Abstract

Dark states of atomic ensembles do not interact with light (can neither emit nor absorb a single photon due to destructive interference). Being free of decoherence, they can be widely used in quantum computing (particularly as a mechanism for creating quantum memory). To date, the structure of dark states of two-level atoms has been sufficiently well studied; meanwhile, this problem remains open for three-level atomic ensembles. For ensembles of two-level atoms (in a chosen range), it was established that the dimension of the dark subspace is equal to the Catalan numbers. It is difficult to generalize this statement to the case of three-level, and even more so, multi-level atomic ensembles and has not been done so far. This paper proposes a supercomputer algorithm for numerical confirmation of a similar statement for ensembles of a limited number (not exceeding several tens) of three-level atoms.

中文翻译：

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确定暗子空间维数的超级计算机算法

摘要

原子系综的暗态不与光相互作用（由于相消干涉，既不能发射也不能吸收单个光子）。由于没有退相干，它们可以广泛用于量子计算（特别是作为创建量子存储器的机制）。迄今为止，两能级原子的暗态结构已经得到了充分的研究。同时，这个问题对于三级原子集合仍然是开放的。对于两能级原子的系综（在选定范围内），已确定暗子空间的维数等于加泰罗尼亚数。很难将这种说法推广到三级原子集成的情况，更是如此，多级原子集成到目前为止还没有完成。