Periodic Reporting for period 1 - QUESCA (Quantum Enhanced Sensing with Cold Atoms) Reporting period: 2017-08-01 to 2019-07-31 Summary of the context and overall objectives of the project Atom sensors based on ultra-cold atoms have demonstrated great potential for fundamental science and technological applications. In the vast majority of these sensors, the system variable that contains the useful information can be mapped into the atom number variable. Uncertainty in the initial atomic population is directly translated into sensing imprecision, limiting the performance of the sensor. A major challenge that the field of cold-atoms has yet to overcome is the preparation of the atomic ensemble with precisely known and controlled atom number. Furthermore, in order to fully exploit the potential of cold atoms, the preparation of the atomic cloud should preserve quantum correlations, so that quantum resources can be harnessed. The overarching goal of the project is to develop a robust technique for measuring the number of atoms in a minimally disturbing way, without increasing the temperature of the atomic cloud and without destroying quantum correlations. This measurement will be used to prepare an ultra-cold cloud with atom number uncertainty significantly reduced compared to the typical precision that can be achieved so far. Achieving a resolution better than the atom shot noise with such a minimally-perturbing measurement will lead to the creation of non-classical atomic states, with properties that offer quantum-enhanced sensitivity. A wide range of instruments that play an important role in the modern civilization can profit from developments in the field of cold atoms. Time-keeping atomic clocks, inertial sensors for navigation or seismography and gravitometers for geophysics exploration are applications that will benefit from sensitivity enhancement of cold-atom sensors. In addition, similar improvements may lead to more precise experiments for the study of quantum systems, advancing our understanding of the universe. Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far 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”. Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far) So far, the majority of experiments with cold atoms rely on the absorption of resonant light. This leads to significant overheating and destruction of quantum correlations. Therefore, the light-absorption method cannot be used to prepare the state of cold clouds. Minimally destructive probing techniques based on the light-atom dispersive interaction, where the refractive index of atoms induces a phase shift in off-resonant light, have been applied. However, to date their use remains limited, mainly due to complexity. Along the lines of the project, it was shown that the Faraday paramagnetic effect can be employed to measure the atom number in a relatively large cold cloud with a resolution better than the atom shot noise [M. Gajdacz et al, PRL 117, 073604 (2016)]. In this work, the signal, appearing at DC, is susceptible to drifts and noise from technical imperfections, while a rather sophisticated electronic system is required for real-time detection. The method developed in the project can be an improvement over the state of the art due to the simplicity of the system and the robustness against technical noise. The proposed technique can be implemented with readily available components, while the detection scheme of balanced polarimetry and sinusoidally modulated signal offer an advantage for suppressing experimental noise. The AC signal also allows for the introduction of stroboscopic probing, which can further improve the precision. The research performed aspires to popularize the use of the Faraday paramagnetic interaction as a precise technology for sample preparation that can be integrated in practical devices with cold atoms. Establishing a technique with the ability to prepare an ensemble with small uncertainty in the atom number will enhance the sensitivity of cold atom sensors. Furthermore, the minimally-disruptive, correlation preserving character of the measurement approach can be used to realize non-classical states and paves the way for quantum technologies based on cold atoms. By contributing advances in the field of cold-atoms, the research performed in the project can ultimately find applications in both practical life and in fundamental science. Schematic of the atom number detection principle.
