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arXiv:2102.01773 · Physical Review Applied

Reducing Number Fluctuations in an Ultracold Atomic Sample Using Faraday Rotation and Iterative Feedback

Ryan Thomas, J.S. Otto, Matthew Chilcott, Amita B. Deb, Niels Kjærgaard

Published Dec 14, 2021• 1 citation
arXivHTMLPDF

Abstract

We demonstrate a method to reduce number fluctuations in an ultracold atomic sample using real-time feedback. By measuring the Faraday rotation of an off-resonant probe laser beam with a pair of avalanche photodetectors in a polarimetric setup, we produce a proxy for the number of atoms in the sample. We iteratively remove a fraction of the excess atoms from the sample to converge on a target proxy value in a way that is insensitive to environmental perturbations and robust to errors in light polarization. Using absorption imaging for out-of-loop verification, we demonstrate a reduction in the number fluctuations from $3\mathrm{%}$ to $0.45\mathrm{%}$ for samples at a temperature of $16.4\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{K}$ over the time scale of several hours, which is limited by temperature fluctuations, beam-pointing noise, and photon shot noise.

DOI
10.1103/physrevapplied.16.064033

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We demonstrate a method to reduce number fluctuations in an ultracold atomic sample using real-time feedback. By measuring the Faraday rotation of an off-resonant probe laser beam with a pair of avalanche photodetectors in a polarimetric setup, we produce a proxy for the number of atoms in the sample. We iteratively remove a fraction of the excess atoms from the sample to converge on a target proxy value in a way that is insensitive to environmental perturbations and robust to errors in light polarization. Using absorption imaging for out-of-loop verification, we demonstrate a reduction in the number fluctuations from 3\mathrm{%} to 0.45\mathrm{%} for samples at a temperature of 16.4\ensuremathμK16.4\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{K}16.4\ensuremathμK over the time scale of several hours, which is limited by temperature fluctuations, beam-pointing noise, and photon shot noise.
We prepare number stabilized ultracold atom clouds through the real-time analysis of nondestructive images and the application of feedback. In our experiments, the atom number N∼10^{6} is determined by high precision Faraday imaging with uncertainty ΔN below the shot noise level, i.e., ΔN<sqrt[N]. Based on this measurement, feedback is applied to reduce the atom number to a user-defined target, whereupon a second imaging series probes the number stabilized cloud. By this method, we show that the atom number in ultracold clouds can be prepared below the shot noise level.
We present a method of diode laser frequency stabilization based on the Faraday rotation of linearly polarized light passing through an atomic sample in the presence of a very modest (1mT) magnetic field. Near the zero crossing of this spectroscopic feature, an optical system capable of very precise polarimetry detects and corrects for very small frequency fluctuations via a feedback system, which keeps the rotation signal at zero. In our application, we have demonstrated robust frequency stabilization over time scales from 10ms to 1h at the 1MHz level or below. We utilize this technique to lock our laser to a “forbidden” M1∕E2 transition in thallium at 1283nm, for which saturated absorption techniques are not straightforward. This technique has broad applicability to spectroscopy of various atomic systems as we also demonstrate using a Rb cell and a 780nm diode laser.
Atomic ensembles have gained a lot of interest in the last decade for their prospective use as quantum memories, in precision measurements and other applications in quantum information processing. The atomic part of the interface presented here is an all-optically trapped atomic ensemble of 87Rb at a temperature of 25 muK. The ensemble consists of 106atoms and has an elongated shape with an aspect ratio of about 250:1. The resonant optical depth is around 50. The light part is an off-resonant polarized laser beam which dispersively probes the atomic state. The detection is a shot-noise limited polarization measurement of light pulses of a few mus and 3 x 105photons.
Abstract We demonstrate that a dispersive imaging technique based on the Faraday effect can measure the atom number in a large, ultracold atom cloud with a precision below the atom shot noise level. The minimally destructive character of the technique allows us to take multiple images of the same cloud, which enables sub-atom shot noise measurement precision of the atom number and allows for an in situ determination of the measurement precision. We have developed a noise model that quantitatively describes the noise contributions due to photon shot noise in the detected light and the noise associated with single atom loss. This model contains no free parameters and is calculated through an analysis of the fluctuations in the acquired images. For clouds containing N ∼ 5 × 10 6 atoms, we achieve a precision more than a factor of two below the atom shot noise level.
High-sensitivity imaging of ultracold atoms is often challenging when interference patterns are imprinted on the imaging light. Such image noises result in low signal-to-noise ratio and limit the capability of extracting subtle physical quantities. Here we demonstrate an advanced fringe removal algorithm for absorption imaging of ultracold atoms, which efficiently suppresses unwanted fringe patterns using a small number of sample images without taking additional reference images. The protocol is based on an image decomposition and projection method with an extended image basis. We apply this scheme to raw absorption images of degenerate Fermi gases for the measurement of atomic density fluctuations and temperatures. A quantitative analysis shows that image noises can be efficiently removed with only tens of reference images, which manifests the efficiency of our protocol. Our algorithm would be of particular interest for quantum emulation experiments in which several physical parameters need to be scanned within a limited time duration.
Optical rotation detection system (ORDS) utilizing quantum nondemolition (QND) measurement methods is widely applied in the field of quantum metrology and quantum information. However, the sensitivity of ORDS is limited by the uncertainty from optical-couple noise during the measurement of the atomic spin ensemble. In this study, we specifically analyze the mechanism of optical-couple noise caused by the fluctuations of probe light’s polarization in the modulated ORDS with a new model established to describe atomic spin precession in this particular condition. It is discovered that transverse electron-spin polarization errors are generated by the residual probe photon spin polarization in the ORDS, which results in extra coupling magnetic noise. In order to suppress this noise, a novel in situ method is proposed that the resultant electron-spin errors are reduced by a specifically designed closed-loop system. The results are verified through the ORDS in a co-magnetometer. After zeroing the extra probe photon spin polarization, an angular sensitivity better than1×10−81 \times 10 ^{\mathrm {-8}}1×10−8rad/Hz1/2^{\mathrm {1/2}}1/2is achieved for frequencies higher than 5 Hz, demonstrating a probe background noise of 0.26 fT/Hz1/2^{\mathrm {1/2}}1/2@14.5 Hz, approaching electronic noise and photon shot noise (PSN). With closed-loop control, the optical rotation bias instability is promoted by 4.2 times (from 107.9 to$25.7 \mu $rad/h), and the angular noise of the ORDS is reduced by 2.4 times at 1–100 Hz. The measurement uncertainty of the realized ORDS nears the standard quantum limit, paving the road for long-term ultrasensitive measurements for new physics explorations.