Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms

Ruprecht, P. A.; Holland, Murray; Burnett, K.; Edwards, Mark

doi:10.1103/physreva.51.4704

Cited by 574 publications

(658 citation statements)

References 17 publications

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“…Theoretical analysis based on the GP equation also confirms the collapse. Thus for a system of atoms with attractive two-body interaction, the condensate has no stable solution above a certain critical number of atoms N max [9,10,11]. However, as reported by Gammal et al [12], the addition of a repulsive potential derived from three-body interaction is consistent with a number of atoms larger than N max .…”

Section: Introductionsupporting

confidence: 63%

Stability of trapless Bose–Einstein condensates with two- and three-body interactions

Sabari¹,

Raja²,

Porsezian³

et al. 2010

J. Phys. B: At. Mol. Opt. Phys.

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Abstract. We study the stabilization of a trapless Bose-Einstein condensate by analyzing the mean-field Gross-Pitaevskii equation with attractive two-and threebody interactions through both analytical and numerical methods. By using the variational method we show that there is an enhancement of the condensate stability due to the inclusion of three-body interaction in addition to the two-body interaction. We also study stability of the condensates in the presence of time varying threebody interaction. Finally we confirm the stabilization of a trapless condensates from numerical simulation.

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Section: Introductionsupporting

confidence: 63%

Stability of trapless Bose–Einstein condensates with two- and three-body interactions

Sabari¹,

Raja²,

Porsezian³

et al. 2010

J. Phys. B: At. Mol. Opt. Phys.

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“…which can be used as a mean-field model describing the dynamics of a cigar-shaped BEC with repulsive interatomic interactions [7,29,30], trapped in the potential:…”

Section: Introductionmentioning

confidence: 99%

Dark soliton dynamics in spatially inhomogeneous media: Application to Bose–Einstein condensates

Theocharis

Frantzeskakis

Kevrekidis

et al. 2005

Mathematics and Computers in Simulation

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We study the dynamics of dark solitons in spatially inhomogeneous media with applications to cigar-shaped Bose-Einstein condensates trapped in a harmonic magnetic potential and a periodic potential representing an optical lattice. We distinguish and systematically investigate the cases with the optical lattice period being smaller, larger, or comparable to the width of the dark soliton. Analytical results, based on perturbation techniques, for the motion of the dark soliton are obtained and compared to direct numerical simulations. Radiation effects are also considered. Finally, we demonstrate that a moving optical lattice may capture and drag a dark soliton.

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“…Feshbach resonances). For moderate attractive interactions and relatively few particles similar stable structures also exist (Ruprecht et al 1995, Baym & Pethick 1996. However, attraction destabilizes these systems and collapse occurs into very dense and highly correlated structures (Bradley et al 1997, Lahaye et al 2008.…”

Section: Conclusion and Perspectivementioning

confidence: 99%

“…For attractive interactions (a < 0), the system collapses unless some measures are taken to avoid this part of the Hilbert space. However, quasi-stable solutions exist of finite size and energy if N |a|/b < 0.65 where b is the trap length of the external harmonic potential (Ruprecht et al 1995, Kagan et al 1998, Pitaevskii & Stringari 2003, Pethick & Smith 2008, Bohn et al 1998, Sørensen et al 2004. Figure 2 shows the effective potential barrier of an attractively interacting condensate based on a gaussian variational calculation including also higher-order effective range corrections (Zinner & Thøgersen 2009).…”

Section: Mean-field Descriptionmentioning

confidence: 99%

Comparing and contrasting nuclei and cold atomic gases

Zinner¹,

Jensen²

2013

J. Phys. G: Nucl. Part. Phys.

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Abstract. The experimental revolution in ultracold atomic gas physics over the past decades have brought tremendous amounts of new insight to the world of degenerate quantum systems. Here we compare and constrast the developments of cold atomic gases with the physics of nuclei since many concepts, techniques, and nomenclatures are common to both fields. However, nuclei are finite systems with interactions that are typically much more complicated than those of ultracold atomic gases. The simularities and differences must therefore be carefully addressed for a meaningful comparison and to facilitate fruitful crossdisciplinary activity. We first consider condensates of bosonic and paired systems of fermionic particles with the mean-field description but take great care to point out potential problems in the limit of small particle numbers. Along the way we review some of the basic results of BEC and BCS theory, as well as the BCS-BEC crossover and the Fermi gas in the unitarity limit, all within the context of ultracold atoms. Subsequently, we consider the specific example of an atomic Fermi gas from a nuclear physics perspective, comparing degrees of freedom, interactions, and relevant length and energy scales of cold atoms and nuclei. Next we address some attempts in nuclear physics to transfer the concepts of condensates in nuclei that can in principle be built from bosonic alpha-particle constituents. We also consider Efimov physics, a prime example of nuclear physics transfered to cold atoms, and consider which systems are more likely to show interesting bound state spectra. Finally, we address some recent studies of the BCS-BEC crossover in light nuclei and compare them to the concepts used in ultracold atomic gases. While many-body concepts such as BEC or BCS states are applicable in both subfields, we find that the interactions and finite particle numbers in nuclei can obscure the clear meaning they have in cold atoms. On the other hand, universal results from atomic physics should have impact in certain limits of the nuclear domain. In particular, with advances in the trapping of few-body atomic systems we expect a more direct exchange of ideas and results.

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Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms

Cited by 574 publications

References 17 publications

Stability of trapless Bose–Einstein condensates with two- and three-body interactions

Stability of trapless Bose–Einstein condensates with two- and three-body interactions

Dark soliton dynamics in spatially inhomogeneous media: Application to Bose–Einstein condensates

Comparing and contrasting nuclei and cold atomic gases

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