Topological classification of quasiperiodically driven quantum systems
Topological classification of quasiperiodically driven quantum systems
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DOI：
10.1103/physrevb.99.064306
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发表时间：
2018-08
影响因子：
3.7
通讯作者：
P. Crowley;I. Martin;A. Chandran
中科院分区：
文献类型：
--
作者：
P. Crowley;I. Martin;A. Chandran
由无公度基频驱动的少数能级量子系统在空间维度上呈现出非相互作用现象的时间相似，这是Floquet理论在频率空间中推广的结果。我们将n=2的频率格子模型的基本解组织成一个准能带结构，并证明每个能带由一个整数陈数来分类。在平凡类中，所有的带都具有零的陈数，并且准周期动力学定性地类似于Floquet动力学。具有非零Chern带的拓扑类具有显著的动力学特征，包括从一个驱动器到另一个驱动器的能量泵浦，对初始条件的混沌敏感性，以及期望值的非周期时间动力学。然而，由于准能谱中的精确能级交叉，拓扑类对一般微扰是不稳定的。然而，通过对准周期变化磁场中自旋的研究，我们证明了拓扑类可以在低频实现为预热相，在有限频率可以用反非绝热工具实现。
Few level quantum systems driven by $n_\mathrm{f}$ incommensurate fundamental frequencies exhibit temporal analogues of non-interacting phenomena in $n_\mathrm{f}$ spatial dimensions, a consequence of the generalisation of Floquet theory in frequency space. We organise the fundamental solutions of the frequency lattice model for $n_\mathrm{f}=2$ into a quasi-energy band structure and show that every band is classified by an integer Chern number. In the trivial class, all bands have zero Chern number and the quasi-periodic dynamics is qualitatively similar to Floquet dynamics. The topological class with non-zero Chern bands has dramatic dynamical signatures, including the pumping of energy from one drive to the other, chaotic sensitivity to initial conditions, and aperiodic time dynamics of expectation values. The topological class is however unstable to generic perturbations due to exact level crossings in the quasi-energy spectrum. Nevertheless, using the case study of a spin in a quasi-periodically varying magnetic field, we show that topological class can be realised at low frequencies as a pre-thermal phase, and at finite frequencies using counter-diabatic tools.