Rabi-induced localization and resonant delocalization of a binary condensate in a spin-asymmetric quasiperiodic potential

Abstract

We theoretically investigate the ground state and dynamics of a Rabi-coupled pseudospin-1/2 Bose-Einstein condensate, where only one spin component is subjected to an external potential. We show that in the quasiperiodic potential the Rabi coupling induces localization between the components as it is raised above the threshold value. Interestingly, the localization is mutually induced by both components for the quasiperiodic confinement, whereas for a harmonic trap the localization is induced in the potential-free component by interaction with that confined in the potential. Further, we explore the condensate dynamics by implementing a periodic driving of the Rabi frequency, where various frequency-dependent delocalization patterns, such as double (triple)-minima, tree-(parquet)-like, and frozen distributions with a correlated propagation of different spin populations are observed in the condensate density. These features pave the way to control the condensate mass and spin density patterns, both in the stationary and dynamical realizations.

Figures (16)

• Figure 1: The BEC density $|\psi_{\uparrow(\downarrow)}|^2$ for different values of Rabi coupling $\Omega_0$: (a) $\Omega_0 = 0.08$, (b) $\Omega_0 = 0.2$, (c) $\Omega_0 = 0.4$, and (d) $\Omega_0 = 0.6.$ Increasing $\Omega_0$ equalizes the spin-up and spin-down profiles. In the insets of (b)-(d), the density is plotted on a semilogarithmic scale to highlight the exponential and Gaussian behavior of the localized condensate, as it depends on $\Omega_0$. Here, all the interactions $g_{\uparrow\uparrow} = g_{\downarrow\downarrow} = 0$.
• Figure 2: (a) Variation of population $N_{\uparrow (\downarrow)}$, (b) width $w_{\uparrow(\downarrow)}$, (c) IPR $\chi_{\uparrow(\downarrow)}$ and (d) chemical potential $\mu$ as a function of $\Omega_0$ at $V_2/V_1 = 0.5, V_1 = 1.0, g = 0$. Here, the solid and dashed lines represent the entities obtained with the matrix method. The quantities obtained by the ITP method are shown by markers. Increase in $\Omega_0$ results in transfer of probability from $\downarrow$ to $\uparrow$ component. The increasing IPR indicates that the spin-down and spin-up components are tending to localize with the same profile due to the Rabi coupling, while spin-up is originally localized by the $V_{\uparrow}(x)$ potential.
• Figure 3: Variation of different energies defined by Eqs.\ref{['eq:Epot']}-\ref{['eq:EOmega']} as a function of Rabi coupling $\Omega_0$ at $V_2/V_1 = 0.5, V_1 = 1.0.$ As $\Omega_0$ increases, the ratio of potential $E_{\rm pot}$ and kinetic $E_{k}$ energies approximately saturates toward $\sim 0.85,$ as shown in the inset, while the dominating negative $E_{\Omega}$ minimizes the total energy $E=E_{\rm pot}+E_{k}+E_{\Omega}.$ The black dotted line is presented to highlight the behavior of $E_\Omega \propto -\Omega_0.$
• Figure 4: The condensate density $|\psi_{\uparrow(\downarrow)}|^2$ for different self-interaction strengths: (a) $g = 0.1$, (b) $g = 0.3$, (c) $g = 0.4$, and (d) $g = 0.5.$ Increasing the repulsive interaction causes the condensate to break into multiple fragments, forming several peaks at potential minima located at $x \neq 0$. The other parameters are kept as follows: $V_1 = 1.0$, $V_2 = 0.5$, $k_1 = 0.35$, $k_2/k_1 = (\sqrt{5}-1)/2$, and $\Omega_0 = 0.3.$
• Figure 5: Pseudo-colormap representation of the condensate densities $|\psi_{\uparrow}|^2$ (upper panel) and $|\psi_{\downarrow}|^2$ (lower panel) in the $(t,x)$ plane for different frequencies $\omega_{\rm osc}$: (a1, b1) $\omega_{\rm osc} = 0.1$, (a2, b2) $\omega_{\rm osc} = 0.2$, (a3, b3) $\omega_{\rm osc} = 0.4$, (a4, b4) $\omega_{\rm osc} = 0.8$, and (a5, b5) $\omega_{\rm osc} = 1.0$. For $\omega_{\rm osc} = 0.2$ (a2, b2) and $\omega_{\rm osc} = 0.8$ (a4, b4), the density expands. However, the expansion dynamics for $\omega_{\rm osc} = 0.8$ differ from those at $\omega_{\rm osc} = 0.2.$ Specifically, at $\omega_{\rm osc} = 0.8$, the density $|\psi_{\uparrow(\downarrow)}|^2$ eventually settles at different potential minima (a4, b4), whereas for $\omega_{\rm osc} = 0.2$ (a2, b2), it expands by emitting jets with a nearly uniform velocity. For other $\omega_{\rm osc}$, the condensate remained localized around $x = 0.$ The other parameters are $\Omega_0 = 0.4$, $\Omega_1 = 0.2$, and $g = 0.$ Panels (a1) and (b1) correspond to double (triple)- minima evolution, panels (a2), (b2) and (a4),(b4) show tree-like patterns while panels (a3),(b3) and (a5),(b5) correspond to a "frozen" behavior.