Fragility of classical Hamiltonian period doubling to quantum fluctuations

Abstract

We add quantum fluctuations to a classical period-doubling Hamiltonian time crystal, replacing the N classical interacting angular momenta with quantum spins of size l. The full permutation symmetry of the Hamiltonian allows a mapping to a bosonic model and the application of exact diagonalization for a quite large system size. In the thermodynamic limit N→∞ the model is described by a system of Gross-Pitaevskii equations whose classical-chaos properties closely mirror the finite-N quantum chaos. For N→∞, and l finite, Rabi oscillations mark the absence of persistent period doubling, which is recovered for l→∞ with Rabi-oscillation frequency tending exponentially to 0. For the chosen initial conditions, we can represent this model in terms of Pauli matrices and apply the discrete truncated Wigner approximation. For finite l this approximation reproduces no Rabi oscillations but correctly predicts the absence of period doubling. Our results show the instability of time-Translation symmetry breaking in this classical system even to the smallest quantum fluctuations, because of tunneling effects.