Spin symmetry breaking and entropy production during the evolution of spinor Bose-Einstein condensate driven by coherent atom beam

The spinor condensate with spin states degenerated in the ground spin-space provides a unique platform for investigating the edge of quantum mechanics and statistical physics. We study the evolution of the condensate under the scattering of a coherent atom beam. The time-dependent magnetization, entanglement entropy, statistical entropy, and the entropy production rate are calculated. A novel spontaneous spin symmetry breaking is found during the evolution. It is shown that the stationary spin distribution can be controlled by the coherent spin state of the incident atom beam, therefore the atom-condensate scattering provides a new way to generate designable spin distributions of the condensate.

Figure 1

The time-dependent spin distributions of spin-1 condensate from initial distributions: (a) ${\lambda }_m\left(0\right)={\delta }_{m,-N}$, (b) ${}_{}\frac{1}{2N+1}$, and (c) ${\delta }_{m,N}$, respectively. The condensate is scattered by the same species of atoms with incident state ${|0\rangle }_a$. The axes $m/N$ is the magnetization quantum number per atom. The time $t_n=n$ is in the unit of times of scattering. Here, $N=100$ is used for an instance.

Figure 2

The steady spin distributions for spin-1 condensate of $N=100$ spinors under the scattering of the atom beam with incident states $\frac{1}{\sqrt{2}}{\left(\right|0\rangle }_a{+cos\theta |-1\rangle }_a+{sin\theta |1\rangle }_a)$. Curves (a), (b), (c), (d), and (e) correspond to $\theta =0,\frac{\pi }{6},\frac{\pi }{4},\frac{\pi }{3},\text{and}\frac{\pi }{2}$, respectively. The inset is the half-width of the distribution (c) for $N\le {10}^3$.

Figure 3

The spin-1 condensate of $N=100$ is scattered from the nonpolarized initial spin distribution ${\lambda }_m\left(0\right)={\delta }_{m,0}$ by the same species of atoms in the incident state $|{\xi }^{0y}{\rangle }_a=\frac{1}{\sqrt{2}}{\left(\right|-1\rangle }_a+{|1\rangle }_a)$. In the lower panel, the curves are the time-dependent magnetization fluctuation (blue dash-dotted), the statistical entropy divided by $ln(2N+1)$ (orange long-dashed), the entanglement entropy (black short-dashed), and the entropy production rate (red solid). The upper panel is the time-dependent spin distribution.