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arXiv:1203.3160 · Physical Review Letters

Collective State Measurement of Mesoscopic Ensembles with Single-Atom Resolution

Hao Zhang, Robert McConnell, Senka Ćuk, Qian Lin, Monika Schleier-Smith, Ian D. Leroux, Vladan Vuletić

Published Sep 27, 2012• 71 citations
arXivHTMLPDF

Abstract

We demonstrate single-atom resolution, as well as detection sensitivity more than 20 dB below the quantum projection noise limit, for hyperfine-state-selective measurements on mesoscopic ensembles containing 100 or more atoms. The measurement detects the atom-induced shift of the resonance frequency of an optical cavity containing the ensemble. While spatially varying coupling of atoms to the cavity prevents the direct observation of a quantized signal, the demonstrated measurement resolution provides the readout capability necessary for atomic interferometry substantially below the standard quantum limit and down to the Heisenberg limit.

DOI
10.1103/physrevlett.109.133603

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Many cold atom experiments rely on precise atom number detection, especially in the context of quantum-enhanced metrology where effects at the single particle level are important. Here, we investigate the limits of atom number counting via resonant fluorescence detection for mesoscopic samples of trapped atoms. We characterize the precision of these fluorescence measurements beginning from the single-atom level up to more than one thousand. By investigating the primary noise sources, we obtain single-atom resolution for atom numbers as high as 1200. This capability is an essential prerequisite for future experiments with highly entangled states of mesoscopic atomic ensembles.
Abstract The analysis of entangled atomic ensembles and their application for interferometry beyond the standard quantum limit requires an accurate determination of the number of atoms. We present an accurate fluorescence detection technique for atoms that is fully integrated into an experimental apparatus for the production of many-particle entangled quantum states. Number-resolved fluorescence measurements with single-atom accuracy for 1 up to 30 atoms are presented. According to our noise analysis, we extrapolate that the single-atom accuracy extends to a limiting atom number of 390(20) atoms. We utilize the accurate atom number detection for a number stabilization of the laser-cooled atomic ensemble. For a target ensemble size of 7 atoms prepared on demand, we achieve a 92(2)% preparation fidelity and reach number fluctuations 18(1) dB below the shot noise level using real-time feedback on the magneto-optical trap.
Atomic projection noise limits the ultimate precision of all atomic sensors, including clocks, inertial sensors, magnetometers, etc. The independent quantum collapse of N atoms into a definite state (for example spin up or down) leads to an uncertainty ΔθSQL= 1/√N in the estimate of the quantum phase accumulated during a Ramsey sequence or its many generalizations. This phase uncertainty is referred to as the standard quantum limit. Creating quantum entanglement between the N atoms can allow the atoms to partially cancel each other's quantum noise, leading to reduced noise in the phase estimate below the standard quantum limit. Recent experiments have demonstrated up to 10 dB of phase noise reduction relative to the SQL by making collective spin measurements. This is achieved by trapping laser-cooled Rb atoms in an optical cavity and precisely measuring the shift of the cavity resonance frequency by an amount that depends on the number of atoms in spin up. Detecting the probe light with high total efficiency reduces excess classical and quantum back-action of the probe. Here we discuss recent progress and a technique for reducing the relative frequency noise between the probe light and the optical cavity, a key requirement for further advances.