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European Frequency and Time Forum

Phase locking an atom interferometer

Andréa D Bertoldi, Ralf Kohlhaas, Etienne Cantin, Alain Aspect, Arnaud Landragin, Philippe Bouyer

Published Apr 1, 2016• 0 citations
Publisher

Abstract

In atom interferometry the phase evolution of a quantum superposition state is measured with respect to a reference signal. The measurement has a limited unambiguous interval, since not the phase but its projection is measured as a population unbalance on two energetic levels. Resolving phase wrapping brings to a longer interrogation interval and hence instrument sensitivity. We extended the unambiguous probe interval using coherence preserving measurements and phase corrections, and demonstrated the phase lock of the clock oscillator to an atomic superposition state. On this basis we implemented a protocol to improve atomic clocks limited by local oscillator noise, which is the case of optical atomic clocks, nowadays the best frequency standard in terms of both accuracy and precision. The technique could be adopted to enhance the sensitivity of atomic gravimeters.

DOI
10.1109/eftf.2016.7477819

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In atom interferometry the phase evolution of a quantum superposition state is measured with respect to a reference signal. The measurement has a limited unambiguous interval, since not the phase but its projection is measured as a population unbalance on two energetic levels. Resolving phase wrapping brings to a longer interrogation interval and hence instrument sensitivity. We extended the unambiguous probe interval using coherence preserving measurements and phase corrections, and demonstrated the phase lock of the clock oscillator to an atomic superposition state. On this basis we implemented a protocol to improve atomic clocks limited by local oscillator noise, which is the case of optical atomic clocks, nowadays the best frequency standard in terms of both accuracy and precision. The technique could be adopted to enhance the sensitivity of atomic gravimeters.
Atom interferometry based sensors provide today the most precise measurements of time, inertial forces and magnetic fields. In the common approach, a superposition state is interrogated for a given time interval and finally destructively measured. Conversely, we can repeatedly probe non-destructively the same quantum system and demonstrate efficient measurement schemes using feedback. First, we protect a spin polarized atomic ensemble from the decoherence induced by a synthetic noise. After the noise action, the state of the atomic system is read out with negligible projection using a non-destructive probe, and later corrected with a coherent manipulation to restore the initial state. The efficiency of the feedback scheme is studied versus the strength of the measurement and a maximum is found from the trade-off between information gain and probe destructivity. Our feedback controller is then applied to stabilize a classical local oscillator on a collective quantum state, and this is used in an atomic clock configuration to demonstrate experimentally that in some contexts a hybrid phase and frequency lock can surpass conventional atomic clocks which rely only on a frequency lock.
Atomic clocks are crucial for fundamental science and practical technology, but their sensitivity is often constrained by the standard quantum limit. With a cold-atom coherent-population-trapping clock, the authors design and experimentally demonstrate an adaptive Bayesian quantum frequency estimation protocol that approaches the Heisenberg scaling with respect to total interrogation time. This atomic clock also yields improved fractional frequency stability and enhanced robustness against technical noises. This work provides a high-precision approach to atomic clock locking, and holds promising applications in various interferometry-based quantum sensors.
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.
Optical atomic clocks that operate at frequencies up to 100,000 times higher than their microwave counterparts permit better resolutions and accuracies, while also providing more leeway in environmental control for out of lab applications. Many of the precision applications of these clocks, including relativistic geodesy and tests of fundamental physics rely on the intercomparison of at least two optical clocks. Relative comparisons that include single ion clocks, however, can require close to one month of continuous averaging to achieve measurement instabilities near 1 part in 1018. The long averaging times result from limits imposed on the quantum project noise as a result of signal detection from a single ion, as well as atom probe time limitations due to laser-atom decoherence. In this talk I will describe how the phase coherent properties of an optical frequency comb can be used to enable correlated and synchronous measurement of atomic clocks as a means to improve their relative measurement instability by close to a factor of 10, and nearly 100 times speed up in averaging time over conventional measurement techniques.
Improving the clock stability is of fundamental importance for the development of quantum-enhanced metrology. One of the main limitations arises from the randomly fluctuating local oscillator (LO) frequency, which introduces ``phase slips'' for long interrogation times and hence the failure of the frequency-feedback loop. Here we propose a strategy to improve the stability of atomic clocks by interrogating two atomic ensembles sharing the same LO. The two ensembles are prepared in coherent spin states pointing along orthogonal directions in the Bloch sphere. While standard Ramsey interrogation can only determine phases unambiguously in the interval $[\ensuremath{-}\ensuremath{\pi}/2,\ensuremath{\pi}/2]$, the joint interrogation allows for an extension to $[\ensuremath{-}\ensuremath{\pi},\ensuremath{\pi}]$, resulting in a relaxed restriction of the Ramsey time and improvement of absolute clock stability. Theoretical predictions are supported by ab initio numerical simulation for white and correlated LO noise. While our basic protocol uses uncorrelated atoms, we further extended it to include spin-squeezing and further improving the scaling of clock stability with the number of atoms. Our protocol can be readily tested in current state-of-the-art experiments.