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arXiv:1307.7598 · Physical Review Letters

Accurate Atom Counting in Mesoscopic Ensembles

David B. Hume, Ion Stroescu, Maxime Joos, Wolfgang Muessel, Helmut Strobel, Markus K. Oberthaler

Published Dec 16, 2013• 88 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.111.253001

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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.
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. Single-particle resolving fluorescence measurements for 111 up to 303030 atoms are presented. According to our noise analysis, we extrapolate that the single-atom resolution extends to a limiting atom number of 390(20)390(20)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 777 atoms prepared on demand, we achieve a 92(2) %92(2)\,\%92(2)% preparation fidelity and reach number fluctuations 18(1) dB18(1)\,\mathrm{dB}18(1)dB below the shot noise level using real-time feedback on the magneto-optical trap.
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.
Atom interferometers belong among today's most precise sensors and offer a broad range of possible metrological applications. Given their ability to measure accelerations and rotations precisely, they are suitable for inertial sensing, navigation and geodesy. Beyond this, they proved indispensible for time-keeping as well as fundamental research. This explains why the improvement of achievable sensitivities of atom interferometers is of particular interest. However the sensitivity of atom interferometers is fundamentally restricted by the standard quantum limit. The standard quantum limit can only be surpassed by employing entangled many-partice states. Entangled states, such as the twin-Fock state, allow atom interferometers to improve the phase sensitivity beyond the standard quantum limit, but they are reliant on an accurate detection of the interferometric out come. In this work, an experimental apparatus is designed and set up that will allow for routine generation of highly entangled twin-Fock states in a Rubidium-87 spinor Bose-Einstein condensate. As the main feature of this apparatus, an accurate atom counting fluorescence detection has been implemented. This detection achieves single-particle resolving fluorescence measurements for 1 up to 30 atoms. According to the noise analysis the single-atom resolution extends to a limiting atom number of 390(20) atoms. The implemented quadrupole coils with their strong gradient of up to 300 G/cm offer a tight confinement that in combination with the 55 W optical dipole trap laser will enable a fast repetition rate of the creation of highly entangled quantum states.
Magnetic microtraps for ultracold atoms combine tight confinement, long storage times, high degree of control over the atomic position, and good optical access. Atom detection can be implemented via fluorescence, absorption, or dispersive measurements. All three types of measurements can be enhanced by an optical resonator, where the enhancement factor is proportional to the resonator finesseF. In the limit of negligible detector counts, in a setup where the detector registers n counts per atom in a fluorescence measurement, the atom number resolution is DeltaNf= (N/n)1/2for a fluorescence measurement, and DeltaNa= (1/4N)1/2for an absorption measurement. This means that absorption and fluorescence measurements perform similarly for one atom, but that the absorption measurement is superior for N >1. However, in absorption measurements the number of atoms must remain sufficiently small for the atomic absorption not to deteriorate the resonator finesse. Larger samples can be probed by dispersive measurements, where the tuning of the resonator due to the atomic index of refraction is measured. In the absence of technical noise, the corresponding atom number resolution is independent of detuning from the atomic transition, and given by DeltaNd= (1/n)1/2. Using fluorescence detection in a resonator of finesse F=8000, we detect two counts per atom in 250 mus, enabling single-atom detection with 75% efficiency (Teper et al., 2006). Absorption detection with 3.3% transmission attenuation enables us to measure small samples with up to 10 atoms with a resolution of about one atom. Absorptive and dispersive detection are interesting in that the resolution is not decreased with higher atom number. The reason is that both rely on the forward scattered signal, where the fields emitted by different atoms add coherently. These methods therefore allow non-destructive measurements below the atom-number shot noise, provided that the optical depth of the sample exceeds unity. We have realized an optical depth of several thousand inside the resonator, which should enable trapped-atom detection significantly below the shot-noise limit. If the detection is applied in a state-selective manner to a sample of two-level atoms (Geremia et al., 2004), conditional spin squeezing results. Such squeezing of the pseudo-spin for an atomic clock transition can be used to realize a hyperfine atomic clock on a microchip (Treutlin et al., 2004) that operates below the atom number shot noise limit (standard quantum limit). We report experimental progress towards pseudo-spin squeezing for87Rb atoms trapped on the microchip.
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.