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非平衡一维 Tonks-Girardeau 气体的单粒子密度矩阵与动量分布：大 $N$ 下的解析结果

One-particle density matrix and momentum distribution of the out-of-equilibrium 1D Tonks-Girardeau gas: Analytical results at large $N$

Stefano Scopa, Paola Ruggiero, Pasquale Calabrese, Jerôme Dubail

备注：
13pages, 6 figures. v2: minor changes; v3: fixed layout issues in appendices
发表信息：
Phys. Rev. A 108, 013324 (2023)
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AI总结：

针对零温非平衡一维 Tonks-Girardeau 气体，推导出大 $N$ 极限下精确的单粒子密度矩阵解析公式，可高精度计算动量分布，并预测了双阱到单阱 quench 下多峰动量分布的周期性形成。

摘要：

在一维（1D）量子气体中，原子的动量分布（MD）是一种标准的实验可观测量，在各种实验装置中常规测量。MD 对关联效应敏感，且在理论上对于大量原子 $N$ 的计算极其困难，这通常阻碍了与实验数据的直接比较。在此，我们针对大 $N$ 渐近极限下的一维 Tonks-Girardeau（TG）气体报告了该问题的重大进展，系统处于零温度，并通过 confinement potential 的 quench 驱动至非平衡态。我们找到了非平衡 TG 气体在 $N \rightarrow \infty$ 极限下单粒子密度矩阵 $\langle \hatΨ^\dagger(x) \hatΨ(x') \rangle$ 的精确解析公式，适用于距离 $|x-x'|$ 远大于粒子间距的情况。通过与含时 Bose-Fermi 映射数值计算进行对比，我们证明该解析公式能够以极高的精度计算出宽泛动量范围内的非平衡 MD（分布中极高端的尾部除外）。对于从双阱势到单一谐振势的 quench（模拟“量子牛顿摆”装置），我们的方法预测了奇特的多峰动量分布的周期性形成。

英文摘要：

In one-dimensional (1D) quantum gases, the momentum distribution (MD) of the atoms is a standard experimental observable, routinely measured in various experimental setups. The MD is sensitive to correlations, and it is notoriously hard to compute theoretically for large numbers of atoms $N$, which often prevents direct comparison with experimental data. Here we report significant progress on this problem for the 1D Tonks-Girardeau (TG) gas in the asymptotic limit of large $N$, at zero temperature and driven out of equilibrium by a quench of the confining potential. We find an exact analytical formula for the one-particle density matrix $\langle \hatΨ^\dagger(x) \hatΨ(x') \rangle$ of the out-of-equilibrium TG gas in the $N \rightarrow \infty$ limit, valid on distances $|x-x'| $ much larger than the interparticle distance. By comparing with time-dependent Bose-Fermi mapping numerics, we demonstrate that our analytical formula can be used to compute the out-of-equilibrium MD with great accuracy for a wide range of momenta (except in the tails of the distribution at very large momenta). For a quench from a double-well potential to a single harmonic well,which mimics a `quantum Newton cradle' setup, our method predicts the periodic formation of peculiar, multiply peaked, momentum distributions.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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