Abstract
We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. Based on the Gross-Pitaevskii equation model and variational method, we derive the original analytical formula for the criteria and lifetime of the formation of the sonic horizon, demonstrating pictorially the interaction parameter dependence for the occur- rence of the sonic horizon and damping effect of the system distribution width. Our analytical results corroborate quantitatively the particular features of the sonic horizon reported in previous numerical study.
Highlights
We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential
The nonlinear phenomena, like soliton, vortex formation and evolution in the Bose-Einstein condensation (BEC) system are the hot topics within the past decade in BEC related studies[1,2,3,4,5,6,7]
Experimental demonstration of sonic black holes[14] and Hawking radiation[15] had been realized by accelerating an elongated condensate in a step like potential. It is shown by numerical study[16] that for a static ground state BEC system trapped in isotropic harmonic potential, when there is abrupt change of scattering length via Feshbach resonance technique, the system will expand/contract with time and under certain parametric setting there exists sonic horizon which is the spherical surface outside which the fluid flow speed surpass that of sound
Summary
We study the sonic horizon phenomena of the oscillating Bose-Einstein condensates in isotropic harmonic potential. The corresponding ultracold fluid analog is sonic horizon, when identifying the fluid flow with curved spacetime and excitation mode with curved spacetime fields Due to their ultracold temperature and well isolation, trapped Bose-Einstein condensates were proposed as promising candidates for observing sonic black holes and Hawking radiation[13]. Experimental demonstration of sonic black holes[14] and Hawking radiation[15] had been realized by accelerating an elongated condensate in a step like potential It is shown by numerical study[16] that for a static ground state BEC system trapped in isotropic harmonic potential, when there is abrupt change of scattering length via Feshbach resonance technique, the system will expand/contract with time and under certain parametric setting there exists sonic horizon which is the spherical surface outside which the fluid flow speed surpass that of sound.
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