The Floquet central spin model: A platform to realize eternal time crystals, entanglement steering, and multiparameter metrology

• URL: http://arxiv.org/abs/2501.18472v1
• Date: Thu, 30 Jan 2025 16:46:48 GMT
• Title: The Floquet central spin model: A platform to realize eternal time crystals, entanglement steering, and multiparameter metrology
• Authors: Hillol Biswas, Sayan Choudhury,
• Abstract summary: We characterize protocols to realize eternal discrete time crystals (DTCs) in the periodically driven central spin model. We prove that the system exhibits eternal period-doubling oscillations when $lambda = 2 pi$ for an arbitrary number of satellite spins. We also propose a protocol to realize eternal higher-order(HO)-DTCs by tuning $lambda$ to $pi$.
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• Abstract: We propose and characterize protocols to realize eternal discrete time crystals (DTCs) in the periodically driven central spin model. These eternal DTCs exhibit perfect periodic revivals of the initial state at a time $mnT$ (where $n>1$ and $\{m,n\} \in \mathbb{Z}$), when the Ising interaction strength, $\lambda$ between the central spin and the satellite spins is tuned to certain values. The combination of perfect initial-state revival and time-translation-symmetry breaking leads to infinitely long-lived oscillations of the stroboscopic magnetization and the entanglement entropy in these DTCs even for a finite number of satellite spins. We analytically determine the conditions for the existence of these eternal DTCs and prove that the system exhibits eternal period-doubling oscillations ($n=2$) when $\lambda = 2 \pi$ for an arbitrary number of satellite spins. Furthermore, we propose a protocol to realize eternal higher-order(HO)-DTCs ($n>2$) by tuning $\lambda$ to $\pi$. Intriguingly, this protocol naturally steers the system through an entangled trajectory, thereby leading to the generation of maximally entangled Bell-cat states during the dynamical evolution of the HO-DTC. Finally, we demonstrate that these HO-DTCs can serve as a resource for Heisenberg-limited multiparameter sensing.

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