Atomic clocks, which are vital for technologies like GPS and space exploration, face a fundamental dilemma when enhanced with quantum entanglement. To make these clocks extraordinarily precise, scientists use a special quantum state involving multiple atoms, known as a Greenberger-Horne-Zeilinger (GHZ) state. This entangles the atoms, allowing them to tick together in perfect sync and measure frequency with a precision that theoretically hits the Heisenberg limit. However, this extreme precision usually comes at a steep cost: it dramatically shrinks the clock's dynamic range, or the frequency window it can accurately measure. A clock that is exquisitely sensitive to a single frequency becomes useless if the actual frequency shifts even slightly outside its narrow focus.
Recently, researchers from Shenzhen University and Sun Yat-sen Univerity have proposed a novel solution to this problem by rethinking how the clock's measurement is guided. Instead of taking fixed-duration measurements, the new protocol adaptively integrates measurements of varying durations based on the Bayesian credible intervals. Think of it like a smart GPS that constantly refines its estimate of your location. Initially, the clock has a rough idea of the frequency (its prior knowledge). It then performs a short measurement, which yields a new result. The Bayesian engine combines this new data with the prior to produce a refined "posterior" distribution—a probabilistic map of where the true frequency likely lies.
The key innovation is that the width of this distribution—known as the credible interval—dictates the next step. The protocol correlates the duration of the next measurement with the period of the likelihood function, effectively matching the "ruler" to the scale of the remaining uncertainty. If the credible interval is wide, the next measurement is short, preventing the signal from becoming ambiguous. As the interval narrows, the measurement time is lengthened, achieving progressively higher precision.
This adaptive strategy, which can be applied to both individual and cascaded groups of GHZ states, breaks the old trade-off. It achieves dual Heisenberg-limited scaling, meaning its precision improves with both the number of entangled atoms (N) and the total elapsed measurement time (t). This surpasses older methods that offered a less efficient hybrid scaling.
Remarkably, this adaptable approach not only extends the dynamic range but also proves more resilient to the real-world disturbances, like noise and dephasing, that typically plague quantum systems. Guided intelligently by the credible interval, the protocol offers a path toward atomic clocks that are not only highly precise but also practical and robust enough for the demanding applications of next-generation navigation and fundamental physics experiments.
Science China Physics Mechanics and Astronomy
Experimental study