Coherent state approach to the cross-collisional effects in the population dynamics of a two-mode Bose–Einstein condensate

Abstract

We reanalyze the non-linear population dynamics of a Bose-Einstein Condensate (BEC) in a double well trap considering a semiclassical approach based on a time dependent variational principle applied to coherent states associated to SU(2) group. Employing a two-mode local approximation and hard sphere type interaction, we show in the Schwinger's pseudo-spin language the occurrence of a fixed point bifurcation that originates a separatrix of motion on a sphere. This separatrix corresponds to the borderline between two dynamical regimes of Josephson oscillations and mesoscopic self-trapping. We also consider the effects of interaction between particles in different wells, known as cross collisions. Such terms are usually neglected for traps sufficiently far apart, but recently it has been shown that they contribute to the effective tunneling constant with a factor growing linearly with the particle number. This effect changes considerably the effective tunneling of the system for sufficiently large number of trapped atoms, in perfect accord with experimental data. Finally, we identify analytically the transition parameter associated to the bifurcation in the generalized phase space of the model with cross-collision terms, and show how the dynamical regime depends on the initial conditions of the system and the collisional parameters values.

Phase transition, entanglement and squeezing in a triple-well condensate

“…Several dynamical processes can be responsible for the loss of purity of an initially coherent state. One of such processes is the squeezing of the state, and it is related to regular dynamical regimes of the semiclassical model [20]. In the semiclassical approximation we also observe chaos [19] in the three mode model, accompanied by other processes of purity loss.…”

“…Many of the fixed points of the semiclassical dynamics are contained in this subregime under the additional condition of φ 1 , φ 2 = 0, π, which implies that w ∈ R 2 . Without loss of generality, we choose only the condition w = w 1 = w 2 ∈ R, so that the SU (3) coherent states reduce to coherent states of SU (2), which thus brings many features observed for a two mode condensate, such as the Rabi Oscillation (RO) of population and the macroscopic self-trapping (MST) of population [20]. The phase space associated with the integrable sub-regime of twin condensates is isomorphic to S 2 , a space that parametrizes the set of SU (2) coherent states |J = The point w 1 = w 2 = 1 is a solution of the fixed point equations, independent of the values of χ and µ, which we call 1 + .…”

“…This same characteristic has been observed in the two local modes model [24], but with some important differences. The two-mode model presents a second order QPT, accompanied by a pitchfork bifurcation with critical parameter equal to the critical parameter χ [20], in the absence of cross-collisions. However, in both models the equilibrium point that minimizes the semiclassical energy H can be described by a single angle θ on S 2 , considered as a function of χ.…”

Pathway toward the formation of supermixed states in ultracold boson mixtures loaded in ring lattices

“…In conclusion, we note that the methodology on which our analysis relies, together with the classical and quantum indicators used to detect critical phenomena, can be easily applied to systems with more complex lattice topologies, interactions and tunnelling processes [34][35][36][37][38]. In view of this, and considering the increasing interest for multicomponent condensates [39][40][41][42], our future work will aim to extend the presented analysis to the soliton formation's mechanism in complex lattices and in presence of multiple condensed species.…”

Fisher-information manifestation of dynamical stability and transition to self-trapping for Bose-Einstein condensates

“…In the system, the total particle number N =â † 1â 1 +â † 2â 2 is a conserved quantity. To obtain the classical dynamics approach, we choose a generalized coherent spin state (CSS) as an initial state, which is defined formally as [43][44][45] |θ…”