Projected Gross–Pitaevskii Equation for Ring-Shaped Bose–Einstein Condensates

Authors

  • O.O. Prikhodko Taras Shevchenko National University of Kyiv, Department of Physics
  • Y.M. Bidasyuk Physikalisch-Technische Bundesanstalt

DOI:

https://doi.org/10.15407/ujpe66.3.198

Keywords:

Bose–Einstein condensation, Gross–Pitaevskii equation, spectral methods

Abstract

We propose an alternative implementation of the projected Gross–Pitaevskki equation adapted for a numerical modeling of the atomic Bose–Einstein condensate trapped in a toroidally shaped potential. We present an accurate efficient scheme to evaluate the required matrix elements and to calculate tthe ime evolution of the matter wave field. We analyze the stability and accuracy of the developed method for equilibrium and nonequilibrium solutions in a ring-shaped trap with an additional barrier potential corresponding to recent experimental realizations.

References

F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari. Theory of Bose-Einstein condensation in trapped gases. Rev. Mod. Phys. 71, 463 (1999).

https://doi.org/10.1103/RevModPhys.71.463

C.J. Pethick, H. Smith. Bose-Einstein Condensation in Dilute Gases (Cambridge Univ. Press, 2008) [ISBN: 0 521

https://doi.org/10.1017/CBO9780511802850

3].

A. Sinatra, C. Lobo, Y. Castin. Classical-field method for time dependent Bose-Einstein condensed gases. Phys. Rev. Lett. 87, 210404 (2001).

https://doi.org/10.1103/PhysRevLett.87.210404

M.J. Davis, S.A. Morgan, K. Burnett. Simulations of Bose fields at finite temperature. Phys. Rev. Lett. 87, 160402 (2001).

https://doi.org/10.1103/PhysRevLett.87.160402

P.B. Blakie, M.J. Davis. Projected Gross-Pitaevskii equation for harmonically confined Bose gases at finite temperature. Phys. Rev. A 72, 063608 (2005).

https://doi.org/10.1103/PhysRevA.72.063608

M.J. Davis, S.A. Morgan. Microcanonical temperature for a classical field: Application to Bose-Einstein condensation. Phys. Rev. A 68, 053615 (2003).

https://doi.org/10.1103/PhysRevA.68.053615

S.J. Rooney, A.J. Allen, U. Z¨ulicke, N.P. Proukakis, A.S. Bradley. Reservoir interactions of a vortex in a trapped three-dimensional Bose-Einstein condensate. Phys. Rev. A 93, 063603 (2016).

https://doi.org/10.1103/PhysRevA.93.063603

M.C. Garrett, T.M. Wright, M.J. Davis. Condensation and quasicondensation in an elongated three-dimensional Bose gas. Phys. Rev. A 87, 063611 (2013).

https://doi.org/10.1103/PhysRevA.87.063611

S.J. Rooney, T.W. Neely, B.P. Anderson, A.S. Bradley. Persistent-current formation in a high-temperature Bose-

Einstein condensate: An experimental test for classical-field theory. Phys. Rev. A 88, 063620 (2013).

https://doi.org/10.1103/PhysRevA.88.063620

S.J. Rooney, A.S. Bradley, P.B. Blakie. Decay of a quantum vortex: Test of nonequilibrium theories for warm Bose-

Einstein condensates. Phys. Rev. A 81, 023630 (2010).

https://doi.org/10.1103/PhysRevA.81.029901

Y.M. Bidasyuk, M. Weyrauch, M. Momme, O.O. Prikhodko. Finite-temperature dynamics of a bosonic Josephson junction. J. Phys. B: Atomic, Mol. and Opt. Phys. 51, 205301 (2018).

https://doi.org/10.1088/1361-6455/aae022

P.B. Blakie. Numerical method for evolving the projected Gross-Pitaevskii equation. Phys. Rev. E 78, 026704 (2008).

https://doi.org/10.1103/PhysRevE.78.026704

A.I. Yakimenko, Y.M. Bidasyuk, M. Weyrauch, Y.I. Kuriatnikov, S.I. Vilchinskii. Vortices in a toroidal Bose-Einstein condensate with a rotating weak link. Phys. Rev. A 91, 033607 (2015).

https://doi.org/10.1103/PhysRevA.91.033607

S.Eckel, J.G. Lee, F. Jendrzejewski,N.Murray,C.W.Clark, C.J. Lobb, W.D. Phillips, M. Edwards, G.K. Campbell.

Hysteresis in a quantized superfluid 'atomtronic' circuit. Nature 506, 200 (2014).

https://doi.org/10.1038/nature12958

A. Kumar, S. Eckel, F. Jendrzejewski, G.K. Campbell. Temperature-induced decay of persistent currents in a superfluid ultracold gas. Phys. Rev. A 95, 021602 (2017).

https://doi.org/10.1103/PhysRevA.95.021602

S.P. Cockburn, N.P. Proukakis. Ab initio methods for finite-temperature two-dimensional Bose gases. Phys. Rev.

A 86, 033610 (2012).

J. Pietraszewicz, P. Deuar. Classical fields in the one-dimensional Bose gas: Applicability and determination of the optimal cutoff. Phys. Rev. A 98, 023622 (2018).

https://doi.org/10.1103/PhysRevA.98.023622

W. Bao, D. Jaksch, P.A. Markowich. Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation. J. Computat. Phys. 187, 318 (2003).

https://doi.org/10.1016/S0021-9991(03)00102-5

M.J. Bijlsma, E. Zaremba, H.T.C. Stoof. Condensate growth in trapped Bose gases. Phys. Rev. A 62, 063609 (2000).

https://doi.org/10.1103/PhysRevA.62.063609

K. Snizhko, K. Isaieva, Y. Kuriatnikov, Y. Bidasyuk, S. Vilchinskii, A. Yakimenko. Stochastic phase slips in toroidal Bose-Einstein condensates. Phys. Rev. A 94, 063642 (2016).

https://doi.org/10.1103/PhysRevA.94.063642

M. Kunimi, I. Danshita. Decay mechanisms of superflow of Bose-Einstein condensates in ring traps. Phys. Rev. A 99, 043613 (2019).

https://doi.org/10.1103/PhysRevA.99.043613

Y. Bidasyuk, W. Vanroose, J. Broeckhove, F. Arickx, V. Vasilevsky. Hybrid method (JM-ECS) combining the J-matrix and exterior complex scaling methods for scattering calculations. Phys. Rev. C 82, 064603 (2010).

https://doi.org/10.1103/PhysRevC.82.064603

Y. Bidasyuk, W. Vanroose. Improved convergence of scattering calculations in the oscillator representation. J. Computat. Phys. 234, 60 (2013).

https://doi.org/10.1016/j.jcp.2012.09.018

Downloads

Published

2021-04-07

How to Cite

Prikhodko, O., & Bidasyuk, Y. (2021). Projected Gross–Pitaevskii Equation for Ring-Shaped Bose–Einstein Condensates. Ukrainian Journal of Physics, 66(3), 198. https://doi.org/10.15407/ujpe66.3.198

Issue

Section

Optics, atoms and molecules