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arXiv:1004.5486

Ultrasensitive Atomic clock with single-mode number-squeezing

Luca Pezzè, Augusto Smerzi

Published Apr 30, 2010• 0 citations
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Abstract

We show that the sensitivity of an atomic clock can be enhanced below the shot-noise level by initially squeezing, and then measuring in output, the population of a single atomic level. This can simplify current experimental protocols which requires squeezing of the relative number of particles of the two populated states. We finally study, as a specific application, the clock sensitivity obtained with a single mode quantum non-demolition measurement.

DOI
10.48550/arxiv.1004.5486

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We show that the sensitivity of an atomic clock can be enhanced below the shot-noise level by initially squeezing, and then measuring in output, the population of a single atomic level. This can simplify current experimental protocols which requires squeezing of the relative number of particles of the two populated states. We finally study, as a specific application, the clock sensitivity obtained with a single mode quantum non-demolition measurement.
A major challenge of the phase estimation problem is the engineering of high-intensity entangled probe states. The goal is to significantly enhance above the shot-noise limit the sensitivity of two-mode interferometers. Here we show that this can be achieved by squeezing in input, and then measuring in output, the population fluctuations of a single mode. The second input mode can be left as an arbitrary nonvacuum (e.g., a bright coherent) state. This two-mode state belongs to a novel class of particle-entangled states which are not spin squeezed. Already a 2.4 db gain above shot noise can be obtained when just a single-particle Fock state is injected into the empty input port of a classical interferometer configuration. Higher gains, up to the Heisenberg limit, can be reached with squeezed states of a larger number of particles. We finally study the robustness of this protocol with respect to detection noise.
Atomic clocks have reached the Standard Quantum Limit (SQL) of precision,1 set by the projection noise inherent in measurements on uncorrelated atoms. It is possible to overcome this limit by entangling the atoms to generate a "squeezed state" of the atomic ensemble. We use the collective interaction of an atomic ensemble with a far-detuned light field in an optical resonator to prepare squeezed states by two different methods: quantum non-demolition (QND) measurement and Hamiltonian evolution. We apply both methods to an ensemble of 5 x 104 87Rb atoms in a superposition of hyperfine clock states. We measure the suppression of projection noise and compare it to the accompanying reduction in signal, thereby quantifying the net gain in spectroscopic sensitivity. By QND measurement, with resolution up to 9 dB below the projection noise level, we achieve 3.0(8) dB of metrologically relevant squeezing. Whereas the measurement-based approach relies on knowledge of the (randomly distributed) measurement outcome to produce a conditionally squeezed state, the method of Hamiltonian evolution produces a known squeezed state independent of detector performance. We mimic the dynamics of the one-axis twisting Hamiltonian, proposed as a generator of squeezed states by Kitagawa and Ueda,2 by using the atom-induced frequency shift of the resonator mode and the corresponding resonator-field-induced shift of the atomic transition frequency to introduce an effective interaction among the atoms. The resulting deterministic squeezing is sufficient to allow a 6.0(4) dB improvement in spectroscopic sensitivity over the SQL.
In general, the process of spin squeezing is employed for atomic sensors that are essentially free from the effect of spontaneous emission. In the case of an atomic clock based on coherent population trapping, spontaneous emission plays a key role. Specifically, when the clock is realized in the Ramsey configuration employing a pair of pulses separated in time, it is the spontaneous emission process during the first pulse that creates the coherent population trapping, by optically pumping the atoms into the so-called dark state. We show in this talk that it is still possible to apply the process of spin squeezing to enhance the sensitivity of such a clock, by designing carefully the sequence of steps in the protocol. Specifically, we consider the approach of using the maximally entangled Schroedinger Cat states, produced via one axis twist squeezing, to achieve Heisenberg Limited sensitivity, representing an improvement in sensitivity by as much as four orders of magnitude.
We propose a hybrid quantum-classical atomic clock where the interrogation of atoms prepared in a spin-coherent (or weakly squeezed) state is used to feed back one or more highly spin-squeezed atomic states toward their optimal phase-sensitivity point. The hybrid clock overcomes the stability of a single Ramsey clock using coherent or optimal spin-squeezed states and reaches a Heisenberg-limited stability while avoiding nondestructive measurements. When optimized with respect to the total number of particles, the protocol surpasses the state-of-the-art proposals that use Greenberger-Horne-Zeilinger or NOON states. We compare analytical predictions with numerical simulations of clock operations, including correlated 1/f local oscillator noise.
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.