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Electronics Letters

Stability limitations from optical detection in Ramsey‐type vapour‐cell atomic clocks

Songbai Kang, Mohammadreza Gharavipour, C. Affolderbach, G. Mileti

Published Oct 1, 2015• 12 citations
Publisher

Abstract

In today's state of the art compact vapour‐cell atomic clocks relying on the pulsed Ramsey‐type interrogation, optical detection noise is a major limitation to the achievable short‐term stability. In this communication, the influence of the optical detection time on the clock's short‐term stability is investigated and a new analytical expression is developed to precisely predict the stability performance, taking into account the details of the optical detection phase of a Ramsey‐type atomic clock. The theory is in good agreement with the experimental results. It is applied for evaluating the clock's shot‐noise limit.

DOI
10.1049/el.2015.1902

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In today's state of the art compact vapour‐cell atomic clocks relying on the pulsed Ramsey‐type interrogation, optical detection noise is a major limitation to the achievable short‐term stability. In this communication, the influence of the optical detection time on the clock's short‐term stability is investigated and a new analytical expression is developed to precisely predict the stability performance, taking into account the details of the optical detection phase of a Ramsey‐type atomic clock. The theory is in good agreement with the experimental results. It is applied for evaluating the clock's shot‐noise limit.
Optical atomic clocks have been rapidly developing in recent decades, resulting in major improvements in both precision and accuracy. As a result, they have become instrumental in multiple areas of applied and fundamental research. Despite all atomic frequency references having more than two energy-levels, the commonly used model for evaluating their ultimate limits assumes a two-level atom. This leads to frequency interrogation protocols and theoretical stability bounds that are suboptimal for a true multi-level atom. The most fundamental stability bound assumes two noise sources - quantum projection noise and spontaneous decay from the excited state. In this work, we analyze a model that includes these noise types and is generalized beyond the two-level assumption, where spontaneous decay can branch to more than a single ground state. This model allows for detection and exclusion of atomic frequency interrogations in which the atom decayed, leading to a frequency stability improvement of up to ≈4.5 dB\approx 4.5 \text{ dB}≈4.5 dB compared with the two-level model. Furthermore, we identify an even greater stability enhancement of ≈5.4 dB\approx 5.4 \text{ dB}≈5.4 dB for frequency comparisons between atoms in an odd parity Bell state. These enhancements are particularly relevant for the numerous trapped-ion optical clock species that operate close to lifetime-limited stability. We calculate new stability limits for those cases and provide a detailed experimental protocol for frequency interrogation with an 27Al+^{27}\text{Al}^{+}27Al+ optical ion clock.
We show that the stability of an optical atomic clock can only be improved by spin squeezed states for ensembles below a critical particle number. This limitation results from a trade-off between measurement noise and instabilities due to limited laser coherence. Our results apply to the case of cyclic Ramsey interrogations on a single atomic ensemble with dead time between each measurement. The combination of analytical models for projection noise, dead time noise (Dick effect) and laser phase noise allows quantitative predictions of the critical particle number and the optimal clock stability for a given dead time and laser noise. Our analytical predictions are confirmed by numerical simulations of the closed servo loop of an optical atomic clock.
Optical atomic clocks are a driving force for precision measurements due to the high accuracy and stability demonstrated in recent years. While further improvements to the stability have been envisioned by using entangled atoms, squeezing the quantum mechanical projection noise, evaluating the overall gain must incorporate essential features of an atomic clock. Here, we investigate the benefits of spin squeezed states for clocks operated with typical Brownian frequency noise-limited laser sources. Based on an analytic model of the closed servo-loop of an optical atomic clock, we report here quantitative predictions on the optimal clock stability for a given dead time and laser noise. Our analytic predictions are in good agreement with numerical simulations of the closed servo-loop. We find that for usual cyclic Ramsey interrogation of single atomic ensembles with dead time, even with the current most stable lasers spin squeezing can only improve the clock stability for ensembles below a critical atom number of about one thousand in an optical Sr lattice clock. Even with a future improvement of the laser performance by one order of magnitude the critical atom number still remains below 100,000. In contrast, clocks based on smaller, non-scalable ensembles, such as ion clocks, can already benefit from squeezed states with current clock lasers.
In this paper, we present the performance of a vapor-cell rubidium frequency standard working in the pulsed regime, in which the clock signal is represented by a Ramsey pattern observed on an optically detected laser absorption signal. The main experimental results agree with previously reported theoretical predictions. In particular, we measured a relative frequency stability of σy(τ) - 1.6 × 10(-13)τ-1/2 for integration times, τ, up to 200 s, which represents a record in short-term stability for a vapor-cell clock. We also discuss the most important physical phenomena that contribute to this result.
We evaluate the influence of 2 types of laser sources with different spectral profiles on the performance of vapor cell atomic clocks based on lin||lin coherent population trapping (CPT) resonances. We show that a short-term stability of 1-2 x 10(-11) tau(-1/2) may be reached in a compact system using a modulated vertical cavity surface-emitting laser. Here the stability is limited by the detection noise level and can be improved up to a factor of 4 by increasing the lock-in detection frequency to several tens of kilohertz, which is not possible in standard double resonance atomic clocks. We compare these results with CPT prepared under the same experimental conditions, using 2 phase-locked extended cavity diode lasers, with which we predict a challenging short-term stability of 1-3 x 10(-13) tau(-1/2), comparable to the state-of-the-art laser-pumped Rb-clocks.