6533b821fe1ef96bd127afc6
RESEARCH PRODUCT
Generalised Kronig-Penney model for ultracold atomic quantum systems
Antonio NegrettiRene GerritsmaFerdinand Schmidt-kalerZbigniew IdziaszekTommaso Calarcosubject
PhysicsCondensed Matter::Quantum GasesOptical latticeQuantum PhysicsBose gasDegenerate energy levelsFOS: Physical sciencesCondensed Matter Physics3. Good healthElectronic Optical and Magnetic MaterialsPseudopotentialsymbols.namesakeQuantum defectParticle in a one-dimensional latticeQuantum Gases (cond-mat.quant-gas)Quantum mechanicsQuantum electrodynamicssymbolsHamiltonian (quantum mechanics)Quantum Physics (quant-ph)Condensed Matter - Quantum GasesQuantumdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-06-23 |