Universality and Anomalous Mean-Field Breakdown of Symmetry-Breaking Transitions in a Coupled Two-Component Bose-Einstein Condensate

We study both mean-field and full quantum dynamics of symmetry-breaking transitions (SBTs) in a coupled two-component Bose-Einstein condensate. By controlling $s$-wave scattering lengths and the coupling strength, it is possible to stimulate SBTs between normal and spontaneously polarized ground states. In static transitions, the probability maxima of full quantum ground states correspond to the mean-field ground states. In dynamical transitions, due to the vanishing of excitation gaps, the mean-field dynamics shows universal scalings obeying the Kibble-Zurek mechanism. Both mean-field and full quantum defect modes appear as damped oscillations, but they appear at different critical points and undergo different oscillation regimes. The anomalous breakdown of mean-field dynamics induced by SBTs depends on the approaching direction.

Figure 1

The MF-FQ correspondence for static SBTs in a coupled two-component condensate of $N=100$ and negative $E_C$. The FQ states are defined as $|\Psi ⟩=\sum _{l=-L}^{L}C(l)|l⟩$ and the probability distributions $|C(l){|}^2$ versus $\Omega /E_C$ for the ground (first-excited) states are shown in the above (bottom) panel. The solid and dashed lines are stable and unstable MF stationary states, respectively.

Figure 2

The MF dynamics of SBTs in Hamiltonian (2). (a) The ${\tau }_t$ and ${\tau }_r$, (b) the longitudinal polarization $(N_{\uparrow }-N_{\downarrow })/2$, and (c) the fidelity to instantaneous ground states versus $\Omega /E_C$ for different values of $\beta$. Parameters are chosen as $N=100$, $G_{\downarrow \downarrow }=G_{\uparrow \uparrow }=1.0$, $G_{\uparrow \downarrow }=2.0$, and $E_{0\downarrow }=E_{0\uparrow }$. So that, $E_C=-2.0$ and $\Delta =0$.

Figure 3

The energy spectrum and FQ dynamics of SBTs shown in Fig. 2. (a) Energy spectrum of four lowest states of Hamiltonian (1), (b) and (c) quantum expectations of the longitudinal polarization $⟨N_{\uparrow }-N_{\downarrow }⟩/2$.