论文标题
时间依赖性变异蒙特卡洛研究玻色子在光学晶格中的动态反应
Time-dependent variational Monte Carlo study of the dynamic response of bosons in an optical lattice
论文作者
论文摘要
我们通过监测对弱探针脉冲的线性响应来研究单位填充的一维玻色气体的动力学，并获得动态结构因子$ {s（k，ω）} $。我们基于时间依赖性变异蒙特卡洛方法（TVMC）引入了一个新过程，该方法允许实时进化系统，用作变分模型jastrow-feenberg波函数，其中包含配对相关。与在Bose-Hubbard限制中的晶格上获得的$ {S（K，ω）} $的确切对角度结果的比较，显示出足够深的光学晶格的分散关系的良好一致，而对于浅层晶格，我们观察到了较高的Bloch带的影响。我们还研究了对强脉冲的非线性反应。从密度波动的功率谱中，我们获得了激发频谱，尽管在具有单个低波数的强脉冲后，通过更高的谐波产生扩大了激发光谱。作为模拟的非凡特征，我们进一步表明，由于任何蒙特卡洛方法中固有的随机噪声而无需应用实际的扰动，因此可以从密度波动的功率谱中检索到完整的激发光谱。
We study the dynamics of a one-dimensional Bose gas at unit filling in both shallow and deep optical lattices and obtain the dynamic structure factor ${S(k,ω)}$ by monitoring the linear response to a weak probe pulse. We introduce a new procedure, based on the time-dependent variational Monte Carlo method (tVMC), which allows to evolve the system in real time, using as a variational model a Jastrow-Feenberg wave function that includes pair correlations. Comparison with exact diagonalization results of ${S(k,ω)}$ obtained on a lattice in the Bose-Hubbard limit shows good agreement of the dispersion relation for sufficiently deep optical lattices, while for shallow lattices we observe the influence of higher Bloch bands. We also investigate non-linear response to strong pulses. From the power spectrum of the density fluctuations we obtain the excitation spectrum, albeit broadened, by higher harmonic generation after a strong pulse with a single low wave number. As a remarkable feature of our simulations we furthermore demonstrate that the full excitation spectrum can be retrieved from the power spectrum of the density fluctuations due to the stochastic noise inherent in any Monte Carlo method, without applying an actual perturbation.
