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.
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Notes
We do not create dense matrices.
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ACKNOWLEDGMENTS
I thank Y. I. Ozhigov and V. V. Voevodin for their participation. I’m also grateful to the reviewers for their careful reading of the manuscript and helpful remarks.
Funding
The work is supported by Russian Foundation for Basic Research, grant no. 20-31-90128.
The research is carried out using the equipment of the shared research facilities of HPC computing resources at Lomonosov Moscow State University.
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(Submitted by V. V. Voevodin)
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Kulagin, A.V. Supercomputer Algorithm for Determining the Dimension of Dark Subspace. Lobachevskii J Math 42, 1521–1531 (2021). https://doi.org/10.1134/S1995080221070143
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DOI: https://doi.org/10.1134/S1995080221070143