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Applied Physics Letters

Precise control of launch velocity vector for cold atomic cloud based on moving optical molasses

Yao Li, Zhiyi Liu, Yu Hu, Jingfeng Xiang, Desheng Lü, Wei Ren, Rong Wei

Published May 25, 2026• 1 citation
Publisher

Abstract

We propose a method for precise control of the launch velocity vector of a cold atomic cloud. By independently adjusting the relative detuning of three pairs of orthogonal counter-propagating laser beams in moving optical molasses, this method achieves accurate regulation of three-dimensional velocity components, thereby realizing precise calibration of atomic launch direction. It can significantly reduce the complexity of mechanical adjustments and mitigate residual errors caused by mechanical tuning, with the advantages of simplicity and easy implementation. Experimental verification on an 87Rb atomic fountain clock shows that the spatial distribution of the cold atomic cloud is obtained via horizontal velocity scanning, and the tilt deviation of the fountain clock is evaluated and corrected. Ultimately, the angles between the cold atom launch direction, the central axis of the fountain clock, and the vertical direction are all less than 0.1 mrad. Time-of-flight signal analysis indicates that under 3% laser power fluctuation, the long-term instability (5000 s) of the velocity reaches 62 μm/s. This method holds significant application value for atomic fountains, atomic gravimeters, atomic gyroscopes, and other cold atomic precision instruments based on moving molasses.

