Quantum Time Crystal by Decoherence in Ring Systems

A quantum time crystal is a quantum mechanical system which spontaneously breaks time translation symmetry [1]. We show that, instead of spontaneous symmetry breaking, decoherence breaks time translation symmetry of a ring system with a macroscopic ground state [2]. In particular, we show that the complex order parameter of an incommensurate charge density wave and an annular Josephson junction with a ring or Möbius ring geometry [3] coupled to their environment oscillates periodically. The Caldeira-Leggett model is used to model the environment as a bath of harmonic oscillators. The Hamiltonians considered in this model are time-independent unlike ``Floquet time crystals". Our model forms a quantum time crystal with a finite length in space and time.

[1] F. Wilczek, Phys. Rev. Lett. 109, 160401 (2012)
[2] K. Nakatsugawa, T. Fujii, and S. Tanda, Phys. Rev. B 96, 094308 (2017)
[3] S. Tanda, T. Tsuneta, Y. Okajima, K. Inagaki, K. Yamaya and N. Hatakenaka, Nature 417, 397–398 (2002)