Beyond discrete time crystal signatures: hidden coherence, causes of decay, and the first ‘discrete time crystal echo’

The phase structure of driven quantum systems can include exotic phenomena, including the recently-described discrete time crystal (DTC). The key signature of a DTC is a response with period nT (n=2,3,…) for drive period T, even when the drive is imperfect. Two experiments recently demonstrated this signature, one in trapped ions [1], and the other in diamond NV centers [2]. We have shown this signature in an NMR system of ³¹P spins on a crystal lattice, with little to no disorder [3,4]. We study the decay of the DTC oscillations, with two main results. First, we use a novel “DTC echo” sequence to demonstrate that the decay is caused in part by coherent evolution. Second, we demonstrate that the observed decay for perfect pi pulses (ε = 0) can be produced by the action of the internal Hamiltonian during the pulses.

[1] J. Zhang et al., Nature 543, 217 (2017).
[2] S. Choi et al., Nature 543, 221 (2017).
[3] J. Rovny, R.L. Blum, S.E. Barrett, Phys. Rev. Lett. 120, 180603 (2018)
[4] J. Rovny, R.L. Blum, S.E. Barrett, Phys. Rev. B 97, 184301 (2018)