Abstract
This paper predicts a spontaneous symmetry breaking in the time evolution of a mesoscopic condensate with degenerate internal degrees of freedom, driven by a coherent atom beam. Both entanglement entropy and the statistical entropy peak at the critical time when the spontaneous symmetry breaking takes place. The condensate approaches a steady state that is dictated by the incident atom beam, providing a way to control the distribution of internal degrees of freedom.
Highlights
There are nine possible scattering channels that correspond to |wσμ = |μ a|sσ, m c for σ = 0, ±1 and μ = 0, ±1, and m = mi + μi − μ due to the conservation of the spin component
The second term in the square bracket of (B5) involves terms that are generated by contractions of cμ with all the creation operators on its right side as well as terms due to the analogues left contractions of cμ+i
(B6)–(B8), we obtain the general expression for the matrix elements c sσ, m|cμ+i cμ|s, mi c
Summary
After a sufficiently long time, the condensate will choose one of two fullyordered states by incident, the spin-reversal symmetry is broken. We obtained the time-dependent: spin distribution of the condensate, magnetization, magnetization fluctuation, statistical and entanglement entropies, and total entropy production rate. It is found that the steady states of the condensate do not depend on the initial state of the condensate but are determined by the incident atom state This provides a possible way to prepare various spin distributions of the condensate, which are neither uniform nor Boltzmann-like distributions, by choosing suitable incident states. A novel spontaneous spin symmetry breaking phenomenon is found in the condensate evolution with the initial magnetization quantum number being zero and the incident atom state being a symmetric coherent superposition of. The phase-transition-like symmetry breaking accompanied with the bifurcation of spin distribution emerges at a mesoscopic time of about twice the atom number of the condensate. Our study can be generalized to the reverse case of td > ts
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