The minimally invasive technique for measuring the atom number in an cold ensemble was based on the the Faraday paramagnetic effect: off-resonant, linearly polarized light propagating through an atomic ensemble experiences polarization rotation and the angle of rotation is proportional to the total atomic spin component along the direction of light propagation. For an ensemble of atoms with well-defined spin state, the total spin is proportional to the number of atoms, which is mapped, through the Faraday effect, to the polarization state of probe light.
The research was performed on Rb atoms, confined in a magnetic trap with a rotating magnetic field. Standard cooling and trapping techniques were used to load at a few microKelvin temperature approximately 2x10^5 atoms in the trap, with shot to shot atom number fluctuations on the order of 15%. Linearly polarized light, far detuned from the optical resonance, was used to probe the atom number in the ensemble. The setup was developed with care to diminish fluctuations and drifts in the probe beam path. The shot to shot fluctuation of the trap position with respect to the light beam was found to be on the order of a few micrometers. To compensate for this, the probe light beam diameter was expanded to be significant larger than the ensemble size so that all the atoms experienced effectively homogeneous probe illumination. A pinhole, introduced in the plane where the atoms were imaged, collected the part of the beam that had interacted with the atoms. The pinhole diameter was chosen according to the size of the atomic ensemble and the shot to shot variation in its position, so that fluctuations in position result in measurement imprecision below the shot noise of atoms. The polarization orientation of probe light was measured with balanced polarimetry, which is robust against technical probe noise. Additional technical noise mitigation was provided by the signal following synchronously the rotating magnetic field of the trap, and thus appearing at a specified frequency away from the low frequency spectrum.
The imprecision of the atom number estimator was limited by the photon shot noise of probe light and the stochastic loss of atoms due to the unavoidable absorption of light that exists in every light-matter interaction. The efficiency of the technique was characterized by evaluating the shot to shot atom number variation after performing a measurement that estimated the atomic population using the Faraday paramagnetic effect. With this scheme, the atom number imprecision was reduced by a factor of 40 to approximately 0.8% for ensembles of 5x10^4 atoms, without any measurable heating. This equates to an x40 improvement in the knowledge of the atomic population for the prepared cold ensemble, which was directly mapped to the precision of the final measurement.
In addition, upgrades in the setup realized during the course of the project led to the development of a waveguide and accelerator ring for neutral atoms. We demonstrated the first hypersonic transport of coherent matter-waves over macroscopic distances without measurable effect on the quantum state. This work was published in the scientific journal “Nature”.
