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Optics Express

Nonlinear focusing of atom clouds by a short-focal-length magnetic lens

Jing Wang, Ziqian Wang, Shan Hua, Yu Wang, Xiaolong Wang, Gewen Sun, Xiaoming Tang, Shuangquan Wang, Zixing Jin, Chenjie Zhai, Bin Wu, Bing Cheng, Helin Wang, Yin Xiu Zhou, Kanxing Weng, Qunli Zhang, Qiang Lin

Published Jun 13, 2025• 0 citations
Publisher

Abstract

Utilizing the Stern-Gerlach effect, magnetic lenses are used to focus atom clouds, reducing their dimensions, and boosting the central cloud density. In this research, a theoretical model based on nonlinear Zeeman splitting in high-intensity magnetic fields is established to explore the nonlinear focusing of a tightly focused magnetic lens. The research concentrates on the motion and focusing of 87 Rb atoms in various Zeeman substates within an atom fountain under pulsed magnetic fields and establishes a correlation between the field curvature and the effective focal length. The nonlinear model has been validated in the experiment conducted in the fountain. Atoms in different Zeeman substates were selectively focused by the magnetic lens which has applications in precise manipulation of atoms including collimation, concentration, and spatial filtering. A spatial filter based on this method has been deployed in the phase-shear atomic interferometer to prepare an atom cloud in a pure Zeeman substate.

DOI
10.1364/oe.566614

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Utilizing the Stern-Gerlach effect, magnetic lenses are used to focus atom clouds, reducing their dimensions, and boosting the central cloud density. In this research, a theoretical model based on nonlinear Zeeman splitting in high-intensity magnetic fields is established to explore the nonlinear focusing of a tightly focused magnetic lens. The research concentrates on the motion and focusing of 87 Rb atoms in various Zeeman substates within an atom fountain under pulsed magnetic fields and establishes a correlation between the field curvature and the effective focal length. The nonlinear model has been validated in the experiment conducted in the fountain. Atoms in different Zeeman substates were selectively focused by the magnetic lens which has applications in precise manipulation of atoms including collimation, concentration, and spatial filtering. A spatial filter based on this method has been deployed in the phase-shear atomic interferometer to prepare an atom cloud in a pure Zeeman substate.
In an atomic fountain, atoms in motion can be spatially separated into discrete Zeeman sub-states by magnetically induced Stern-Gerlach effect. With resonant light pulses acting as a shutter, specific states are selected for subsequent experiments. Such separation-selection process in atomic optics is the analogue of a spatial filter in physical optics which selects and purifies the modes of light. This technique is demonstrated by injecting a pulsed current in a circular coil around a vertical atomic fountain, separating the pre-cooled Rubidium atoms by a distance of centimeters in between, and filtering each single sub-state with block pulses. The filtered atoms after the process is highly purified in the desired sub-state. The apparatus of the atomic spatial filter is adaptable in atomic optics and can be integrated into the high-vacuum chamber of an atomic fountain.
The loading and guiding of a launched cloud of cold atoms with the optical dipole force are theoretically and numerically modelled. A far-off resonance trap can be realised using a high power Gaussian mode laser, red-detuned with respect to the principal atomic resonance (Rb 5s-5p). The optimum strategy for loading typically 30% of the atoms from a Magneto optical trap and guiding them vertically through 22 cm is discussed. During the transport the radial size of the cloud is confined to a few hundred microns, whereas the unconfined axial size grows to be approximately 1 cm. It is proposed that the cloud can be focused in three dimensions at the apex of the motion by using a single magnetic impulse to achieve axial focusing. A theoretical study of six current-carrying coil and bar arrangements that generate magnetic lenses is made. An investigation of focusing aberrations show that, for typical experimental parameters, the widely used assumption of a purely harmonic lens is often inaccurate. A new focusing regime is discussed: isotropic 3D focusing of atoms with a single magnetic lens. The baseball lens offers the best possibility for isotropically focusing a cloud of weak-field-seeking atoms in 3D.A pair of magnetic lens pulses can also be used to create a 3D focus (the alternate-gradient method). The two possible pulse sequences are discussed and it is found that they are ideal for loading both 'pancake' and 'sausage’ shaped magnetic/optical microtraps. It is shown that focusing aberrations are considerably smaller for double-impulse magnetic lenses compared to single- impulse magnetic lenses. The thesis concludes by describing the steps taken towards creating a 3D quasi- electrostatic lattice for 85Ilb， using a CՕշ laser. The resulting lattice of trapped atoms will have a low decoherence, and with resolvable lattice sites, it therefore provides a useful system to implement quantum information processing.
Summary form only given. Spatial coherences are measured by means of a new atom interferometry technique. First, a coherent superposition of the Zeeman components of the atom is built by means of well-controlled magnetic interactions. Second, pulsed inhomogeneous magnetic fields are employed to coherently separate and reunite the atomic substates via the Stern-Gerlach induced forces. Finally, atomic interference fringes are recorded on the state-selected outcoming sample by changing the spatial separation. This method bears strong similarities with the Fourier-transform spectroscopy of light. The interferogram visibility curve yields the atom sample spatial coherences. For example, when the applied magnetic gradients are parallel to the atom trajectory, one gets the coherence length by varying the overlap of the separated wavepackets. Several experiments on cold cesium atoms have been performed and are presented. Furthermore, we have used our magnetic cooling method to prepare the atom cloud upstream from the interferometer. Large enhancements of the coherence length are demonstrated.
An atom interferometer based on a Stern-Gerlach beam splitter is proposed. Atom scattering from a combination of magnetic quadrupole and homogeneous magnetic fields is considered. Using Raman transitions, atoms are coherently excited into and de-excited from sublevels having nonzero magnetic quantum numbers. The spatial regions in which the atoms are in such sublevels are small and have magnetic fields designed to have constant gradients. Therefore, the atoms experience position-independent accelerations, and the aberration of the coherently separated and recombined atomic beams remains small. We find that because of these properties it is possible to envision an apparatus producing atomic density gratings with nm-scale periods and large contrasts over 10-100 μμμm. We use a new method of describing the atomic interaction with a pulsed spatially homogeneous field. In our detailed analysis, we calculate corrections caused by the non-linear part of the potential and the finite value of the de-Broglie wave length. The chromatic aberration and the effects of an angular beam divergence are analyzed, and optimal conditions for an experimental demonstration of the technique are identified.%The lin⊥lin\bot %linlin⊥ combination of resonant co-propagating traveling waves splits %atoms between different Zeeman sublevels. %For a given desirable atom %grating period and length, characteristics of the atomic beam and %magnetic field are found from requirements that corrections remain %below 1010%.10
We have theoretically investigated the focusing of a launched cloud of cold atoms. Time-dependent spatially-varying magnetic fields are used to impart impulses leading to a three-dimensional focus of the launched cloud. We discuss possible coil arrangements for a new focusing regime: isotropic 3D focusing of atoms with a single-impulse magnetic lens. We investigate focusing aberrations and find that, for typical experimental parameters, the widely used assumption of a purely harmonic lens is often inaccurate. The baseball lens offers the best possibility for isotropically focusing a cloud of weak-field-seeking atoms in 3D.