Atomic Clocks Become More Stable by Accounting for Atomic Complexity

A new theoretical framework for optical atomic clocks redefines the limits of precision timekeeping. Ravid Shaniv and colleagues at University of Oxford, in a collaboration between the University of Oxford and University of Colorado, show that current models evaluating atomic clock stability are suboptimal due to their assumption of a simplified two-level atomic system. Their analysis, incorporating a more realistic multi-level atomic model and accounting for spontaneous decay, reveals potential stability improvements of up to approximately 4.5 dB. Notably, they predict even greater enhancements, around 5.4 dB, when comparing atoms in a specific quantum state, offering key benefits for trapped-ion optical clocks and advancing the field of applied and fundamental research.

Bell state parity improves optical atomic clock stability through decay accounting

Frequency stability in optical atomic clocks has improved by 5.4 dB when comparing atoms existing in an odd parity Bell state, exceeding the limitations of previous two-level atomic models. This enhancement allows for frequency comparisons with a precision previously unattainable, opening new avenues for applications requiring extremely accurate timekeeping. The new methodology accounts for spontaneous decay, the loss of an atom’s energy as light branching to multiple ground states, a phenomenon ignored in simpler models; this enables discarding ‘failed’ measurement attempts caused by decay, improving overall accuracy. Optical atomic clocks operate by precisely measuring the frequency of transitions between energy levels within atoms, and their performance is directly linked to the stability of these atomic references. Traditional evaluations of these clocks have often relied on the simplification of atomic systems as two-level atoms, where only the ground and excited states are considered. However, real atomic systems possess numerous energy levels, and transitions between these levels can be influenced by various factors, including spontaneous emission. Spontaneous emission, or decay, represents the natural tendency of an excited atom to return to a lower energy state, releasing a photon in the process. When an atom can decay to multiple ground states, the situation becomes more complex, and the simplified two-level model no longer accurately reflects the system’s behaviour.

Trapped-ion optical clocks, nearing their theoretical limits of stability, will now be able to operate beyond them thanks to this advance. A frequency stability improvement of approximately 4.5 dB has been achieved by accounting for spontaneous decay branching to multiple ground states, a previously unconsidered factor allowing for the rejection of inaccurate readings caused by atomic energy loss. This advancement builds upon existing techniques for enhancing clock precision, such as utilising odd parity Bell states, which yielded a further improvement to 5.4 dB in frequency comparisons, particularly benefitting trapped-ion clocks nearing their performance limits. Detailed analysis of a specific isotope, $^{27}\text{Al}^{+}$, revealed a viable experimental protocol for implementing this enhanced interrogation method, involving a three-level atomic model where decay to either of two ground states is possible, enabling detection of decay events via projective measurements. Furthermore, the introduction of ‘mid-interrogation decay detection’ allows for the restarting of measurements after spontaneous emission, increasing the number of valid readings obtained per unit time. The use of Bell states, specifically odd parity states, introduces quantum entanglement between ions, which can further enhance clock stability. These states exhibit a unique property where the measurement outcome is correlated between the entangled ions, allowing for the suppression of certain types of noise. The combination of accounting for multi-level atomic structure and utilising Bell state parity represents a significant step forward in optical atomic clock technology. The $^{27}\text{Al}^{+}$ isotope was chosen for detailed analysis due to its favourable properties for trapped-ion clock implementations, including a relatively long coherence time and well-defined energy levels. Projective measurements are used to determine the state of the ion after the interrogation period, allowing for the identification and rejection of measurements affected by spontaneous decay.

Multi-level atomic modelling enhances ion clock stability through accurate decay pathway

Atomic clocks promise a new era of precision, underpinning everything from navigation to fundamental physics tests; however, a persistent tension exists between squeezing ever more performance from increasingly complex systems and the practical realities of maintaining coherence. While accounting for the intricacies of atomic decay, specifically branching to multiple ground states, has demonstrated strong stability gains, the benefits of entanglement, using states like odd parity Bell states, appear subtle in some scenarios. Nevertheless, refining models to accurately reflect complex atomic structures remains important for optimising clock performance. The implications of improved atomic clocks extend far beyond simply telling time more accurately. They are crucial for fundamental tests of physics, such as verifying the validity of Einstein’s theory of general relativity and searching for variations in fundamental constants. Furthermore, they are essential for advanced technologies like global navigation satellite systems (GNSS), where even tiny timing errors can lead to significant positional inaccuracies. The development of increasingly precise atomic clocks is therefore a key driver of scientific and technological progress.

Up to 4.5 decibels of improvement in frequency stability can be achieved by accounting for branching decay, where an atom loses energy to multiple lower states, compared to simpler two-level models. This enhancement is particularly valuable for ion-based optical clocks approaching their theoretical limits, with detailed protocols for aluminium-ion clocks already developed utilising these principles. Refinement of models of atomic decay is ongoing to further boost clock stability. Accounting for how atoms lose energy to multiple states improves frequency precision by up to 4.5 decibels, a vital consideration as ion-based optical clocks approach fundamental performance limits. Advancing beyond simplified models of atomic behaviour unlocks substantial gains in clock stability, particularly for trapped-ion systems already approaching known performance boundaries; previously, these branching pathways were disregarded in theoretical evaluations of complex atomic structures and spontaneous decay branching to multiple ground states. The 4.5 dB improvement represents a significant reduction in the uncertainty of the frequency measurement, allowing for more precise timekeeping and more sensitive tests of fundamental physics. The researchers are currently exploring methods to further refine their models and optimise the experimental protocols for implementing these improvements in real-world atomic clocks. This includes investigating different isotopes and exploring new techniques for suppressing noise and enhancing coherence. The ongoing research aims to push the boundaries of precision timekeeping and unlock the full potential of optical atomic clocks for a wide range of scientific and technological applications.

The research demonstrated a frequency stability improvement of up to 4.5 decibels by modelling atomic behaviour beyond the traditional two-level system. This matters because more accurate modelling of how atoms lose energy allows for more precise timekeeping and improved stability in optical atomic clocks. The findings are especially relevant for ion-based clocks nearing their performance limits, and the authors are currently refining these models to further optimise experimental protocols. This advancement contributes to technologies reliant on precise timing, such as global navigation satellite systems.