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Studies of Magneto-Optically and Magnetostatically Trapped Cesium in a Cryogenic Vacuum Apparatus

Phil A. Willems

Published Sep 9, 2026• 0 citations
Publisher

Abstract

The use of a cryogenic apparatus has several advantages for the magneto-optical and magnetostatic trapping of atoms. We have measured the lifetimes of magneto-optical and magnetostatic traps for cesium to be greatly increased in a cryogenic vacuum environment relative to a room-temperature vacuum environment, due to reduced background pressure and reduced mass and kinetic energy of background gas atoms. Another advantage of a cryogenic apparatus is that superconducting magnetic field coils can easily be used to generate very high magnetic field gradients for stronger confinement of the trapped atoms. We report the first measurements of the stability of MOT's at high magnetic field gradients and laser intensities, and compare the results to a model based on evaporation of atoms from the MOT using a Fokker-Planck equation approach. This model is more consistent with the data than an alternative model based on ejection of atoms by magnetic dipole forces. We also measure the dynamical parameters for magneto-optically trapped atoms at both high and low magnetic field gradients and with trapping laser intensities above saturation and compare the data to a simple physical model based on polarization gradient cooling. Consistent with measurements by other groups, the measured friction is consistent with the polarization gradient model, but the measured spring constant is drastically reduced and more consistent with the predictions of the Doppler theory.

