Archive ouverte HAL – Dimensional crossover for the beyond-mean-field correction in Bose gases

Tobias Ilg 1 Jan Kumlin 1 Luis Santos 2 Dmitry S. Petrov 3 Hans Peter Büchler 1

Physical Review A, American Physical Society, 2018, 98 (5), 〈10.1103/PhysRevA.98.051604〉

We present a detailed beyond-mean-field analysis of a weakly interacting Bose gas in the crossover from three to low dimensions. We find an analytical solution for the energy and provide a clear qualitative picture of the crossover in the case of a box potential with periodic boundary conditions. We show that the leading contribution of the confinement-induced resonance is of beyond-mean-field order and calculate the leading corrections in the three- and low-dimensional limits. We also characterize the crossover for harmonic potentials in a model system with particularly chosen short- and long-range interactions and show the limitations of the local-density approximation. Our analysis is applicable to Bose-Bose mixtures and gives a starting point for developing the beyond-mean-field theory in inhomogeneous systems with long-range interactions such as dipolar particles or Rydberg-dressed atoms.

  • 1. University of Stuttgart
  • 2. LUH – Leibniz Universität Hannover [Hannover]
  • 3. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques

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