  Quantum noise is inherent in any open quantum system as it affects not only
the statistical properties of the initial state but also the time evolution of
the system. A transversely pumped atom-cavity setup is a prototypical example
of such an open system, wherein limit cycles (LCs) have been observed and
identified as continuous time crystals (CTCs). Using truncated Wigner
approximation (TWA), we show that the inherent quantum noise pushes the system
to exhibit signatures of LCs for interaction strengths lower than the critical
value predicted by mean-field theory, suggesting a noise-induced enhancement of
temporal ordering. By comparing the oscillation frequencies of the LCs for the
one-dimensional (1D) and two-dimensional (2D) regimes, we find that the LC
frequencies have larger shot-to-shot fluctuations in 1D than in 2D. We
demonstrate that this has an important consequence in the effectiveness of
entrainment of LCs for a periodically driven pump intensity or light-matter
coupling strength.
