We find a different mechanism for suppression of decay in an open one-dimensional lattice system, which originates from a dark Floquet state, a sink state to which the system is asymptotically driven, whose overall probability is determined only by the parameters of the periodic driving field. The zero-quasienergy of dark Floquet state is shown to be not a real zero, but a vanishingly small negative imaginary number which will cause undesirable physical effect in long-time evolution of quantum states, being extremely different from the conservative counterpart. Another intriguing finding is that the value of the system’s effective decay, determined by the size of the non-zero imaginary part of the dark-Floquet-state-related quasienergy, depends not on how many localized lossy sites there are but on which one of the lossy sites is nearest to the driven site. Thus, for specially designed local dissipation, by controlling the driving parameters, it is possible for us to drive the system to a dark Floquet state with a much lower level of overall probability loss as compared to the undriven case and with good stability over enough longer evolution time. These results are applicable to the multisite lattice system with an odd number of sites and may be significant for long-time control of decay in a vast family of multistate physical systems with localized dissipation.

中文翻译：

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周期驱动晶格阵列中耗散动力学的相干控制

我们发现了一种不同的机制来抑制开放的一维晶格系统中的衰变，该机制源自黑暗的Floquet状态（系统渐近驱动到的沉状态），其总概率仅由周期性驱动的参数确定领域。暗浮球状态的零准能量不是真正的零，而是逐渐消失的负虚数，这将在量子态的长时间演化中引起不良的物理效应，与保守的对应极不同。另一个有趣的发现是，系统有效衰减的值取决于与暗浮子状态有关的拟能的非零虚部的大小，取决于有多少个本地有损站点，而是取决于哪个有损站点最靠近驱动站点。因此，对于特殊设计的局部耗散，通过控制驱动参数，我们有可能将系统驱动到暗浮球状态，与无驱情况相比，总概率损失要低得多，并且在足够长的时间内具有良好的稳定性进化时间。这些结果适用于具有奇数个位点的多位点晶格系统，对于长期控制大量具有局部耗散的多状态物理系统中的衰变可能具有重要意义。与非驱动情况相比，我们有可能将系统驱动到暗浮空状态，总概率损失水平要低得多，并且在足够长的演化时间内具有良好的稳定性。这些结果适用于具有奇数个位点的多位点晶格系统，对于长期控制大量具有局部耗散的多状态物理系统中的衰变可能具有重要意义。与非驱动情况相比，我们有可能将系统驱动到暗浮空状态，总概率损失水平要低得多，并且在足够长的演化时间内具有良好的稳定性。这些结果适用于具有奇数个位点的多位点晶格系统，对于长期控制大量具有局部耗散的多状态物理系统中的衰变可能具有重要意义。