LAUSR

The deflection of an atomic beam in an inhomogeneous magnetic field, known as the Stern-Gerlach effect, is a textbook experiment [1] at the foundation of modern physics. In the original work [2], performed by Otto Stern and Walter Gerlach in 1922, a collimated beam of silver atoms was passed through a permanent, spatially varying magnetic field. The deflected trajectories, detected on a screen downstream, showed two distinct lines, thereby demonstrating the quantized nature of atomic angular momentum and the existence of electron spin. The effect has since found applications in atom optics [3–9], atom interferometry [10,11], and isotope separation [12]. The collimating slit used in the original experiment minimized the beam divergence expected from Maxwell’s equations, which forbid a purely one-dimensional magnetic field gradient. Creating a one-dimensional Stern-Gerlach effect has practical implications for the ability to control atoms with magnetic fields [13] and the design of “flat” mirrors capable of reflecting particles specularly without the dispersion of wave vectors [3–5]. Additionally, the proposed method of magneto-optical cooling, which relies on cycles of optical pumping and one-dimensional pulsed magnetic kicks, will compress atomic phase space one dimension at a time without loss of atoms [14]. Another exciting application is the ability to simulate microgravity conditions. Using a one-dimensional force to cancel gravity, one may conduct noncontact studies of levitated magnetic nanoparticles, improve loading of atoms into optical dipole traps [15], and further research of cold atoms in force-free environments without leaving Earth [16]. A one-dimensional Stern-Gerlach effect can be created if we consider a cloud of atoms, each with a magnetic dipole moment μ in the presence of a spatially dependent magnetic field B(r). Atoms will experience the combination of rectilinear motion and precession of the magnetic moment caused by the force ∇(μ · B) and torque μ × B, respectively. For sufficiently fast precession ( 100 MHz for fields greater than 10 G), an adiabatic approximation is valid in which the magnetic moment is taken as always parallel to the magnetic field. In this approximation the average force F = μ∇|B| determines the motion of each atom, which indicates the existence of magnetic field configurations that provide an approximately