用重复条件测量驱动量子系统
Driving quantum systems with repeated conditional measurements
摘要：
我们研究了条件零测量对量子系统的影响，发现了丰富多样的行为。具体地说，在有限维希尔伯特空间中的时间无关的$H$的量子动力学被认为是与指定状态的重复强零测量。我们讨论了四个通用的行为，出现在这些监控系统。第一种情况出现在没有对称性的系统中，伴随着它们在能谱中的相关简并，因此也没有暗态。在这种情况下，可以找到唯一的最终状态，其由生存算子的最大本征值确定，非酉算子编码测量之间的酉演化和测量本身。对于三级系统，这类似于众所周知的搁置效应。其次，对于具有内在对称性和相应的简并能谱的系统，零测量动态地选择简并能级，而非简并能级被有效地消除。第三，在没有暗态的情况下，并且对于特定的参数选择，存活算子的两个或更多个本征值在幅度上匹配，并且这导致由测量速率而不仅仅由能级控制的振荡行为。最后，当调整控制参数时，使得生存算子的本征值全部合并为零，则具有与违反零测量条件的情况相对应的例外点，使得条件测量过程不可能。
英文摘要：
We investigate the effect of conditional null measurements on a quantum system and find a rich variety of behaviors. Specifically, quantum dynamics with a time independent $H$ in a finite dimensional Hilbert space are considered with repeated strong null measurements of a specified state. We discuss four generic behaviors that emerge in these monitored systems. The first arises in systems without symmetry, along with their associated degeneracies in the energy spectrum, and hence in the absence of dark states as well. In this case, a unique final state can be found which is determined by the largest eigenvalue of the survival operator, the non-unitary operator encoding both the unitary evolution between measurements and the measurement itself. For a three-level system, this is similar to the well known shelving effect. Secondly, for systems with built-in symmetry and correspondingly a degenerate energy spectrum, the null measurements dynamically select the degenerate energy levels, while the non-degenerate levels are effectively wiped out. Thirdly, in the absence of dark states, and for specific choices of parameters, two or more eigenvalues of the survival operator match in magnitude, and this leads to an oscillatory behavior controlled by the measurement rate and not solely by the energy levels. Finally, when the control parameters are tuned, such that the eigenvalues of the survival operator all coalesce to zero, one has exceptional points that corresponds to situations that violate the null measurement condition, making the conditional measurement process impossible.
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。
