环形囚禁离子和中性原子的试探波函数：量子时空晶体的微观描述
Trial wave functions for ring-trapped ions and neutral atoms: Microscopic description of the quantum space-time crystal
摘要：
描述量子时空晶体的一个建设性的理论平台揭示了$N$相互作用和环限制旋转粒子的存在与适当的时空晶体行为的低躺状态。相应的多体试验波函数的建设收益首先通过对称性破缺的平均场水平，然后使用投影技术的对称性恢复。由此产生的关联多体波函数是定态的，保持了转动对称性，同时反映了平均场晶体的点群对称性。这一行为导致了选择幻角动量序列$L_m$的出现。当角动量远离魔值时，试函数消失。这种良好的- $L_m$多体定态的叠加可以导致对称性破缺。我们发现，叠加一对相邻的魔角动量态导致形成特殊的破缺对称态，表现出量子时空晶体行为。特别是，相应的粒子密度围绕环旋转，显示无阻尼和非分散的周期性晶体演化的空间和时间。这种量子时空晶体波包的实验合成预测将有利于通过外部施加的磁场访问的Aharonov-Bohm型光谱的基态能量交叉附近。这些结果在这里说明库仑排斥费米子离子和一个块的接触相互作用吸引玻色子。
英文摘要：
A constructive theoretical platform for the description of quantum space-time crystals uncovers for $N$ interacting and ring-confined rotating particles the existence of low-lying states with proper space-time crystal behavior. The construction of the corresponding many-body trial wave functions proceeds first via symmetry breaking at the mean-field level followed by symmetry restoration using projection techniques. The ensuing correlated many-body wave functions are stationary states and preserve the rotational symmetries, and at the same time they reflect the point-group symmetries of the mean-field crystals. This behavior results in the emergence of sequences of select magic angular momenta $L_m$. For angular-momenta away from the magic values, the trial functions vanish. Symmetry breaking beyond mean field can be induced by superpositions of such good-$L_m$ many-body stationary states. We show that superposing a pair of adjacent magic angular momenta states leads to formation of special broken-symmetry states exhibiting quantum space-time-crystal behavior. In particular, the corresponding particle densities rotate around the ring, showing undamped and nondispersed periodic crystalline evolution in both space and time. The experimental synthesis of such quantum space-time-crystal wave packets is predicted to be favored in the vicinity of ground-state energy crossings of the Aharonov-Bohm-type spectra accessed via an externally applied magnetic field. These results are illustrated here for Coulomb-repelling fermionic ions and for a lump of contact-interaction attracting bosons.
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