Journal of the Optical Society of America B

Liouvillian slow modes and metrological advantage in boundary time crystals

Muhammad Noman, Emad K. Jaradat, Heba Allhibi, Fahad Aljuaydi

Published Jul 20, 2026• 0 citations

Abstract

Boundary time crystals (BTCs) provide a route to persistent symmetry-breaking oscillations in open quantum systems without an external clock. We study finite-size BTC-like dynamics in collectively driven and dissipative spin ensembles using a hardware-motivated spin–cavity description and an autonomous collective-spin Liouvillian. A unified diagnostic pipeline identifies late-time oscillatory pockets, quantifies their metrological resource through the long-time averaged quantum Fisher information (QFI), and tests their compatibility with complex Liouvillian slow modes. In the autonomous regime, the QFI displays near-Heisenberg scaling over the accessible sizes. The corresponding Liouvillian modes are oscillatory, but their real decay rates do not show reliable finite-size closing; the spectrum is therefore used as a consistency check rather than proof of a thermodynamic BTC phase. Local dephasing simultaneously suppresses the oscillatory response and metrological gain. The results establish a finite-size connection among autonomous oscillations, slow modes, and persistent metrological resources while leaving the thermodynamic gap-closing question open.

DOI: 10.1364/josab.603587

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