Microchips for single atom detection and spin squeezing

Abstract

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 finesse <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</i> . 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 DeltaN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> = (N/n) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> for a fluorescence measurement, and DeltaN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a</sub> = (1/4N) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> for 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 DeltaN <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> = (1/n) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> . 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 for <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">87</sup> Rb atoms trapped on the microchip.