DOI
10.7907/vw79-yj10

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The use of a cryogenic apparatus has several advantages for the magneto-optical and magnetostatic trapping of atoms. We have measured the lifetimes of magneto-optical and magnetostatic traps for cesium to be greatly increased in a cryogenic vacuum environment relative to a room-temperature vacuum environment, due to reduced background pressure and reduced mass and kinetic energy of background gas atoms. Another advantage of a cryogenic apparatus is that superconducting magnetic field coils can easily be used to generate very high magnetic field gradients for stronger confinement of the trapped atoms. We report the first measurements of the stability of MOT's at high magnetic field gradients and laser intensities, and compare the results to a model based on evaporation of atoms from the MOT using a Fokker-Planck equation approach. This model is more consistent with the data than an alternative model based on ejection of atoms by magnetic dipole forces. We also measure the dynamical parameters for magneto-optically trapped atoms at both high and low magnetic field gradients and with trapping laser intensities above saturation and compare the data to a simple physical model based on polarization gradient cooling. Consistent with measurements by other groups, the measured friction is consistent with the polarization gradient model, but the measured spring constant is drastically reduced and more consistent with the predictions of the Doppler theory.
We describe techniques for creating long-lived magneto-optical and magnetostatic traps for neutral atoms. These traps exist in a sealed cryogenic environment with a temperature near 4 K, where the background gas pressure can be extremely low. To date we have observed cesium magneto-optical traps with background-limited lifetimes in excess of 1 h, and magnetostatic traps with lifetimes of nearly 10 min. From these observations we use the known He-Cs van der Waals collision cross section to infer typical background gas pressures in our apparatus below 4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$ Torr. With hardware improvements we expect this pressure can be made much lower, extending the magnetostatic-trap lifetimes one to two orders of magnitude. Furthermore, with a cryogenic system one can use superconducting magnets and SQUID detectors to trap and to nondestructively sense spin-polarized atoms. With superconducting microstructures one can achieve very large magnetic-field gradients and curvatures, as high as \ensuremath{\sim}106{10}^{6}106 G/cm and \ensuremath{\sim}109{10}^{9}109 G/cm2{\mathrm{cm}}^{2}cm2, respectively, for use in magnetic and magneto-optical traps.
We report measurements of the stability of magneto-optical traps (MOTs) for neutral atoms in the limit of tight confinement of a single atom. For quadrupole magnetic field gradients at the trap center greater than $\ensuremath{\sim}1\mathrm{kG}/\mathrm{cm}$, we find that stochastic diffusion of atoms out of the trapping volume becomes the dominant particle loss mechanism, ultimately limiting the MOT size to greater than $\ensuremath{\sim}5\ensuremath{\mu}\mathrm{m}$. We measured and modeled the diffusive loss rate as a function of laser power, detuning, and field gradient for trapped cesium atoms. In addition, for as few as two atoms, the collisional loss rates become very high for tightly confined traps, allowing the direct observation of isolated two-body atomic collisions in a MOT.
We have constructed a Zeemanshift Optical Trap (ZOT) for neutral cesium atoms within a sealed cryostat cooled to 4.2K. The low residual background pressure of these temperatures, plus low velocities and masses of the background molecules (mostly He and H{sub 2}), leads to an exceptionally long holding time for trapped Cs atoms in the ZOT. In our initial attempts we measured trap holding times {approximately}5-10 minutes, but increasing this to several hours should be possible. Our latest experimental results will be presented. Long trap holding times may be useful for achieving a Bose condensed gas via evaporative cooling, since thermal relaxation times are fairly long and background gas collisions are therefore important. We are also beginning experiments to trap atoms with superconducting coils inside the cryostat. Our initial aim is to construct microscopic neutral atom traps and other structures with large magnetic field gradients (as high as 10{sup 8} G/cm), where the {triangledown}({rvec {mu}}{center_dot}{rvec B}) force is much greater than has been realized in previous trapping geometries.
In this work, we have explored ab initio the capture process in a magneto-optical trap by theory, simulation and experiment. We measured the capture velocity vc of a cesium vapor cell magneto-optical trap (VCMOT) from its capture rate R and developed an exact model for the capture rate of a VCMOT in terms of its capture velocity, background density and trap laser beam diameter. We measured the capture velocity of a cesium VCMOT for various trap laser intensities and magnetic field gradients. We observed that the capture velocity is a damping force as well as a restoring force phenomenon. We supported our findings by performing simulations for single atom trajectories in a 1D cesium MOT. Finally, we concluded that two MOTs can have the same capture velocities but very different capture rates, thereby revealing that these are two fundamentally different characteristics of the MOT.
Magneto-optical traps (MOTs) are a workhorse technology for neutral-atom quantum sensing, simulation, and computing. Here, we demonstrate a MOT optimized for inertial quantum sensing and precision metrology applications. Our MOT traps 4×1084\times10^84×108 cesium (Cs) atoms in a robust, modular system that achieves stable operation through two design features: (1) we use divergent cooling laser beams to reduce unwanted reflections and (2) optical elements are mounted in a fiber-coupled, compact, and modular cage rigidly attached to the vacuum chamber. Following polarization-gradient cooling (PGC), the system produces atom samples with temperatures below 10 μμμK, similar to those achieved in conventional MOTs that use collimated laser beams. In addition, we observe trapping of 2×1072\times10^72×107 Cs atoms in a non-conventional MOT geometry, where the cooling laser beams are diagonal to the principal axis of the quadrupole magnetic field.
Alkaline-earth-metal atoms present an ideal platform for exploring magneto-optic trap (MOT) dynamics, enabling unique and definitive tests of laser cooling and trapping mechanisms. We have measured the trapping beam intensity, detuning, magnetic-field gradient, trap density, and lifetime dependence of the spring constant $\ensuremath{\kappa}$ and damping coefficient $\ensuremath{\alpha}$ for a ${}^{1}{S}_{0}{\ensuremath{-}}^{1}{P}_{1}$ 88Sr{}^{88}\mathrm{Sr}88Sr MOT by fitting the oscillatory response of the atom cloud to a step-function force. We find that the observed behavior of $\ensuremath{\kappa}$ and $\ensuremath{\alpha}$ provide a unified and consistent picture of trap dynamics that agrees with Doppler cooling theory at the level of 1010%.10 Additionally, we demonstrate that the trapped atom temperature can be determined directly from measured value of $\ensuremath{\kappa}$ and the trap size, in excellent agreement with free-expansion temperature measurements. However, the experimentally determined temperature is much higher than Doppler cooling theory, implying significant additional heating mechanisms.