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arXiv:2304.12716 · Physical Review Applied

Calibrating the Absorption Imaging of Cold Atoms under High Magnetic Fields

Yuqi Liu, Zhongchi Zhang, Shiwan Miao, Zihan Zhao, Huaichuan Wang, Wenlan Chen, Jiazhong Hu

Published Jul 18, 2023• 6 citations
arXivHTMLPDF

Abstract

We develop a theoretical model for calibrating the absorption imaging of cold atoms under high magnetic fields. Particularly it also works when the hyperfine structure is decoupled and cannot provide good quantum numbers anymore. Compared with zero or low magnetic fields, for high magnetic fields the efficiency of the absorption imaging is lower, while an additional correction factor is required to obtain the absolute atom number under the Beer-Lambert law. Our model is based on the rate equations and can account for many experimental imperfections, such as Zeeman level crossing, off-resonant couplings, and low repumping efficiency. On the basis of this method, we can precisely calculate the correction factor for atom-number measurement without any empirical or fitting parameters. Meanwhile, we use a cold-atom apparatus based on ${}^{85}\mathrm{Rb}$ to experimentally verify our model. In addition, we find our work can also serve as a benchmark to measure the polarization impurity of a circularly polarized laser beam with high sensitivity. We believe this work will be beneficial for most cold-atom experiments using absorption imaging.

DOI
10.1103/physrevapplied.20.014037

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We develop a theoretical model for calibrating the absorption imaging of cold atoms under high magnetic fields. Particularly it also works when the hyperfine structure is decoupled and cannot provide good quantum numbers anymore. Compared with zero or low magnetic fields, for high magnetic fields the efficiency of the absorption imaging is lower, while an additional correction factor is required to obtain the absolute atom number under the Beer-Lambert law. Our model is based on the rate equations and can account for many experimental imperfections, such as Zeeman level crossing, off-resonant couplings, and low repumping efficiency. On the basis of this method, we can precisely calculate the correction factor for atom-number measurement without any empirical or fitting parameters. Meanwhile, we use a cold-atom apparatus based on 85Rb{}^{85}\mathrm{Rb}85Rb to experimentally verify our model. In addition, we find our work can also serve as a benchmark to measure the polarization impurity of a circularly polarized laser beam with high sensitivity. We believe this work will be beneficial for most cold-atom experiments using absorption imaging.
Two methods of absorption imaging to detect cold atoms in a magnetic trap are implemented for a high-precision cold atom interferometer. In the first method, a probe laser which is in resonance with a cycle transition frequency is used to evaluate the quantity and distribution of the atom sample. In the second method, the probe laser is tuned to an open transition frequency, which stimulates a few and constant number of photons per atom. This method has a shorter interaction time and results in absorption images which are not affected by the magnetic field and the light field. We make a comparison of performance between these two imaging methods in the sense of parameters such as pulse duration, light intensity, and magnetic field strength. The experimental results show that the second method is more reliable when detecting the quantity and density profiles of the atoms. These results fit well to the theoretical analysis.
Abstract Cold atom experiments often use images of the atom clouds as their exclusive source of experimental information. The most commonly used technique is absorption imaging, which provides accurate information about the shapes of the atom clouds, but requires care when seeking the absolute atom number for small atom samples. In this paper, we present an independent, absolute calibration of the atom numbers. We directly compare the atom number detected using dark-ground imaging to the one observed by fluorescence imaging of the same atoms in a magneto-optical trap. We normalise the signal using single-atom resolved fluorescence imaging. In order to be able to image the absorption of the very low atom numbers involved, we use diffractive dark-ground imaging as a novel, ultra-sensitive method of in situ imaging for untrapped atom clouds down to only 100 atoms. We demonstrate that the Doppler shift due to the acceleration of the atoms by the probe beam has to be taken into account when measuring the atom-number.
Abstract Absorption imaging is a fundamental technique for quantitatively extracting information from ultracold atom experiments. Since ultracold 6Li atoms are prepared and detected under high magnetic fields, the suitable detuning of the probe light can reach the GHz level compared to zero-field imaging. Therefore, based on the energy level structure of 6Li atoms and the requirements of subsequent experiments, we design a high-field imaging system with a large frequency range and good robustness, starting from the rationality of the optical layout design and employing offset locking techniques. This imaging system covers the entire crossover region from Bose–Einstein condensate to Bardeen–Cooper–Schrieffer (BEC–BCS) and realizes free switching between zero-field and high-field imaging. Additionally, by introducing a proportionality coefficient to correct for the intensity fluctuations of the probe light, we mitigate its disturbance on the statistical measurement of particle numbers in the experiment. This work not only provides a design reference for other quantum gas experiments requiring absorption imaging under strong bias magnetic fields, but also serves as an important reference for improving the imaging performance.
Cold atom states are prepared by laser cooling, evaporation cooling and other cooling methods to cool down the atoms close to almost absolute zero in temperature. As a popular research frontier of quantum physics, cold atom physics has been developed to explore, study and measure the spin degrees of freedom in atoms. The precise measurement of the rich quantum magnetism presented by the hyperfine structure of the internal spin freedom is undoubtedly of great significance to basic physics and the innovation of new technologies. With the advantages of microgravity environment and the creation of new extreme conditions, cold atom experimentalists can achieve long-time precision measurement and ultra-low temperature of pK level which is not viable on the ground. The manipulation and precision measurement of quantum magnetism can break through the gravitational limit and reach new parameter regions. In this paper, we review the principles, devices and schemes of cold atom experiments in ground and microgravity environment, the transfer between Zeeman states with different magnetic quantum numbers, magnetic phase transition, time-of-flight imaging and phase contrast imaging. As for the precise measurement, two aspects are emphasized: the deep cooling of atoms under microgravity and the use of non-destructive phase contrast imaging.
Absorption imaging of ultracold atoms is the foundation for quantitative extraction of information from experiments with ultracold atoms. Due to the limited exposure time available in these systems, the signal-to-noise ratio is largest for high intensity absorption imaging where the intensity of the imaging light is on the order of the saturation intensity. In this case, the absolute value of the intensity of the imaging light enters as an additional parameter making it more sensitive to systematic errors. Here, we present a novel and robust technique to determine the imaging beam intensity in units of the effective saturation intensity to better than 5%. We do this by measuring the momentum transferred to the atoms by the imaging light while varying its intensity. We further utilize the method to quantify the purity of the polarization of the imaging light and to determine the correct imaging detuning.
We investigate experimentally and theoretically the Faraday effect in an atomic medium in the hyperfine Paschen–Back regime, where the Zeeman interaction is larger than the hyperfine splitting. We use a small permanent magnet and a micro-fabricated vapour cell, giving magnetic fields of the order of a tesla. We show that for low absorption and small rotation angles, the refractive index is well approximated by the Faraday rotation signal, giving a simple way to measure the atomic refractive index. Fitting to the atomic spectra, we achieve magnetic field sensitivity at the 10−4 level. Finally we note that the Faraday signal shows zero crossings which can be used as temperature insensitive error signals for laser frequency stabilization at large detuning. The theoretical sensitivity for 87Rb is found to be ∼40 kHz °C−1.