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arXiv:cond-mat/0411702 · Physical Review A

Energy barrier for collapse in a pair of tunnel-coupled condensates with scattering lengths of opposite signs

V. S. Shchesnovich, Solange Bessa Cavalcanti

Published Feb 15, 2005• 8 citations
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Abstract

We predict the existence of an energy barrier for collapse in a system of two tunnel-coupled repulsive and attractive quasi-two-dimensional condensates trapped in a double-well potential. The ground state in such a system can have a lower energy than that of the collapsing state. We find such ground states numerically and analytically determine the domain of their existence; they have a much larger share of atoms confined in the repulsive condensate. The energy barrier for collapse is due to the fact that the energy of the system increases if atoms tunnel from the repulsive condensate to the attractive one.

DOI
10.1103/physreva.71.023607

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We predict the existence of an energy barrier for collapse in a system of two tunnel-coupled repulsive and attractive quasi-two-dimensional condensates trapped in a double-well potential. The ground state in such a system can have a lower energy than that of the collapsing state. We find such ground states numerically and analytically determine the domain of their existence; they have a much larger share of atoms confined in the repulsive condensate. The energy barrier for collapse is due to the fact that the energy of the system increases if atoms tunnel from the repulsive condensate to the attractive one.
We study solitons in the condensate trapped in a double-well potential with far-separated wells, when the sss-wave scattering length has different signs in the two parts of the condensate. By employing the coupled-mode approximation it is shown that there are unusual stable bright solitons in the condensate, with the larger share of atoms being gathered in the repulsive part. Such unusual solitons derive their stability from the quantum tunneling and correspond to the strong coupling between the parts of the condensate. The ground state of the system, however, corresponds to weak coupling between the condensate parts, with the larger share of atoms being gathered in the attractive part of the condensate.
We study, analytically and numerically, the stationary states in the system of two linearly coupled nonlinear Schr{ö}dinger equations in two spatial dimensions, with the nonlinear interaction coefficients of opposite signs. This system is the two-dimensional analog of the coupled-mode equations for a condensate in the double-well trap [\textit{Physical Review A} \textbf{69}, 033609 (2004)]. In contrast to the one-dimensional case, where the bifurcation from zero leads to stable bright solitons, in two spatial dimensions this bifurcation results in the appearance of unstable soliton solutions (the Townes-type solitons). With the use of a parabolic potential the ground state of the system is stabilized. It corresponds to strongly coupled condensates and is stable with respect to collapse. This is in sharp contrast to the one-dimensional case, where the ground state corresponds to weakly coupled condensates and is unstable. Moreover, the total number of atoms of the stable ground state can be much higher than the collapse threshold for a single two-dimensional condensate with a negative s-wave scattering length.
The fragmentation of the ground state of a repulsive condensate immersed into a double-trap potential is found to be a general and critical phenomenon. It takes place for a given number of bosons if their scattering length is larger than some critical value or for a given value of the scattering length if the number of bosons is above some critical number. We demonstrate that the geometry of the inner trap determines these critical parameters while the number of the fragments and the fraction of bosons in the various fragments can be manipulated by the outer trap. There is also a maximal number of bosons for which the ground state is fragmented. If this number is exceeded, the fragmented state becomes a very low-lying excited state of the condensate. This maximal number of bosons can be substantially manipulated by varying the inner and outer traps. To study threefold fragmentation we have chosen a potential well with two barriers as the inner trap and embedded in two types of outer ones. A manifold fragmentation is also addressed.
Bose–Einstein condensates are studied in a potential of finite depth which supports both bound and quasi-bound states. This potential, which is harmonic for small radii and decays as a Gaussian for large radii, models experimentally relevant optical traps. The nonlinearity, which is proportional to both the number of atoms and the interaction strength, can transform bound states into quasi-bound ones. The latter have a finite lifetime due to tunnelling through the barriers at the borders of the well. We predict the lifetime and stability properties for repulsive and attractive condensates in one, two and three dimensions, for both the ground state and excited soliton and vortex states. We show, via a combination of the variational and WKB approximations, that macroscopic quantum tunnelling in such systems can be observed on time scales of 10 ms to 10 s.
The stability of a low-temperature Bose–Einstein condensate with attractive interactions in one- and three-dimensional double-well potentials is discussed. In particular, the tunnelling dynamics of a condensate under the influence of a time-dependent potential gradient is investigated. The condensate is shown to collapse at a critical potential gradient which corresponds to a critical number of atoms in one of the two wells. The sensitivity of this tunnelling-induced collapse could provide a useful tool in the study of condensates with attractive interactions.
The stability of a low temperature Bose-Einstein condensate with attractive interactions in one and three dimensional double-well potentials is discussed. In particular, the tunnelling dynamics of a condensate under the influence of a time-dependent potential gradient is investigated. The condensate is shown to collapse at a critical potential gradient which corresponds to a critical number of atoms in one of the two wells. The sensitivity of this tunnelling induced collapse could provide a useful tool in the study of condensates with attractive interactions.