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arXiv:quant-ph/9712046

Note on the stability of a confined Bose gas: Comment on quant-ph/9712030 by L. Salasnich

F. Brosens, J. T. Devreese, L. F. Lemmens

Published Dec 19, 1997• 0 citations
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Abstract

We demonstrate analytically that a Bose-Einstein condensate confined in a harmonic trap with zero-range attractive interparticle interactions is unstable if there is more than 1 boson. Replacing the zero-range interaction by a short-range attractive interaction lifts the instability, and leads to a pronounced clustering, by which the particles leak out of the condensate.

DOI
10.48550/arxiv.quant-ph/9712046

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In this letter we reply to a comment of Brosens, Devreese and Lemmens (quant-ph/9712046) on our paper (Mod. Phys. Lett.B11, 1249 (1997)) that analyzes the role of dimensionality in the stability of a confined condensed Bose gas. We generalize our previous results and discuss the e ect of a short range attractive interaction between the bosons.

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We demonstrate analytically that a Bose-Einstein condensate confined in a harmonic trap with zero-range attractive interparticle interactions is unstable if there is more than 1 boson. Replacing the zero-range interaction by a short-range attractive interaction lifts the instability, and leads to a pronounced clustering, by which the particles leak out of the condensate.
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.
Here we describe a weakly interacting Bose gas on a curved smooth manifold, which is embedded in the three-dimensional Euclidean space. To this end we start by considering a harmonic trap in the normal direction of the manifold, which confines the three-dimensional Bose gas in the vicinity of its surface. Following the notion of dimensional reduction as outlined in [L Salasnich et al, Phys. Rev. A 65, 043614 (2002)], we assume a large enough trap frequency so that the normal degree of freedom of the condensate wave function can be approximately integrated out. In this way we obtain an effective condensate wave function on the quasi-two-dimensional surface of the curved manifold, where the thickness of the cloud is determined self-consistently. For the particular case when the manifold is a sphere, our equilibrium results show how the chemical potential and the thickness of the cloud increase with the interaction strength. Furthermore, we determine within a linear stability analysis the low-lying collective excitations together with their eigenfrequencies, which turn out to reveal an instability for attractive interactions.
It is well known that bosonic particles with attractive interaction in a uniform gas do not form a condensate. Here we investigate a dilute Bose gas and study stationary solutions of the Gross–Pitaevskii equation with attractive interaction. We have also used a higher order stabilising term in the presence of a harmonic confining potential. We show that there are three possible types of stationary solutions corresponding to stable, metastable and unstable phases. These results are discussed in relation to a 7Li condensate.
Abstract Here we describe a weakly interacting Bose gas on a curved smooth manifold, which is embedded in the three-dimensional Euclidean space. To this end we start by considering a harmonic trap in the normal direction of the manifold, which confines the three-dimensional Bose gas in the vicinity of its surface. Following the notion of dimensional reduction as outlined in [L Salasnich et al, Phys. Rev. A 65, 043614 (2002)], we assume a large enough trap frequency so that the normal degree of freedom of the condensate wave function can be approximately integrated out. In this way we obtain an effective condensate wave function on the quasi-two-dimensional surface of the curved manifold, where the thickness of the cloud is determined self-consistently. For the particular case when the manifold is a sphere, our equilibrium results show how the chemical potential and the thickness of the cloud increase with the interaction strength. Furthermore, we determine within a linear stability analysis the low-lying collective excitations together with their eigenfrequencies, which turn out to reveal an instability for attractive interactions.