Generalised Kronig-Penney model for ultracold atomic quantum systems

Abstract

We study the properties of a quantum particle interacting with a one dimensional structure of equidistant scattering centres. We derive an analytical expression for the dispersion relation and for the Bloch functions in the presence of both even and odd scattering waves within the pseudopotential approximation. This generalises the well-known solid-state physics text-book result known as the Kronig-Penney model. Our generalised model can be used to describe systems such as degenerate Fermi gases interacting with ions or with another neutral atomic species confined in an optical lattice, thus enabling the investigation of polaron or Kondo physics within a simple formalism. We focus our attention on the specific atom-ion system and compare our findings with quantum defect theory. Excellent agreement is obtained within the regime of validity of the pseudopotential approximation. This enables us to derive a Bose-Hubbard Hamiltonian for a degenerate quantum Bose gas in a linear chain of ions.

14 pages, 10 figures

References in corpus (13)

• Cold atom dynamics in a quantum optical lattice potential
• Polaron Physics in Optical Lattices
• Cold atom-ion experiments in hybrid traps
• Emulating Solid-State Physics with a Hybrid System of Ultracold Ions and Atoms
• Cold Atoms and Molecules in Self-Assembled Dipolar Lattices
• Theory of spinor Fermi and Bose gases in tight atom waveguides
• Controlled collisions of a single atom and ion guided by movable trapping potentials
• Multichannel quantum-defect theory for ultracold atom-ion collisions
• A bosonic Josephson junction controlled by a single trapped ion
• Quantum dynamics of an atomic double-well system interacting with a trapped ion
• A Single Atom Mirror for 1D Atomic Lattice Gases
• Optical lattices with large scattering length: Using few-body physics to simulate an electron-phonon system
• Ground state properties of a Tonks-Girardeau Gas in a periodic potential

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• Quantum Simulation of Abelian Lattice Gauge Theories via State-Dependent Hopping
• Trapped ions in Rydberg-dressed atomic gases
• P-wave superfluidity of atomic lattice fermions
• Confinement-Induced Resonances in Ultracold Atom-Ion Systems
• Bootstrapping the Kronig-Penney Model
• Impact of ion motion on atom-ion confinement-induced resonances in hybrid traps
• Quantum simulation of extended polaron models using compound atom-ion systems
• Ultracold ion-atom experiments: cooling, chemistry, and quantum effects
• Compound atom-ion Josephson junction: Effects of finite temperature and ion motion
• Experimental setup for studying an ultracold mixture of trapped Yb${}^{+}$-${}^6$Li
• Ion-induced interactions in a Tomonaga-Luttinger liquid
• Quantum simulation of extended electron-phonon coupling models in a hybrid Rydberg atom setup
• Bound states of an ultracold atom interacting with a set of stationary impurities
• A novel exact solution to transmission problem of electron wave in a nonlinear Kronig-Penney superlattice
• Cooling dynamics of a free ion in a Bose-Einstein condensate
• Phonon-mediated quantum gates in trapped ions coupled to an ultracold atomic gas
• One-Dimensional Quantum Systems - From Few to Many Particles
• Periodic Ultranarrow Rods as 1D Subwavelength Optical Lattices
• Energy Band Engineering of Periodic Scatterers by Quasi-1D Confinement
• Superfluidity of identical fermions in an optical lattice: atoms and polar molecules