Lifetime-Limited Interrogation of Two Independent Al+27 Clocks Using Correlation Spectroscopy

A quantum network of entangled optical atomic clocks

“…We find that entanglement reduces the measurement uncertainty by a factor close to √ 2, as predicted for the Heisenberg limit, thus halving the number of measurements required to reach a given precision. Practically, today's optical clocks are typically limited by dephasing of the probe laser 17 ; in this regime, we find that using entangled clocks confers an even greater benefit, yielding a factor 4 reduction in the number of measurements compared to conventional correlation spectroscopy techniques 17,18 . As a proof of principle, we demonstrate this enhancement for measuring a frequency shift applied to one of the clocks.…”

“…In this regime, entanglement offers an additional advantage as φ − has complete cancellation of common phase fluctuations and is only affected by differential phase noise between the two systems. If entanglement is not available as a resource, this insensitivity can also be accessed by using conventional correlation spectroscopy [37][38][39][40] , which involves simultaneous measurements with a common probe laser and an unentangled twoatom state 18 , as recently demonstrated by Clements et al 17 for two macroscopically-separated clocks. However, in this scenario P + = P − = 1 2 which sets the limit on the measurement uncertainty to δ ∆ −,u = 2δ ∆ i = √ 2δ ∆ −,s , a factor of √ 2 worse than independent single-ion measurements.…”

High precision differential clock comparisons with a multiplexed optical lattice clock

“…This motivates the use of simultaneous differential comparisons [4,27], also known as correlated noise spectroscopy [28], for applications involving clock comparisons [6,11]. Common-mode rejection of Dick noise and 10-second-scale atomatom coherence times well beyond that of the clock laser have recently been demonstrated between two independent ion-clocks [29], between sub-ensembles in a three-dimensional Fermidegenerate OLC [2], and between sub-ensembles in a tweezer-array clock [30]. In each of these cases the atoms are individually and tightly confined, suggesting that strong confinement and a lack of atom-atom interactions may be necessary ingredients to achieve such long coherent interrogation times.…”

Prospects of a Pb$^{2+}$ ion clock

“…This is elucidated in Ref. [73], where correlation spectroscopy was used to reject common-mode LO noise in a pair of Al + clocks. Using interrogation times up to 8 s, a coherence time consistent with the 20.6 s [74] natural lifetime of the excited clock state was observed.…”

“…Finally, we note that lead has three stable and two long-lived (half-life > 20 y) I = 0 isotopes. Using correlation spectroscopy, isotope shifts may be precisely measured using interrogation times far exceeding available LO coherence times [73].…”