Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps

Gammal, A.; Frederico, T.; Tomio, Lauro

doi:10.1103/physreva.64.055602

Cited by 124 publications

(220 citation statements)

References 23 publications

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“…Both situations increase N c , while in a spherical-shape N c reaches its the minimal value. For example, in a cigar-shape trap λ = 0.1 and N c = 7157, in a disc-shape trap λ = 10 and N c = 5586 and in a spherical-shape trap λ = 1 with N c = 1350.These values are in a good agreement with those in references [11,13].…”

Section: Resultssupporting

confidence: 81%

“…It was shown by Gammal et al [11][12] within the GrossPitaevskii formalism, that the critical number of particles for BEC in cylindrical traps can be obtained numerically for the case attractive interactions. It was also calculated in reference [13] the spectrum of the Gross-Pitaevskii Equation (GPE) for a system composed of attractive bosons confined in a harmonic trap through the Controlled Perturbation Theory.…”

Section: Introductionmentioning

confidence: 99%

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An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

Sousa¹,

Bagnato²,

Silva³

2008

Braz. J. Phys.

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We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

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Section: Resultssupporting

confidence: 81%

Section: Introductionmentioning

confidence: 99%

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

Sousa¹,

Bagnato²,

Silva³

2008

Braz. J. Phys.

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“…The precise value of k depends on the aspect ratio of the magnetic trap 3 . a ho is the harmonic oscillator length, which sets the size of the condensate in the ideal-gas (a = 0) limit.…”

mentioning

confidence: 99%

Dynamics of collapsing and exploding Bose–Einstein condensates

Donley

Claussen

Cornish

et al. 2001

Nature

745

909

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We explored the dynamics of how a Bose-Einstein condensate collapses and subsequently explodes when the balance of forces governing the size and shape of the condensate is suddenly altered. A condensate's equilibrium size and shape is strongly affected by the inter-atomic interactions. Our ability to induce a collapse by switching the interactions from repulsive to attractive by tuning an externally-applied magnetic field yields a wealth of detailed information on the violent collapse process. We observe anisotropic atom bursts that explode from the condensate, atoms leaving the condensate in undetected forms, spikes appearing in the condensate wave function, and oscillating remnant condensates that survive the collapse. These all have curious dependencies on time, the strength of the interaction, and the number of condensate atoms. Although ours would seem to be a simple well-characterized system, our measurements reveal many interesting phenomena that challenge theoretical models.Although the density of the atoms in an atomic BoseEinstein condensate (BEC) is typically five orders of magnitude lower than the density of air, the inter-atomic interactions greatly affect a wide variety of BEC properties. These include static properties like the BEC size and shape and the condensate stability, and dynamic properties like the collective excitation spectrum and soliton and vortex behavior. Since all of these properties are sensitive to the inter-atomic interactions, they can be quite dramatically affected by tuning the interaction strength and sign.The vast majority of BEC physics is well described by mean-field theory 1 , in which the strength of the interactions depends on the atom density and on one additional parameter called the s-wave scattering length a. a is determined by the atomic species. When a > 0, the interactions are repulsive. In contrast, when a < 0 the interactions are attractive and a BEC tends to contract to minimize its overall energy. In a harmonic trap, the contraction competes with the kinetic zero-point energy, which tends to spread out the condensate. For a strong enough attractive interaction, there is not enough kinetic energy to stabilize the BEC and it is expected to implode. A BEC can avoid implosion only as long as the number of atoms N 0 is less than a critical value given by 2where dimensionless constant k is called the stability coefficient. The precise value of k depends on the aspect ratio of the magnetic trap 3 . a ho is the harmonic oscillator length, which sets the size of the condensate in the ideal-gas (a = 0) limit. Under most circumstances, a is insensitive to external fields. This is different in the vicinity of a so-called Feshbach resonance, where a can be tuned over a huge range by adjusting the externally applied magnetic field 4,5 . This has been demonstrated in recent years with cold 85 Rb and Cs atoms 6,7,8 , and with Na and 85 Rb BoseEinstein condensates 9,10 . For 85 Rb atoms, a is usually negative, but a Feshbach resonance at ∼155 G allows us to tune a by orders ...

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“…As in Section 3, the numerical and variational results can also be compared in order to investigate how bright-soliton-like the bright solitary matter wave ground states are in terms of their shape; such a comparison is, however, only meaningful in cases which approach the quasi-1D limit [43]. Studies have investigated traps with spherical [23,66] and cylindrical [16] symmetry, cylindrically symmetric waveguides without axial trapping [62], and the case of a generally asymmetric trap [17]. Several works also investigated the configurations of specific experiments in detail [61,72].…”

Section: Numerical Approachesmentioning

confidence: 99%

“…The collapse instability has been investigated experimentally [15,[26][27][28]. Numerous theoretical studies have focused on identifying the parameters associated with the onset of collapse in condensates of various geometries, using variational [43,44,61,62,64], perturbative [24], and numerical [16,17,23,43,61,62,66] methods. The condensate dynamics during collapse are the subject of continuing theoretical study [30,[67][68][69][70].…”

Section: Collapse and The Critical Parametermentioning

confidence: 99%

Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Malomed¹

2013

Progress in Optical Science and Photonics

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In recent years, bright soliton-like structures composed of gaseous Bose-Einstein condensates have been generated at ultracold temperature. The experimental capacity to precisely engineer the nonlinearity and potential landscape experienced by these solitary waves offers an attractive platform for fundamental study of solitonic structures. The presence of three spatial dimensions and trapping implies that these are strictly distinct objects to the true soliton solutions. Working within the zero-temperature mean-field description, we explore the solutions and stability of bright solitary waves, as well as their interactions. Emphasis is placed on elucidating their similarities and differences to the true bright soliton. The rich behaviour introduced in the bright solitary waves includes the collapse instability and symmetry-breaking collisions. We review the experimental formation and observation of bright solitary matter waves to date, and compare to theoretical predictions. Finally we discuss the current state-of-the-art of this area, including beyond-mean-field descriptions, exotic bright solitary waves, and proposals to exploit bright solitary waves in interferometry and as surface probes.

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Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps

Cited by 124 publications

References 23 publications

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

Dynamics of collapsing and exploding Bose–Einstein condensates

Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

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