic spin models, including the Kitaev honeycomb model. Treating each molecule as a rigid rotor, we use DC electric and microwave fields to define superpositions of rotational levels as effective spin degrees of freedom, while dipole-dipole interactions give rise to interactions between the spins. In particular, we show that, with sufficient microwave control, the interaction between two spins can be written as a sum of five independently controllable Hamiltonian terms proportional to the five rank-2 spherical harmonics Y_{2,q}(theta,phi), where (theta,phi) are the spherical coordinates of the vector connecting the two molecules. To demonstrate the potential of this approach beyond the simplest examples studied in [S. R. Manmana et al., arXiv:1210.5518v2], we focus on the realization of the Kitaev honeycomb model, which can support exotic non-Abelian anyonic excitations. We also discuss the possibility of generating spin Hamiltonians with arbitrary spin S, including those exhibiting SU(N=2S+1) symmetry.

8 pages, 2 figures, submitted to a special issue of Molecular Physics

References in corpus (24)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• A High Phase-Space-Density Gas of Polar Molecules
• Bose-Einstein Condensation of Erbium
• Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
• Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential
• Room temperature entanglement between distant single spins in diamond
• Quantum degenerate dipolar Fermi gas
• Ultracold Gases of Ytterbium: Ferromagnetism and Mott States in an SU(6) Fermi System
• Mott Insulators of Ultracold Fermionic Alkaline Earth Atoms: Underconstrained Magnetism and Chiral Spin Liquid
• Implementation of Spin Hamiltonians in Optical Lattices
• Cold polar molecules in 2D traps: Tailoring interactions with external fields for novel quantum phases
• Stable Topological Superfluid Phase of Ultracold Polar Fermionic Molecules
• Realizing Fractional Chern Insulators with Dipolar Spins
• Dirac-point engineering and topological phase transitions in honeycomb optical lattices
• Topological phases in ultracold polar-molecule quantum magnets
• Repulsive shield between polar molecules
• Anisotropic Polarizability of Ultracold Polar ${}^{40}$K${}^{87}$Rb Molecules
• The Prediction of a Gapless Topological "Haldane Liquid" Phase in a One-Dimensional Cold Polar Molecular Lattice
• External field control of collective spin excitations in an optical lattice of ${}^2\Sigma$ molecules
• Electric field-dependent dynamic polarizability and "magic" conditions for optical trapping of polar molecules
• Designing spin-1 lattice models using polar molecules
• Tunable disorder in a crystal of cold polar molecules
• Non-adiabatic preparation of spin crystals with ultracold polar molecules
• Shaping interactions between polar molecules with far-off-resonant light

Cited by in corpus (54)

• Cold molecules: Progress in Quantum Engineering of Chemistry and Quantum Matter
• Quantum control of molecular rotation
• Manipulation of Molecules with Electromagnetic Fields
• Nonequilibrium many-body steady states via Keldysh formalism
• Long-range Ising and Kitaev Models: Phases, Correlations and Edge Modes
• Robust encoding of a qubit in a molecule
• Ultracold molecules for quantum simulation: rotational coherences in CaF and RbCs
• Materials design of Kitaev spin liquids beyond the Jackeli-Khaliullin mechanism
• Topological properties of a dense atomic lattice gas
• Quantum correlations and entanglement in far-from-equilibrium spin systems
• Strongly interacting ultracold polar molecules
• Radical chiral Floquet phases in a periodically driven Kitaev model and beyond
• A robust entangling gate for polar molecules using magnetic and microwave fields
• Synthetic dimensions in ultracold molecules: quantum strings and membranes
• Realizing unconventional quantum magnetism with symmetric top molecules
• Causality and quantum criticality in long-range lattice models
• Exceptional Spin Liquids from Couplings to the Environment
• Simulating quantum magnets with symmetric top molecules
• Fractional Quantum Hall States of Rydberg Polaritons
• Quantum spin liquid in the semiclassical regime
• A new quantum gas apparatus for ultracold mixtures of K and Cs and KCs ground-state molecules
• Towards Kitaev Spin Liquid in 3d Transition Metal Compounds
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Controlling the ac Stark effect of RbCs with dc electric and magnetic fields
• Strings of ultracold molecules in a synthetic dimension
• Kitaev spin models from topological nanowire networks
• Floquet Engineering Ultracold Polar Molecules to Simulate Topological Insulators
• Complexes formed in collisions between ultracold alkali-metal diatomic molecules and atoms
• Magic Conditions for Multiple Rotational States of Bialkali Molecules in Optical Lattices
• Realizing Exactly Solvable SU(N) Magnets with Thermal Atoms
• Coherent Manipulation of the Internal State of Ultracold ${}^{87}$Rb${}^{133}$Cs Molecules with Multiple Microwave Fields
• Cross-dimensional universality classes in static and periodically driven Kitaev models
• Preparation of ${}^{87}$Rb and ${}^{133}$Cs in the motional ground state of a single optical tweezer
• Correlations and enlarged superconducting phase of $t$-$J_{\perp }$ chains of ultracold molecules on optical lattices
• Floquet engineering from long-range to short-range interactions
• Quantum simulation of the central spin model with a Rydberg atom and polar molecules in optical tweezers
• Photoassociation of ultracold long-range polyatomic molecules
• Tuneable defect interactions and supersolidity in dipolar quantum gases on a lattice potential
• Tailored jump operators for purely dissipative quantum magnetism
• Feasibility of Kitaev quantum spin liquids in ultracold polar molecules
• Bilayer fractional quantum Hall states with ultracold dysprosium
• Controllable quantum spin glasses with magnetic impurities embedded in quantum solids
• Measuring Majorana fermions qubit state and non-Abelian braiding statistics in quenched inhomogeneous spin ladders
• Interaction potential for NaCs for ultracold scattering and spectroscopy
• Field-driven spatiotemporal manipulation of Majorana zero modes in a Kitaev spin liquid
• Quantum annealing with pairs of ${}^2\Sigma$ molecules as qubits
• Interacting in-plane molecular dipoles in a zig-zag chain
• On cold gases with anisotropic interactions
• Topological Majorana flat bands in the Kitaev model on a Bishamon-kikko lattice
• Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation
• Molecule-molecule and atom-molecule collisions with ultracold RbCs molecules
• Higher-order topological quantum paramagnets
• Emergent Kitaev materials in synthetic Fermi-Hubbard bilayers
• Magnetic field effects on the Kitaev model coupled to environment