Figure 1

(a) Potential $\mathcal{V}$ for several values of $\gamma$ and zero bias ($\epsilon =0$). (b) Separation between the two minima (solid black) and height of the barrier as functions of $\gamma$ (dashed red), also in the case of zero bias.Reuse & Permissions

Figure 2

Potential $\mathcal{V}$ (solid black) compared to the three parabolas used to approximate it near its extrema in building the analytical model. $N=50$, $\gamma =-2.1$.Reuse & Permissions

Figure 3

Ground-state energies of Eq. (12) (solid black), compared to the approximate ones given by Eq. (16) (dashed red), for $N=$ 20, 50, and 90, respectively.Reuse & Permissions

Figure 4

(a) Different ground-state properties predicted by the analytic model for three different regimes, separated by blue dotted lines. The three regions correspond to the bias-dominated fully condensed (i), transition asymmetric catlike (ii), and symmetric catlike (iii) states. We depict the behavior of $-\langle z\rangle {}_{\mathrm{g}.\mathrm{s}.}$ (black solid line), and ${\sigma }_z$ (black dashed line) as functions of $\gamma$. $z_m$ is shown in as a thin blue line. The overlap $\langle \mathcal{L}|\mathcal{R}\rangle$ is the black dot-dashed line. (b) Condensed fractions $n_{\pm }$ (upper and lower black solid lines) and the mixing angle $\theta /2$ of the ${\phi }_{+}$ eigenvector [see Eq. (26)] of the one-body density matrix associated with the ground state of the two-mode model. (c) Energy splitting between the symmetric and antisymmetric (ground and first excited) states. The solid black line is calculated with Eq. (22). The blue empty circles are the exact numerical result obtained by solving Eq. (12). Red dot-dashed and red dashed lines depict $2t$ and $\varepsilon z_m$, respectively. In all cases $\varepsilon =-0.0002$ and $N=50$. (d), (e), and (f): $|\psi (z)|{}^2$ computed with the two-mode model for $\gamma =-1.6,-1.4,$ and $-1.2,$ respectively.Reuse & Permissions