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Journal of Applied Physics

Assessment of a time-of-flight detection technique for measuring small velocities of cold atoms

Henrik Hagman, Peder Sjölund, S.J.H. Petra, Mats Nylén, Anders Kastberg, Harald Ellmann, Johan Jersblad

Published Apr 15, 2009• 10 citations

Abstract

A low noise time-of-flight detection system for laser cooled atoms has been constructed and incrementally optimized. Here, a thorough description of the construction is presented along with an analysis of the capabilities of the system. The quality of the detection (the resolution, the reproducibility, the sensitivity, etc.) is crucial for, e.g., the ability to see details in the velocity distribution profile, which is of interest for fundamental studies of statistical physics and of the laser cooling processes, and for detection of small initial velocities of an atomic cloud, important, e.g., when studying small drifts induced by Brownian motors and ratchets. We estimate the signal-to-noise ratio of our signal to be better than 1000:1 for a typical single shot, and we discuss the effect of the initial atomic cloud size, the probe size, and the effects of the wave packet spread during the fall time on the measured quantities. We show that the shape of the velocity distribution is well conserved during the mapping done in the detection, i.e., in the convolution with the probe beam, and that velocities as small as a few percent of the single photon recoil velocity can be resolved.

DOI: 10.1063/1.3097466

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A low noise time-of-flight detection system for laser cooled atoms has been constructed and incrementally optimized. Here, a thorough description of the construction is presented along with an analysis of the capabilities of the system. The quality of the detection (the resolution, the reproducibility, the sensitivity, etc.) is crucial for, e.g., the ability to see details in the velocity distribution profile, which is of interest for fundamental studies of statistical physics and of the laser cooling processes, and for detection of small initial velocities of an atomic cloud, important, e.g., when studying small drifts induced by Brownian motors and ratchets. We estimate the signal-to-noise ratio of our signal to be better than 1000:1 for a typical single shot, and we discuss the effect of the initial atomic cloud size, the probe size, and the effects of the wave packet spread during the fall time on the measured quantities. We show that the shape of the velocity distribution is well conserved during the mapping done in the detection, i.e., in the convolution with the probe beam, and that velocities as small as a few percent of the single photon recoil velocity can be resolved.

The time-of-flight (TOF) method is one of the most common ways to measure the temperature of cold atoms. In the cold atomic fountain setup, the geometry of the probe beam will introduce the measurement errors to the spatial distribution of cold atomic cloud, which will lead to the measurement errors on atomic temperature. Using deconvolution, we recover the atomic cloud profile from the TOF signal. Then, we use the recovered signals other than the TOF signals to obtain a more accurate atomic temperature. This will be important in estimating the effects of cold atom collision shift and the shift due to transverse cavity phase distribution on an atomic fountain clock.

We calculate the contribution of the atomic shot noise in the detection of the laser-induced fluorescence signal emitted by atoms in a beam. We point out a filtering of such a contribution which is the consequence of the finite transit time of the atoms through the laser beam. Moreover, we demonstrate that the distribution of the atomic velocities in the beam induces an extra noise which degrades the measured signal-to-noise ratio and modifies the observed statistics of the fluorescence photons emitted by the whole interaction zone.

A fluorescence detection scheme coupled to a highly sensitive nitrogen-cooled CCD camera is used to image the spatial distribution of a low-density falling rubidium atomic cloud released from an optical trap. The falling cloud passes through a thin probe laser beam tuned to resonance. The performance of the scheme is illustrated in the analysis of cold atomic clouds collimated by pinholes during their free fall under the influence of gravity. Clouds of approximately 10(4) atoms and with typically 10(6) at./cm(3) density are analyzed spatially with 24-mum resolution. This method is compared with different atomic cloud imaging techniques.

In this paper we report on the first purely ``pump-probe'' nonlinear laser spectroscopy results in a slow atomic beam. We have observed Raman, Rayleigh, and recoil-induced resonances (RIR) in a continuous beam of slow and cold cesium atoms extracted from a two-dimensional (2D) magneto-optical-trap (MOT) with the moving molasses technique. The RIR enabled us to measure the velocity distribution, therefore the average speed (0.6--4 m/s) and temperature (50--500 \ensuremath{\mu}K) of the atomic beam. Compared to time of flight, this technique has the advantage of being local, more sensitive in the low-velocity regime

(v<1 \mathrm{m}/\mathrm{s}),

and it gives access to transverse velocities and temperatures. Moreover, it may be extended to measure atomic velocities in the 2D MOT source of the atomic beam.

We consider the ballistic expansion of a cloud of trapped atoms falling under the influence of gravity. Using a simple coordinate transformation, we derive an analytical expression for the time-of-flight signal. The properties of the signal can be used to infer the initial temperature of the cloud. We first assume a point size cloud with an isotropic velocity distribution to explain the physical basis of the calculation. The treatment is then generalized to include a finite-size cloud with an anisotropic velocity distribution, and an exact result for the signal is derived. The properties of the signal are discussed, and an intuitive picture is presented to explain how initial conditions determine the features of the signal.