Pseudopotential treatment of two aligned dipoles under external harmonic confinement
Abstract
Dipolar Bose and Fermi gases, which are currently being studied extensively experimentally and theoretically, interact through anisotropic, longrange potentials. Here, we replace the longrange potential by a zerorange pseudopotential that simplifies the theoretical treatment of two dipolar particles in a harmonic trap. Our zerorange pseudopotential description reproduces the energy spectrum of two dipoles interacting through a shapedependent potential under external confinement very well, provided that sufficiently many partial waves are included, and readily leads to a classification scheme of the energy spectrum in terms of approximate angular momentum quantum numbers. The results may be directly relevant to the physics of dipolar gases loaded into optical lattices.
 Authors:
 Department of Physics and Astronomy, Washington State University, Pullman, Washington 991642814 (United States)
 JILA, NIST and Department of Physics, University of Colorado, Boulder, Colorado 803090440 (United States)
 (United States)
 (Italy)
 Publication Date:
 OSTI Identifier:
 20982523
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.75.052705; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANGULAR MOMENTUM; ANISOTROPY; BOSEEINSTEIN GAS; BOSONS; DIPOLES; ENERGY SPECTRA; FERMI GAS; FERMIONS; HARMONIC OSCILLATORS; PARTIAL WAVES; POTENTIALS; QUANTUM NUMBERS; RADIATION PRESSURE; TRAPS
Citation Formats
Kanjilal, K., Bohn, John L., Blume, D., JILA, NIST and Department of Physics, University of Colorado, Boulder, Colorado 803090440, and INFMBEC, Dipartimento di Fisica, Universita di Trento, Sommarive 4, I38050 Povo. Pseudopotential treatment of two aligned dipoles under external harmonic confinement. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.052705.
Kanjilal, K., Bohn, John L., Blume, D., JILA, NIST and Department of Physics, University of Colorado, Boulder, Colorado 803090440, & INFMBEC, Dipartimento di Fisica, Universita di Trento, Sommarive 4, I38050 Povo. Pseudopotential treatment of two aligned dipoles under external harmonic confinement. United States. doi:10.1103/PHYSREVA.75.052705.
Kanjilal, K., Bohn, John L., Blume, D., JILA, NIST and Department of Physics, University of Colorado, Boulder, Colorado 803090440, and INFMBEC, Dipartimento di Fisica, Universita di Trento, Sommarive 4, I38050 Povo. Tue .
"Pseudopotential treatment of two aligned dipoles under external harmonic confinement". United States.
doi:10.1103/PHYSREVA.75.052705.
@article{osti_20982523,
title = {Pseudopotential treatment of two aligned dipoles under external harmonic confinement},
author = {Kanjilal, K. and Bohn, John L. and Blume, D. and JILA, NIST and Department of Physics, University of Colorado, Boulder, Colorado 803090440 and INFMBEC, Dipartimento di Fisica, Universita di Trento, Sommarive 4, I38050 Povo},
abstractNote = {Dipolar Bose and Fermi gases, which are currently being studied extensively experimentally and theoretically, interact through anisotropic, longrange potentials. Here, we replace the longrange potential by a zerorange pseudopotential that simplifies the theoretical treatment of two dipolar particles in a harmonic trap. Our zerorange pseudopotential description reproduces the energy spectrum of two dipoles interacting through a shapedependent potential under external confinement very well, provided that sufficiently many partial waves are included, and readily leads to a classification scheme of the energy spectrum in terms of approximate angular momentum quantum numbers. The results may be directly relevant to the physics of dipolar gases loaded into optical lattices.},
doi = {10.1103/PHYSREVA.75.052705},
journal = {Physical Review. A},
number = 5,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}

Atomatom scattering of bosonic onedimensional (1D) atoms has been modeled successfully using a zerorange {delta}function potential, while that of bosonic 3D atoms has been modeled successfully using FermiHuang's regularized swave pseudopotential. Here, we derive the eigenenergies of two spinpolarized 1D fermions under external harmonic confinement interacting through a zerorange potential, which only acts on oddparity wave functions, analytically. We also present a divergentfree zerorange potential treatment of two spinpolarized 3D fermions under harmonic confinement. Our pseudopotential treatments are verified through numerical calculations for shortrange model potentials.

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