NMR observations of discrete time crystalline signatures in an ordered crystal of ammonium dihydrogen phosphate

The discrete time crystal (DTC) is a recently-described phase of driven quantum systems that breaks the discrete time translation symmetry of its drive. If the Hamiltonian has period T, the signature of a DTC is a response of period nT that is robust to "error" in the drive. Two experiments recently reported this signature in trapped ions [1] and in diamond NV centers [2]. We present signatures of DTC order [3,4] in an NMR system of ³¹P spins in an oriented crystal of ammonium dihydrogen phosphate (ADP), a clean sample with multiple dipolar-coupled spin species (¹H, ³¹P, ¹⁴N). By varying the pulse angle θ and delay time τ of the DTC pulse sequence, we observe robust DTC oscillations across a much greater range in (θ, τ) than has been observed in earlier experiments [1,2], both with and without ¹H decoupling.

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