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Oscillating Quantum Droplets From the Free Expansion of Logarithmic One-dimensional Bose Gases

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Abstract

We analyse some issues related to the stability and free expansion of a one-dimensional logarithmic Bose–Einstein condensate, particularly its eventual relation to the formation of quantum droplet-type configurations. We prove that the corresponding properties, such as the energy of the associated N-body ground state, differ substantially with respect to its three-dimensional counterpart. Consequently, the free velocity expansion also shows remarkable differences with respect to the three-dimensional system when logarithmic interactions are taken into account. The one-dimensional logarithmic condensate tends to form quantum droplet-type configurations when the external trapping potential is turned off, i.e., the self-sustainability or self-confinement appears as in three-dimensions. However, we obtain that for some specific values of the self-interaction parameters and the number of particles under consideration, the cloud oscillates during the free expansion around to a specific equilibrium size. These results show that we are able to describe scenarios in which the one-dimensional cloud reaches stable configurations, i.e., oscillating quantum droplets.

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Notes

  1. See for instance Ref. [44] and references therein for some insights related to this topic.

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Acknowledgements

E. C. acknowledges the receipt of the grant from the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy. This work was partially supported also by CONACyT México under Grant No. 304001.

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Authors and Affiliations

  1. Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, 01000, Ciudad de México, Mexico

    Omar Abel Rodríguez-López

  2. Mesoamerican Centre for Theoretical Physics, Universidad Autónoma de Chiapas. Ciudad Universitaria, Carretera Zapata Km. 4, Real del Bosque (Terán), 29040, Tuxtla Gutiérrez, Chiapas, Mexico

    Elías Castellanos

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Rodríguez-López, O.A., Castellanos, E. Oscillating Quantum Droplets From the Free Expansion of Logarithmic One-dimensional Bose Gases. J Low Temp Phys 204, 111–128 (2021). https://doi.org/10.1007/s10909-021-02601-y

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