Floquet Engineering Ultracold Polar Molecules to Simulate Topological Insulators

Abstract

We present a quantitative, near-term experimental blueprint for the quantum simulation of topological insulators using lattice-trapped ultracold polar molecules. In particular, we focus on the so-called Hopf insulator, which represents a three-dimensional topological state of matter existing outside the conventional tenfold way and crystalline-symmetry-based classifications of topological insulators. Its topology is protected by a \emph{linking number} invariant, which necessitates long-range spin-orbit coupled hoppings for its realization. While these ingredients have so far precluded its realization in solid state systems and other quantum simulation architectures, in a companion manuscript [1901.08597] we predict that Hopf insulators can in fact arise naturally in dipolar interacting systems. Here, we investigate a specific such architecture in lattices of polar molecules, where the effective `spin' is formed from sublattice degrees of freedom. We introduce two techniques that allow one to optimize dipolar Hopf insulators with large band gaps, and which should also be readily applicable to the simulation of other exotic bandstructures. First, we describe the use of Floquet engineering to control the range and functional form of dipolar hoppings and second, we demonstrate that molecular AC polarizabilities (under circularly polarized light) can be used to precisely tune the resonance condition between different rotational states. To verify that this latter technique is amenable to current generation experiments, we calculate from first principles the AC polarizability for ${\sigma }^{+}$ light for ${}^{40}$K${}^{87}$Rb. Finally, we show that experiments are capable of detecting the unconventional topology of the Hopf insulator by varying the termination of the lattice at its edges, which gives rise to three distinct classes of edge mode spectra.

arXiv comment15 pages, 8 figures. See companion manuscript arxiv:1901.08597 for an overview on realizing the Hopf insulator via dipolar interactions

References in corpus (75)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• Classification of topological insulators and superconductors in three spatial dimensions
• Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
• Topological invariants of time-reversal-invariant band structures
• Topological Crystalline Insulators
• A High Phase-Space-Density Gas of Polar Molecules
• Higher-Order Topological Insulators
• Search for New Physics with Atoms and Molecules
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Order of Magnitude Smaller Limit on the Electric Dipole Moment of the Electron
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Realizing a lattice spin model with polar molecules
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Bose-Einstein condensation of atoms in a uniform potential
• Ultracold dense samples of dipolar RbCs molecules in the rovibrational and hyperfine ground state
• Optical Production of Ultracold Polar Molecules
• Topological Flat Band Models and Fractional Chern Insulators
• Ultracold Dipolar Gas of Fermionic ${}^{23}$Na${}^{40}$K Molecules in their Absolute Ground State
• Creation of ultracold ${}^{87}$RbCs molecules in the rovibrational ground state
• Exponentially slow heating in periodically driven many-body systems
• Creation of an ultracold gas of ground-state ${}^{23}{\mathrm{Na}}^{87}\mathrm{Rb}$ molecules
• Cold Molecule Spectroscopy for Constraining the Evolution of the Fine Structure Constant
• A Fermi Degenerate Gas of Polar Molecules
• Nodal-link semimetals
• Controlling the hyperfine state of rovibronic ground-state polar molecules
• New frontiers with quantum gases of polar molecules
• Building one molecule from a reservoir of two atoms
• Topological Insulators in Random Lattices
• Experimental Measurement of the Berry Curvature from Anomalous Transport
• Cold polar molecules in 2D traps: Tailoring interactions with external fields for novel quantum phases
• Realizing Fractional Chern Insulators with Dipolar Spins
• Dipolar Exchange Quantum Logic Gate with Polar Molecules
• Mapping the Berry Curvature from Semiclassical Dynamics in Optical Lattices
• Creation of a low-entropy quantum gas of polar molecules in an optical lattice
• Measuring topology by dynamics: Chern number from linking number
• Topological surface states in three-dimensional magnetic insulators
• Imaging optical frequencies with 100 $\mu$Hz precision and 1.1 $\mu$m resolution
• Ultra-precise holographic beam shaping for microscopic quantum control
• Measuring Topological Number of a Chern-Insulator from Quench Dynamics
• Ultracold polar molecules as qudits
• The hyperfine energy levels of alkali metal dimers: ground-state polar molecules in electric and magnetic fields
• The coupling of the X${}^1{\Sigma }^{+}$ and a${}^3{\Sigma }^{+}$ states of KRb
• Far from equilibrium quantum magnetism with ultracold polar molecules
• Anisotropic Polarizability of Ultracold Polar ${}^{40}$K${}^{87}$Rb Molecules
• Hopf Insulators and Their Topologically Protected Surface States
• A Quantum Dipolar Spin Liquid
• Ultracold mixtures of atomic Li-6 and Cs-133 with tunable interactions
• Controlling Polar Molecules in Optical Lattices
• Topological bands with Chern number C=2 by dipolar exchange interactions
• Electric field-dependent dynamic polarizability and "magic" conditions for optical trapping of polar molecules
• Kitaev honeycomb and other exotic spin models with polar molecules
• Symmetry Protected Topological Hopf Insulator and its Generalizations
• Floquet Mechanism for Non-Abelian Fractional Quantum Hall States
• Topological Hopf-Chern Insulators and the Hopf Superconductor
• The permanent dipole moment of LiCs in the ground state
• Manipulating ultracold polar molecules with microwave radiation: the influence of hyperfine structure
• Prospects for Narrow-line Cooling of KRb Molecules in Rovibrational Ground State
• Floquet Hopf Insulators
• Homotopy Theory of Strong and Weak Topological Insulators
• Teleportation of Berry curvature on the surface of a Hopf insulator
• Realizing Hopf Insulators in Dipolar Spin Systems
• The RbSr ${}^2{\Sigma }^{+}$ ground state investigated via spectroscopy of hot & ultracold molecules
• Emergent Weyl excitations in systems of polar particles
• Observation of topological links associated with Hopf insulators in a solid-state quantum simulator
• Systematic Construction of tight-binding Hamiltonians for Topological Insulators and Superconductors
• An approach to quantum gas microscopy of polar molecules
• Floquet engineering from long-range to short-range interactions
• Quench dynamics of Hopf insulators
• Non-Hermitian three-dimensional two-band Hopf insulator
• Three dimensional two-band Floquet topological insulator with $Z_2$ index
• Probe knots and Hopf insulators with ultracold atoms

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• Realization of a Hopf insulator in circuit systems
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Realizing Hopf Insulators in Dipolar Spin Systems
• Two-axis twisting using Floquet-engineered XYZ spin models with polar molecules
• Massless multifold Hopf semimetals
• Extrinsic and Intrinsic Nonlinear Hall Effects across Berry-Dipole Transitions
• Real Hopf Insulator
• Dipolar Weyl semimetals
• Flat Bands in Three-dimensional Lattice Models with Non-trivial Hopf Index
• PT-symmetric Non-Hermitian Hopf Metal
• Topological states in chiral electronic chains
• Correlated Hopf insulators