Dynamics of Bec Mixtures Loaded into the Optical Lattice in the Presence of Linear Inter-Component Coupling

Abstract

We consider dynamics of a two-component Bose-Einstein condensate where the components correspond to different hyperfine states of the same sort of atoms. External microwave radiation leads to resonant transitions between the states. The condensate is loaded into the optical lattice. We invoke the tightbinding approximation and examine the interplay of spatial and internal dynamics of the mixture. It is shown that internal dynamics qualitatively depends on the intra-component interaction strength and the phase configuration of the initial state. We focus attention on two intriguing phenomena occurring for certain parameter values. The first phenomenon is the spontaneous synchronization of Rabi oscillations running inside neighbouring lattice sites. Another one is the demixing of the condensate with formation of immiscible solitons when nonlinearity becomes sufficiently strong. Demixing is preceded by the transient regime with highly irregular behavior of the mixture.

Chaos-assisted formation of immiscible matter-wave solitons and self-stabilization in the binary discrete nonlinear Schrödinger equation

“…As in Ref. [10], we assume that the interaction between atoms belonging to different hyperfine states is weak and can be neglected, g 12 = g 21 = 0. Indeed, both intra-species and inter-species scattering lengths can be readily tuned in experiments by means of the Feshbach resonance [16,17], that is, one has some freedom in choosing their values.…”

“…This suggest that such solitons should be well spatially separated (in order to reduce the kinetic energy) and consist of only one species (to reduce the Rabi energy). Results of [10] indicate that solitons of this kind can arise spontaneously, provided wavepacket spreading is weak.…”

“…Under certain conditions, their formation can be studied within the variational approach that relies upon a priori assumptions about the wavepacket form in course of its evolution [9]. However, as it was found in a recent work [10], solitons in the binary DNLSE can arise spontaneously after a transient regime of highly irregular dynamics, when the variational approach doesn't apply. A distinctive feature of such solitons is that they consist of only one species and well separated from each other.…”

Zitterbewegung with spin–orbit coupled ultracold atoms in a fluctuating optical lattice

“…The case of χ n = 0 (25) corresponds to onset of resonance in Eqs. (15), when c n1 = c n2 = −c n3 = c n4 = 1/2, therefore, α n and β n+l oscillate with frequency Ω/2.…”

“…Further we omit the subscript n. From Eq. (29) it is clear that quantityΩ stands for effective Rabi frequency taking into account momentum-dependent detuning from the resonance (25).…”