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Title: Stability of Bose-Einstein condensates in a Kronig-Penney potential

Abstract

We study the stability of Bose-Einstein condensates with superfluid currents in a one-dimensional periodic potential. By using the Kronig-Penney model, the condensate and Bogoliubov bands are analytically calculated and the stability of condensates in a periodic potential is discussed. The Landau and dynamical instabilities occur in a Kronig-Penney potential when the quasimomentum of the condensate exceeds certain critical values as in a sinusoidal potential. It is found that the onsets of the Landau and dynamical instabilities coincide with the point where the perfect transmission of low energy excitations through each potential barrier is forbidden. The Landau instability is caused by the excitations with small q and the dynamical instability is caused by the excitations with q={pi}/a at their onsets, where q is the quasimomentum of excitation and a is the lattice constant. A swallow-tail energy loop appears at the edge of the first condensate band when the mean-field energy is sufficiently larger than the strength of the periodic potential. We find that the upper portion of the swallow-tail is always dynamically unstable, but the second Bogoliubov band has a phonon spectrum reflecting the positive effective mass.

Authors:
 [1];  [2];  [3]
  1. National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States)
  2. (Japan)
  3. Dipartimento di Fisica, Universita di Trento and CNR-INFM BEC Center, I-38050 Povo, Trento (Italy)
Publication Date:
OSTI Identifier:
20982381
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.033612; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BOGOLYUBOV METHOD; BOSE-EINSTEIN CONDENSATION; EFFECTIVE MASS; EXCITATION; INSTABILITY; MEAN-FIELD THEORY; ONE-DIMENSIONAL CALCULATIONS; PERIODICITY; PHONONS; POTENTIALS; SIMULATION; SPECTRA; STABILITY; SUPERFLUIDITY; TRANSMISSION

Citation Formats

Danshita, Ippei, Department of Physics, Waseda University, Okubo, Shinjuku, Tokyo 169-8555, and Tsuchiya, Shunji. Stability of Bose-Einstein condensates in a Kronig-Penney potential. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.033612.
Danshita, Ippei, Department of Physics, Waseda University, Okubo, Shinjuku, Tokyo 169-8555, & Tsuchiya, Shunji. Stability of Bose-Einstein condensates in a Kronig-Penney potential. United States. doi:10.1103/PHYSREVA.75.033612.
Danshita, Ippei, Department of Physics, Waseda University, Okubo, Shinjuku, Tokyo 169-8555, and Tsuchiya, Shunji. Thu . "Stability of Bose-Einstein condensates in a Kronig-Penney potential". United States. doi:10.1103/PHYSREVA.75.033612.
@article{osti_20982381,
title = {Stability of Bose-Einstein condensates in a Kronig-Penney potential},
author = {Danshita, Ippei and Department of Physics, Waseda University, Okubo, Shinjuku, Tokyo 169-8555 and Tsuchiya, Shunji},
abstractNote = {We study the stability of Bose-Einstein condensates with superfluid currents in a one-dimensional periodic potential. By using the Kronig-Penney model, the condensate and Bogoliubov bands are analytically calculated and the stability of condensates in a periodic potential is discussed. The Landau and dynamical instabilities occur in a Kronig-Penney potential when the quasimomentum of the condensate exceeds certain critical values as in a sinusoidal potential. It is found that the onsets of the Landau and dynamical instabilities coincide with the point where the perfect transmission of low energy excitations through each potential barrier is forbidden. The Landau instability is caused by the excitations with small q and the dynamical instability is caused by the excitations with q={pi}/a at their onsets, where q is the quasimomentum of excitation and a is the lattice constant. A swallow-tail energy loop appears at the edge of the first condensate band when the mean-field energy is sufficiently larger than the strength of the periodic potential. We find that the upper portion of the swallow-tail is always dynamically unstable, but the second Bogoliubov band has a phonon spectrum reflecting the positive effective mass.},
doi = {10.1103/PHYSREVA.75.033612},
journal = {Physical Review. A},
number = 3,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • All Bloch states of the mean field of a Bose-Einstein condensate in the presence of a one-dimensional lattice are presented in closed analytic form. The band structure is investigated by analyzing the stationary states of the nonlinear Schroedinger, or Gross-Pitaevskii, equation for both repulsive and attractive condensates. The appearance of swallowtails in the bands is examined and interpreted in terms of the condensates superfluid properties. The nonlinear stability properties of the Bloch states are described and the stable regions of the bands and swallowtails are mapped out. We find that the Kronig-Penney potential has the same properties as a sinusoidalmore » potential. Bose-Einstein condensates are trapped in sinusoidal optical lattices. The Kronig-Penney potential has the advantage of being analytically tractable, unlike the sinusoidal potential, and, therefore, serves as a good model for understanding experimental phenomena.« less
  • In their recent paper [Phys. Rev. A 71, 033622 (2005)], Seaman et al. studied Bloch states of the condensate wave function in a Kronig-Penney potential and calculated the band structure. They argued that the effective mass is always positive when a swallowtail energy loop is present in the band structure. In this Comment, we reexamine their argument by actually calculating the effective mass. It is found that there exists a region where the effective mass is negative even when a swallowtail is present. Based on this fact, we discuss the interpretation of swallowtails in terms of superfluidity.
  • In response to Danshita and Tsuchiya's comment on our work on nonlinear band theory, we show that the size of the region of the swallowtail with a negative effective mass is inversely proportional to the interaction strength, i.e., for large interaction strengths, the region becomes negligibly small. We explain why the appearance of swallowtails is not related to superfluidity, but instead to a more universal nonlinear feature valid for both signs of the underlying atomic interactions: period doubling.
  • We investigate the excitation spectrum of a Bose-Einstein condensate in a Kronig-Penney potential. We solve the Bogoliubov equations analytically and obtain the band structure of the excitation spectrum. We find that the excitation spectrum is gapless and linear at low energies. This property is found to be attributed to the anomalous tunneling behavior of low energy excitations, which has been predicted by Kagan et al.