Proposed test of quantum mechanics with three connected atomic clock transitions

We consider possible extensions to quantum mechanics proposed by Weinberg [S. Weinberg, Phys. Rev. A 94, 042117 (2016)] and reanalyze his prediction of a new test based upon three atomic clocks in the same atom. We propose realistic experimental systems where this hypothesis can be tested. Two systems already set limits on deviations from quantum mechanics, while with another system one would be able to search for new physics at the limit of sensitivity of the best atomic clocks.