Growing quantum states with topological order

Abstract

We discuss a protocol for growing states with topological order in interacting many-body systems using a sequence of flux quanta and particle insertion. We first consider a simple toy model, the superlattice Bose Hubbard model, to explain all required ingredients. Our protocol is then applied to fractional quantum Hall systems in both, continuum and lattice. We investigate in particular how the fidelity, with which a topologically ordered state can be grown, scales with increasing particle number N. For small systems exact diagonalization methods are used. To treat large systems with many particles, we introduce an effective model based on the composite fermion description of the fractional quantum Hall effect. This model also allows to take into account the effects of dispersive bands and edges in the system, which will be discussed in detail.

References in corpus (32)

• Non-Abelian Anyons and Topological Quantum Computation
• Photonic Floquet Topological Insulators
• Experimental realisation of the topological Haldane model
• Imaging topological edge states in silicon photonics
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Quantized Rotation of Atoms From Photons with Orbital Angular Momentum
• Fractional quantum Hall states of atoms in optical Lattices
• Exponential localization of Wannier functions in insulators
• Fractional Quantum Hall States and Jack Polynomials
• Condensation of `composite bosons' in a rotating BEC
• Do attractive bosons condense?
• 1/2-Anyons in small atomic Bose-Einstein condensates
• Fractional quantum Hall states of photons in an array of dissipative coupled cavities
• Quantum Hall fractions in rotating Bose-Einstein condensates
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Topological edge states in the one-dimensional super-lattice Bose-Hubbard model
• A Composite Fermion Description of Rotating Bose-Einstein Condensates
• Measuring topological invariants in photonic systems
• Induced self-stabilization in fractional quantum Hall states of light
• Phase Diagram for Ultracold Bosons in Optical Lattices and Superlattices
• Quantum Hall fractions for spinless Bosons
• Fractional Chern Insulators beyond Laughlin states
• Fractional-filling loophole insulator domains for ultracold bosons in optical superlattices
• Quantized pumping and phase diagram topology of interacting bosons
• Topological growing of Laughlin states in synthetic gauge fields
• Quantum Spin Pump in S=1/2 antiferromagnetic chains -Holonomy of phase operators in sine-Gordon theory-
• Cell strong coupling perturbative approach to the phase diagram of ultracold bosons in optical superlattices
• Characterization of topological states on a lattice with Chern number
• Quantum particle in a parabolic lattice in the presence of a gauge field
• Ultracold bosons in disordered superlattices: Mott-insulators induced by tunneling

Cited by in corpus (5)

• Topological Photonics
• Topological Photonics
• ${\mathbb{Z}}_2$ lattice gauge theories and Kitaev's toric code: A scheme for analog quantum simulation
• Reversal of quantised Hall drifts at non-interacting and interacting topological boundaries
• Adiabatic flux insertion and growing of Laughlin states of cavity Rydberg polaritons