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Soviet Journal of Low Temperature Physics

Condensate stability in the Bose-gas model with two- and three-particle interaction

Vladmir G. Makhankov, Kholmirzo T. Kholmurodov

Published Jan 1, 1989• 0 citations
Publisher

Abstract

The problem of Bose-condensate stability is studied in the model with two-particle attraction and three-particle repulsion. Two channels of condensate decomposition are established, one of which is associated with an excitation of one bubble and the other with bubble gas in the condensate. Calculations show that the gas channel of decomposition is more advantageous from the energy point of view since it takes place at lower temperatures in comparison with the one-soliton channel.

DOI
10.1063/10.0032098

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The problem of Bose-condensate stability is studied in the model with two-particle attraction and three-particle repulsion. Two channels of condensate decomposition are established, one of which is associated with an excitation of one bubble and the other with bubble gas in the condensate. Calculations show that the gas channel of decomposition is more advantageous from the energy point of view since it takes place at lower temperatures in comparison with the one-soliton channel.
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We study analytically the ground-state stability of a Bose–Einstein condensate (BEC) confined in an harmonic trap with repulsive or attractive zero-range interaction by minimizing the energy functional of the system. In the case of repulsive interaction the BEC mean radius grows by increasing the number of bosons, instead in the case of attractive interaction the BEC mean radius decreases by increasing the number of bosons: to zero if the system is one-dimensional and to a constant minimum radius, with a maximum number of bosons, if the system is three-dimensional.
This paper investigates the collective excitation and stability of low-dimensional Bose–Einstein condensates with two- and three-body interactions by the variational analysis of the time-dependent Gross–Pitaevskii–Ginzburg equation. The spectrum of the low-energy excitation and the effective potential for the width of the condensate are obtained. The results show that: (i) the repulsive two-body interaction among atoms makes the frequency red-shifted for the internal excitation and the repulsive or attractive three-body interaction always makes it blue-shifted; (ii) the region for the existence of the stable bound states is obtained by identifying the critical value of the two- and three-body interactions.