Feshbach resonance and growth of a Bose-Einstein condensate

Yüce, C.; Kılıç, Ali Yavuz

doi:10.1103/physreva.74.033609

Cited by 24 publications

(21 citation statements)

References 26 publications

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“…For further study we cite Refs. [35,36]. In addition, it is found more interesting that nearly all desired analytic solutions of the non-relativistic equation have been expressed in terms of hypergeometric functions [38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields

2018

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We need to solve a suitable exponential form of the position-dependent mass (PDM) Schrödinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the influence of the external magnetic and Aharonov-Bohm (AB) flux fields. The bound state energies and their corresponding wave functions are calculated for spatiallydependent mass distribution function of a physical interest. A few plots of some numerical results to the energy are shown.

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Section: Introductionmentioning

confidence: 99%

Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields

2018

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“…Finally, the conditions (15)- (17), together with compatibility condition (12) give the following equation…”

Section: Introductionmentioning

confidence: 99%

Integrability of the Gross–Pitaevskii equation with Feshbach resonance management

2008

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In this paper we study the integrability of a class of Gross-Pitaevskii equations managed by Feshbach resonance in an expulsive parabolic external potential. By using WTC test, we find a condition under which the Gross-Pitaevskii equation is completely integrable. Under the present model, this integrability condition is completely consistent with that proposed by Serkin, Hasegawa, and Belyaeva [V. N. Serkin et al., Phys. Rev. Lett. 98, 074102 (2007)]. Furthermore, this integrability can also be explicitly shown by a transformation, which can convert the Gross-Pitaevskii equation into the well-known standard nonlinear Schrödinger equation. By this transformation, each exact solution of the standard nonlinear Schrödinger equation can be converted into that of the Gross-Pitaevskii equation, which builds a systematical connection between the canonical solitons and the so-called nonautonomous ones. The finding of this transformation has a significant contribution to understanding the essential properties of the nonautonomous solitions and the dynamics of the Bose-Einstein condensates by using the Feshbach resonance technique.

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“…(1) coincides with the cubic G PE w ith a gain or loss term (y ) em ployed in Refs. [5,6], In Ref. [6], the cubic G PE with the gain term has been used to model the condensate growth in a trap, and it appears that as the condensate grows, its center o f mass oscillates in the trap.…”

Section: + Ctc -G(f)|'i'(xf)|2'i'(xf)mentioning

confidence: 99%

Dynamics of kink, antikink, bright, generalized Jacobi elliptic function solutions of matter-wave condensates with time-dependent two- and three-body interactions

2015

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By using the F-expansion method associated with four auxiliary equations, i.e., the Bernoulli equation, the Riccati equation, the Lenard equation, and the hyperbolic equation, we present exact explicit solutions describing the dynamics of matter-wave condensates with time-varying two- and three-body nonlinearities. Condensates are trapped in a harmonic potential and they exchange atoms with the thermal cloud. These solutions include the generalized Jacobi elliptic function solutions, hyperbolic function solutions, and trigonometric function solutions. In addition, we have also found rational function solutions. Solutions constructed here have many free parameters that can be used to manipulate and control some important features of the condensate, such as the position, width, velocity, acceleration, and homogeneous phase. The stability of the solutions is confirmed by their long-time numerical behavior.

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Feshbach resonance and growth of a Bose-Einstein condensate

Cited by 24 publications

References 26 publications

Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields

Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields

Integrability of the Gross–Pitaevskii equation with Feshbach resonance management

Dynamics of kink, antikink, bright, generalized Jacobi elliptic function solutions of matter-wave condensates with time-dependent two- and three-body interactions

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