Demonstration of Z3 Time Crystalline Order in a Superconducting Qutrit Array (part 1 of 2)

Abstract: (part 1 of 2 Theory) Periodically driven quantum many body systems can exhibit remarkable non-equilibrium phenomena such as discrete time-translation symmetry breaking, giving rise to an exotic state of matter known as a discrete time crystal (DTC). Thus far, most studies have focused on spin ½ (qubit) systems with π Floquet-Ising order. We investigate a ℤ₃ time crystal displaying a 2π/3 eigenstate order on a chain of superconducting qutrits. This spin 1 many body quantum system is distinguished from its spin ½ counterpart by its ability to host a richer spectrum of behavior with chiral interactions. Furthermore, unlike the Floquet Ising/Majorana model, this system has no noninteracting limit and can host exotic parafermionic edge modes.

Experimentally, we observe a thermal to ℤ₃ DTC phase transition in a chain of 14 superconducting qutrits in a kicked, disordered spin-1 clock Hamiltonian. We implement our qutrit spin-spin interactions via fast flux pulses on tunable couplers, and perform kicks with local microwave pulses. Our system exhibits robust subharmonic period tripling that is independent of the initial state. Using finite system size analysis, we extract the critical kicking strength and confirm it matches closely with numerical predictions.