Effects of three-body interactions on the instabilities and self-oscillations of the four-wave mixing in Bose–Einstein condensates

Abstract

In this paper, we analyze and discuss instabilities and self-oscillations of four-wave mixing in two-component Bose–Einstein condensates with two- and three-body interatomic interactions. The model is very accurately described in the mean-field approximation by the cubic–quintic Gross–Pitaevskii equation. The relation between the input and output field intensities is multivalued and the effects of the quintic nonlinearity on the self-oscillations of the system are studied. We have also found that the magnitude of the signal beam increases with the increase of the intensity of the probe beam, up to a saturated value, then it decreases with the increase of the intensity of the probe beam. We have shown that the three-body interatomic interactions enhance this saturated value.

Modulation instability induced by four coupled of matter waves with two-and three-body interactions

“…Our basic model which has already been used [50,51] is the coupled GP equations in the presence of two-and three-body interatomic interactions and has the following form…”

“…Experiments have been achieved by adjusting the axial frequency much smaller than the radial frequency by which motion is also strongly confined. To get the uni-dimensional coupled GP equations, we follow Ngounga Makoundit et al, [50]. We then use a separable ansatz, ( )…”

“…, the coupled Gross-Pitaevskii equations are 1) and (2) with the SVEA, we have obtained [50] where the indices j and l are different and take the values 1 and 2, with β j , β l the fractions of the intensities g j and g l , i.e., χ j = β j g j , χ l = β l g l , such that |β j | 1 and |β l | 1. The functions f jf , f lf and f jb , f lb represent respectively the forward and backward propagating beams of matter waves, the superscript ' * ' indicates the complex conjugate.…”

Nonlinear speed-ups in ultracold quantum gases

“…However, it has been noted [66] that in some situations the description of Bose systems requires a fundamental modification. This is, in particular, the case when accounting for three particles interactions [67][68][69]. Such scenarios are better described by…”