DOI
10.1063/5.0333698

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We propose a method for precise control of the launch velocity vector of a cold atomic cloud. By independently adjusting the relative detuning of three pairs of orthogonal counter-propagating laser beams in moving optical molasses, this method achieves accurate regulation of three-dimensional velocity components, thereby realizing precise calibration of atomic launch direction. It can significantly reduce the complexity of mechanical adjustments and mitigate residual errors caused by mechanical tuning, with the advantages of simplicity and easy implementation. Experimental verification on an 87Rb atomic fountain clock shows that the spatial distribution of the cold atomic cloud is obtained via horizontal velocity scanning, and the tilt deviation of the fountain clock is evaluated and corrected. Ultimately, the angles between the cold atom launch direction, the central axis of the fountain clock, and the vertical direction are all less than 0.1 mrad. Time-of-flight signal analysis indicates that under 3% laser power fluctuation, the long-term instability (5000 s) of the velocity reaches 62 μm/s. This method holds significant application value for atomic fountains, atomic gravimeters, atomic gyroscopes, and other cold atomic precision instruments based on moving molasses.
Laser-cooled low-velocity (v < 10 m/s) atomic beams have been considered to be feasible cold atom sources in developing compact and highly stable atomic clocks for satellite applications. A cold atomic beam can be realized by laser-accelerating an ensemble of ultracold (T < 1 mK) atoms from a laser-cooled magneto-optical trap (MOT). This technique has the unique advantage of generating a useful cold atomic beam just outside the volume of a MOT and, hence, can greatly reduce the size of the atomic clock physics package. In this paper, we present our design and experimental results towards demonstration of a MOT-based cold Cs beam atomic clock. We have generated a continuous cold Cs beam from a Cs MOT and have determined the typical longitudinal velocity of the Cs beam by Time of Flight (TOF) method to be 7 m/s with a velocity spread of 1 m/s. By adjusting the MOT parameters, the atomic beam velocity can be tuned continuously, with the velocity spread remaining to be 1 m/s. In order to separate the atomic beam from the MOT laser beam, we have used a one-dimensional optical molasses to efficiently deflect the cold Cs beam through an angle of 30 degrees. The 1-D optical molasses is set up in such a way that the molasses laser beams are perpendicular to the final atomic beam propagation path. Thus, the Cs-beam velocity components along the molasses axis are efficiently damped to nearly zero, while the Cs velocity component along the final atomic beam propagation path is unaffected. Our simulation indicates that a deflection efficiency of 100% is achievable for MOT-based cold atomic beams. Our cold Cs beam has an instantaneous atomic flux of 3.6 10 (exp 10) atoms/s when operated in pulsed mode and an estimated continuous beam flux of 2 10 (exp 8) atoms/s.
By the moving molasses technique we have extracted laser-cooled cesium atoms in a continuous way directly from an optical molasses. The mean launching velocity is precisely tunable from 1 to 12 m/s. The atomic beam has a flux of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{8} \mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}/\mathrm{s}$ at 7 m/s and a longitudinal temperature of $70 \ensuremath{\mu}\mathrm{K},$ which represents the highest flux and lowest velocity spread obtained so far in a continuous beam of cold atoms. These features makes it well suited for atomic fountains. The atomic flux can be slightly increased in a two-dimensional magneto-optical trap operation (+40(+40%).(+40 A simple model accounts for the observed dependence of the flux with the magnetic-field gradient.
We demonstrate launching of laser-cooled Yb atoms in a continuous atomic beam. The continuous cold beam has significant advantages over the more-common pulsed fountain, which was also demonstrated by us recently. The cold beam is formed in the following steps---(i) Atoms from a thermal beam are first Zeeman slowed to a small final velocity, (ii) the slowed atoms are captured in a two-dimensional magneto-optic trap (2D-MOT), and (iii) atoms are launched {\em continuously} in the vertical direction using two sets of moving-molasses beams, inclined at ±15∘\pm 15^\circ±15∘ to the vertical. The cooling transition used is the strongly-allowed 1S0→1P1{^1S}_0 \rightarrow {^1P}_11S0​→1P1​ transition at 399 nm. We capture about 7×1067 \times 10^67×106 atoms in the 2D-MOT, and then launch them with a vertical velocity of 13 m/s at a longitudinal temperature of 125(6) mK.
Accurately measuring the three-dimensional position of an atomic cloud is essential for improving the precision of atom interferometers. In the work presented here, the three-dimensional position of an atomic cloud in an atom interferometer is measured with only one laser beam, generated by a phase modulator. The vertical position is determined from the change in the additional-sideband effect with the time interval TTT between adjacent Raman pulses in the atom interferometer. Based on this method, the vertical position of the atomic cloud is measured with an uncertainty of 0.2 mm; therefore, the uncertainty in a gravity measurement contributed by the gravity gradient is not limited by the uncertainty in the measurement of the vertical position at the level of $0.1\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{Gal}$. Furthermore, a method of measuring Rabi oscillations at different horizontal positions to determine the horizontal position of the atomic cloud is proposed and is demonstrated experimentally. With this method, the horizontal position can be determined with an uncertainty of less than 0.1 mm, and the horizontal velocity of the atomic cloud can also be deduced. The methods demonstrated in this paper are helpful for evaluating systematic errors in atom interferometers, and also useful in precision measurements based on an atomic fountain.
We have measured the temperature of cesium atoms released from optical molasses. For a wide range of laser intensity and detuning from resonance, the temperature depends only on the intensity to detuning ratio. The lowest temperature achieved is 2.5±0.6 μK, which corresponds to an rms velocity of 12.5 mm/s or 3.6 times the single‐photon recoil velocity. This is, to our knowledge, the coldest kinetic temperature ever measured for three dimensional (3D) cooling. We then discuss the possibility of using such a cold sample of atoms for realizing a high performance atomic clock in a fountain geometry. In particular, a method for launching the atoms upwards, while maintaining the very cold temperature, is demonstrated.
The Gaussian radius and temperature of cold atomic cloud are important parameters in describing the state of cold atoms. The precise measuring of these two parameters is of great significance for studying the cold atoms. In this paper, we propose a new method named knife-edge to measure the Gaussian radius and temperature of the cold atomic cloud. A near-resonant and supersaturated laser beam, whose size is controlled by a knife-edge aperture, is used to push away the cold atoms in the free falling process of cold atomic cloud. By detecting the intensity of fluorescence signal, the numbers of residual atoms under different-sized near-resonant beams can be obtained. According to the characteristic of cold atoms′ distribution, we construct a theoretical model to derive the Gaussian radius of cold atomic cloud from the recorded residual atom number and near-resonant beam size. Since the Gaussian radius and temperature of cold atomic cloud are associated with each other, we can finally obtain the temperature of cold atomic cloud through the recorded residual atom number and beam size. By using this method, we successfully measure the Gaussian radii of cold atomic cloud at the heights of 10 mm and 160 mm below the center of 3D-MOT (three dimensional magneto-optical trap) to be (1.54 ± 0.05) mm and (3.29 ± 0.08) mm, respectively. The corresponding temperature of cold atomic cloud is calculated to be (7.50 ± 0.49) μK, which is well consistent with the experimental result obtained by using the time-of-flight method under the same condition. This experiment is conducted on the platform of Cesium atomic fountain clock of National Time Service Center, China.