P-band in a rotating optical lattice

Abstract

We investigate the effects of rotation on the excited bands of a tight binding lattice, focusing particulary on the first excited (p-) band. Both the on-site energies and the hopping between lattice sites are modified by the effective magnetic field created by rotation, causing a non-trivial splitting and magnetic fine structure of the p-band. We show that Peierls substitution can be modified to describe p-band under rotation, and use this method to derive an effective Hamiltonian. We compare the spectrum of the effective Hamiltonian with a first principles calculation of the magnetic band structure and find excellent agreement, confirming the validity of our approach. We also discuss the on-site interaction terms for bosons and argue that many-particle phenomena in a rotating p-band can be investigated starting from this effective Hamiltonian.

7 pages, 4 figures, new discussion of effective Hamiltonian, references added

References in corpus (18)

• Flat bands and Wigner crystallization in the honeycomb optical lattice
• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Observation of dipole-dipole interaction in a degenerate quantum gas
• Fractional Quantum Hall Effect in Optical Lattices
• Observation of Vortex Pinning in Bose-Einstein Condensates
• The $p_{x,y}$-orbital counterpart of graphene: cold atoms in the honeycomb optical lattice
• State preparation and dynamics of ultracold atoms in higher lattice orbitals
• Atomic matter of non-zero momentum Bose-Einstein condensation and orbital current order
• High field fractional quantum Hall effect in optical lattices
• Orbital ordering and frustration of $p$-band Mott-insulators
• Trapped Fermi Gases in Rotating Optical Lattices: Realization and Detection of the Topological Hofstadter Insulator
• Orbital order in Mott insulators of spinless p-band fermions
• Prediction of quantum stripe ordering in optical lattices
• Vortex configurations of bosons in an optical lattice
• Phase Boundary of the Boson Mott Insulator in a Rotating Optical Lattice
• Quantum Antiferromagnetism of Fermions in Optical Lattices with Half-filled p-band
• Quantum Hall-like effect for cold atoms in non-Abelian gauge potentials
• Magnetism of Cold Fermionic Atoms on p-Band of an Optical Lattice

Cited by in corpus (9)

• Physics of higher orbital bands in optical lattices: a review
• Unconventional Bose-Einstein Condensations Beyond the "No-node" Theorem
• Loop Structure Stability of a Double-Well-Lattice BEC
• Dynamical instability and loss of p-band bosons in optical lattices
• Hofstadter Butterfly Evolution in the Space of Two-Dimensional Bravais Lattices
• Evolution of the Hofstadter butterfly in a tunable optical lattice
• Topological-Fermi-Liquid to Quantum-Hall-Liquid Transitions: $p$-Band and $d$-Band Fermions in a Magnetic Field
• Orbital order in a bosonic $p$-band triangular lattice
• Phase diagram of strongly attractive $p$-orbital fermions on optical lattices