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Decoherence of a singlet-triplet superposition state under dipolar interactions of an uncorrelated environment

Recently it was shown that by means of an STM it is experimentally possible to stimulate clock transitions between the singlet and the non-magnetic triplet state of a Heisenberg-coupled spin dimer (Bae et al., Science Advances 4, eaau4159). This leads to more strongly protected clock transitions while ordinary ones only provide first-order protection against magnetic noise. However, large decoherence times of clock like states normally refer to ensembles of spins which do not dephase. In the cited experiment only one single dimer is manipulated and not an ensemble. For this reason we simulate how a single dimer behaves in an environment of other spins which couple to the dimer via dipolar interactions. We perform unitary time evolutions in the complete Hilbert space including dimer and a reasonably large environment. We will see that for a weak environment this approach confirms long decoherence times for the clock like state, but with stronger couplings this statement does not hold. As a reference we compare the behavior of the dimer with other, non-clock like, superposition states. Furthermore, we show that the internal dynamics of the bath plays an important role for the decoherence time of the system. In a regime where the system is weakly coupled to the bath, stronger interactions among environmental spins worsen the decoherence time up to a certain degree, while if system and bath are strongly coupled, stronger interactions in the environment improve decoherence times.