A bosonic bright soliton in a mixture of repulsive Bose–Einstein condensate and polarized ultracold fermions under the influence of pressure evolution

Abstract

Repulsive Bose-Einstein condensates, where short-range interaction is included up to the third order by the interaction radius, demonstrate the existence of bright solitons in a narrow interval of parameters. These solitons are studied here for the boson-fermion mixture, where spin-1/2 fermions are considered in the regime of full-spin polarization. The influence of fermions on bosonic bright solitons via the boson-fermion interaction is considered up to the third order by the interaction radius. Fermions themselves are considered within the hydrodynamic model, which includes the kinetic pressure-evolution equation. The interactions between fermions are also considered. The first order by the interaction radius makes a zero contribution to the Euler equation and the kinetic pressure evolution equation for fermions, but the third order by the interaction radius provides nonzero contributions to both equations. The repulsive (attractive) boson-fermion interaction leads to bright (dark) fermionic solitons.

Grey solitons in the ultracold fermions at the full spin polarization

“…Hence, there is no direct relation between the grey soliton given here and the fermion part of the relation demonstrated in Ref. [49]. obtained from the expression (15) derived up to the TOIR approximation can be written in the following form 4) presents the Sagdeev potential for the same values of the interaction constant, but it is obtained for the larger velocity α = 0.1.…”

“…Particularly, the boson-fermion mixture of the spin-0 BEC and spin-polarized spin-1/2 fermions is considered in Ref. [49], where focus is made on the modification of properties of the beyond mean-field bright soliton existing in the repulsive BECs under influence of the fermions. Hence, there is no direct relation between the grey soliton given here and the fermion part of the relation demonstrated in Ref.…”

Quantum hydrodynamics of the spinor Bose-Einstein condensate at non-zero temperatures

“…Variety of waves phenomena is observed in BECs. It includes the density waves [19], [20], [21] solitons [22], [23], [24], vortices [25], turbulence, shock waves [26], [27]. Collective excitations are considered in Fermi gas either [28].…”

“…For the many-particle wave function we have 3N dimensional configurational space. Moreover, the spin part of the wave function is the direct product of N columns of three component each (23). Here, we can express the amplitude a(R, t) and phase S(R, t)…”

Hydrodynamic model of skyrmions and vorticities in the spin-1 Bose-Einstein condensate in ferromagnetic phase at finite temperatures

“…Majority of papers on the ultracold bosons, bosonfermion and boson-boson mixtures are focused on the zero temperature regime [13], [14], [15], [16], [17], [18], [19], [20], [21], [22]. However, the number of work including the finite temperature effects in quantum gases [23], [24], [25], [26], [27], [28], [29].…”