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arXiv · 1806.01784

Dimensional crossover for the beyond-mean-field correction in Bose gases

Tobias Ilg·Jan Kumlin·Luis Santos·Dmitry S. Petrov·Hans Peter Büchler
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Abstract

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.

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Tobias Ilg, Jan Kumlin, Luis Santos, Dmitry S. Petrov, Hans Peter Büchler. 2018-06-05. Dimensional crossover for the beyond-mean-field correction in Bose gases. https://doi.org/10.1103/physreva.98.051604

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