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The European Physical Journal D

Soliton dynamics for an ingenious trap combination in a Bose-Einstein condensate

Ajay Nath, Jayanta Bera, Suranjana Ghosh, Prasanta Kumar Panigrahi, Utpal Roy

Published Feb 1, 2020• 13 citations
Publisher
DOI
10.1140/epjd/e2019-100103-y

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•Mar 5, 2021•0 citations
We explore the energy dynamics of a two dimensional (2D) trapped Bose-Einstein condensate (BEC) excited by a moving red-detuned laser potential (RDLP). The trap is a combination of a power-law (PL) potential cutoff by a hard-wall box potential (HWBP). It is found that by a restricted measurment of the energy within the boundaries of the HWBP, the energy demonstrates oscillations indicative of solitons. It is then demonstrated, that the geometry of the PL potential influences the lifetime of these oscillations, i.e., the lifetime of the ensuing solitons inside the HWBP. We argue that the energy dynamics in this setup are a good tool for measuring their lifetime. It is also found, that the condensate density dynamics display oscillatory patterns of a magnitude and order controlled by the velocity of the RDLP. A connection to oscillations in the chemical potential dynamics is also discussed. Essentially, we suggest future experiments for this kind of setup, which would measure the phonon energy dynamics to trace the lifetime of solitons.
A model of the perturbed complex Toda chain (PCTC) to describe the dynamics of a Bose–Einstein condensate (BEC) N-soliton train trapped in an applied combined external potential consisting of both a weak harmonic and tilted periodic component is first developed. Using the developed theory, the BEC N-soliton train dynamics is shown to be well approximated by 4N coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude, velocity, centre-of-mass position, and phase. The simplified analytic theory allows for an efficient and convenient method for characterizing the BEC N-soliton train behaviour. It further gives the critical values of the strength of the potential for which one or more localized states can be extracted from a soliton train and demonstrates that the BEC N-soliton train can move selectively from one lattice site to another by simply manipulating the strength of the potential.
We present a method to detect the presence and depth of dark solitons within repulsive one-dimensional harmonically trapped Bose-Einstein condensates. For a system with one soliton, we provide numerical evidence that the shift of the density in Fourier space directly maps onto the depth of the soliton. For multi-soliton systems, combining our spectral method with established imaging techniques, the character of the solitons present in the condensate can be determined. We verify that the detection of solitons by the spectral shift works in the presence of waves induced by density engineering methods. Finally we discuss implications for vortex detection in three-dimensional Bose-Einstein condensates.