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

arXiv:2501.18472v2 Announce Type: replace Abstract: We propose and characterize protocols to engineer exact quantum revivals, discrete time crystals (DTCs), and entanglement oscillations in the periodically driven central spin model. While period-doubling DTCs have been observed in this system before, we uncover a unifying interaction-induced echo mechanism underlying several distinct dynamical regimes. We first demonstrate that this echo can enable exact period-doubling revivals when the Ising interaction strength, $\lambda$, between the central spin and the $N_{\rm sat}$ satellite spins is tuned to $2 \pi$. Notably, these revivals persist for arbitrary $N_{\rm sat}$ and transverse field $g$. This not only stabilizes the DTC response over a wide parameter regime, but also leads to a dynamical freezing regime. Furthermore, when $\lambda=(2m+1)\pi$ and $g= (2n+1)\pi/2$ ($\forall \, m,n \in \mathbb{Z}$), this echo induces a Clifford group structure. Consequently, higher-period revivals emerge that naturally steer the system through an entangled manifold of Bell-cat and spin-cat states. We establish that due to parity-dependent phases accumulated during the echo, the recurrence period is $12 T\,\, (24 T)$ for even (odd) $N_{\rm sat}$. Finally, we demonstrate that the multipartite entanglement generated by the Clifford dynamics can be harnessed for multiparameter metrology, with odd $N_{\rm sat}$ enabling Heisenberg-limited sensitivity.

Abstract:We propose and characterize protocols to engineer exact quantum revivals, discrete time crystals (DTCs), and entanglement oscillations in the periodically driven central spin model. While period-doubling DTCs have been observed in this system before, we uncover a unifying interaction-induced echo mechanism underlying several distinct dynamical regimes. We first demonstrate that this echo can enable exact period-doubling revivals when the Ising interaction strength, $\lambda$, between the central spin and the $N_{\rm sat}$ satellite spins is tuned to $2 \pi$. Notably, these revivals persist for arbitrary $N_{\rm sat}$ and transverse field $g$. This not only stabilizes the DTC response over a wide parameter regime, but also leads to a dynamical freezing regime. Furthermore, when $\lambda=(2m+1)\pi$ and $g= (2n+1)\pi/2$ ($\forall \, m,n \in \mathbb{Z}$), this echo induces a Clifford group structure. Consequently, higher-period revivals emerge that naturally steer the system through an entangled manifold of Bell-cat and spin-cat states. We establish that due to parity-dependent phases accumulated during the echo, the recurrence period is $12 T\,\, (24 T)$ for even (odd) $N_{\rm sat}$. Finally, we demonstrate that the multipartite entanglement generated by the Clifford dynamics can be harnessed for multiparameter metrology, with odd $N_{\rm sat}$ enabling Heisenberg-limited sensitivity.

Quantum Physics (quant-ph); Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2501.18472 [quant-ph]

(or arXiv:2501.18472v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2501.18472 Focus to learn more arXiv-issued DOI via DataCite

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

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