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 $μ$m. 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 $lin\bot %lin$ 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 $10%.$
We demonstrate qubit state measurement for ~160 Cesium atoms in a 3D optical lattice based on coherent spatial splitting of the atoms' wavefunctions. The measurement fidelity is 0.9994, essentially independent of the number of qubits measured. The detection scheme is reminiscent of the Stern-Gerlach experiment, but carried out in light traps. The measurement causes no loss, which allows us to demonstrate re-initialization of the 3D qubit array after state measurement, including the replacement of an atom lost to a background gas collision.
The Zeeman hyperfine state dependent force in a Stern-Gerlach (SG) experiment has been exploited to separate and detect atoms having different Zeeman hyperfine states in a cold atom cloud. Utilizing this SG technique, we have made the quantitative estimate of atoms in different Zeeman hyperfine states in an atom cloud, which has been helpful in optimizing the optical pumping of atoms for efficient preparation of atomic state. Employing an optimized optical pumping, nearly $92 \% $ of cold $^{87}Rb$ atoms from a grey magneto-optical trap (G-MOT) on atom-chip have been optically pumped to the tr…
We show that the inclusion of counter rotating terms, usually dropped, in the interaction Hamiltonian of the electric dipole of a two level atom with an electromagnetic field leads to significant modification of the splitting of an atomic beam known as Optical Stern Gerlach Effect which now acquires a fine structure.
We present a unique matter-wave interferometer whose phase scales with the cube of the time the atom spends in the interferometer. Our scheme is based on a full-loop Stern-Gerlach interferometer incorporating four magnetic field gradient pulses to create a state-dependent force. In contrast to typical atom interferometers which make use of laser light for the splitting and recombination of the wave packets, this realization uses no light and can therefore serve as a high-precision surface probe at very close distances.
We present a feasibility study with several magnetic field configurations for creating spin-dependent forces that can split a low-energy ion beam by the Stern-Gerlach effect. To the best of our knowledge, coherent spin-splittings of charged particles have yet to be realised. Our proposal is based on ion source parameters taken from a recent experiment that demonstrated single-ion implantation from a high-brightness ion source combined with a radio-frequency Paul trap. The inhomogeneous magnetic fields can be created by permanently magnetised microstructures or from current-carrying wires with …
We numerically study the spin flip in the Frisch$\unicode{x2013}$Segrè experiment, the first multi-stage Stern$\unicode{x2013}$Gerlach experiment, within the context of the novel co-quantum dynamics theory. We model the middle stage responsible for spin rotation by sampling the atoms with the Monte Carlo method and solving the dynamics of the electron and nuclear magnetic moments numerically according to the Bloch equation. Our results show that, without using any fitting parameters, the co-quantum dynamics closely reproduces the experimental observation reported by Frisch and Segrè in 1933, w…
Atomic interferometers have been studied as a promising device for precise sensing of external fields. Among various configurations, a particular configuration with a butterfly-shaped geometry has been designed to sensitively probe field gradients. We introduce a Stern-Gerlach (SG) butterfly interferometer by incorporating magnetic field in the conventional butterfly-shaped configuration. Atomic trajectories of the interferometer can be flexibly adjusted by controlling magnetic fields to increase the sensitivity of the interferometer, while the conventional butterfly interferometer using Raman…
In this invited review in honor of 100 years since the Stern-Gerlach (SG) experiments, we describe a decade of SG interferometry on the atom chip. The SG effect has been a paradigm of quantum mechanics throughout the last century, but there has been surprisingly little evidence that the original scheme, with freely propagating atoms exposed to gradients from macroscopic magnets, is a fully coherent quantum process. Specifically, no full-loop SG interferometer (SGI) has been realized with the scheme as envisioned decades ago. Furthermore, several theoretical studies have explained why it is a f…
We combine the Ramsey interferometry protocol, the Stern-Gerlach detection scheme, and the use of elongated geometry of a cloud of fully polarized cold cesium atoms to measure the selected component of the magnetic field gradient along the atomic cloud in a single shot. In contrast to the standard method where the precession of two spatially separated atomic clouds is simultaneously measured to extract their phase difference, which is proportional to the magnetic field gradient, we here demonstrate a gradiometer using a single image of an expanding atomic cloud with the phase difference imprin…
We describe the design, assembly, and testing of a magnet intended to deflect beams of paramagnetic nanoclusters, molecules, and atoms. It is energized by high-grade permanent neodymium magnets. This offers a convenient option in terms of cost, portability, and scalability of the construction, while providing field and gradient values (1.1 T, 330 T/m) which are fully comparable with commonly used electromagnet deflectors.
We analyze idealized sequential Stern-Gerlach experiments with higher spin particles. This analysis serves at least two purposes: The widely discussed spin-1/2 case leads to some misunderstandings which hopefully is removed by the higher spin discussion. Secondly, Wigner rotation matrices for generic spins become conceptually more transparent with this physical example. We also give compact formulas for the probabilities in terms of the angle between the sequential SG apparatuses for generic spins. We work out the spin-$1/2$, spin-$1$ and spin-$2$ cases explicitly. Since there are some confusi…
Electromagnetically induced transparency allows for light transmission through dense atomic media by means of quantum interference. Media exhibiting electromagnetically induced transparency have very interesting properties, such as extremely slow group velocities. Associated with the slow light propagation are quasiparticles, the so-called dark polaritons, which are mixtures of a photonic and an atomic contribution. We here demonstrate that these excitations behave as particles with a nonzero magnetic moment, which is in clear contrast to the properties of a free photon. It is found that light…
The Stern-Gerlach (SG) effect, discovered almost a century ago, has become a paradigm of quantum mechanics. Surprisingly there is little evidence that the original scheme with freely propagating atoms exposed to gradients from macroscopic magnets is a fully coherent quantum process. Specifically, no high-visibility spatial interference pattern has been observed with such a scheme, and furthermore no full-loop SG interferometer has been realized with the scheme as envisioned decades ago. On the contrary, numerous theoretical studies explained why it is a near impossible endeavor. Here we demons…
We demonstrate the non-dispersive deflection of an optical beam in a Stern-Gerlach magnetic field. An optical pulse is initially stored as a spin-wave coherence in thermal rubidium vapour. An inhomogeneous magnetic field imprints a phase gradient onto the spin wave, which upon reacceleration of the optical pulse leads to an angular deflection of the retrieved beam. We show that the obtained beam deflection is non-dispersive, i.e. its magnitude is independent of the incident optical frequency. Compared to a Stern-Gerlach experiment carried out with propagating light under the conditions of elec…
A spin-polarizing electron beam splitter is described which relies on an arrangement of linearly polarized laser waves of nonrelativistic intensity. An incident electron beam is first coherently scattered off a bichromatic laser field, splitting the beam into two portions, with electron spin and momentum being entangled. Afterwards, the partial beams are coherently superposed in an interferometric setup formed by standing laser waves. As a result, the outgoing electron beam is separated into its spin components along the laser magnetic field, which is shown by both analytical and numerical sol…
It is proved that, according to Classical Mechanics and Electrodynamics, the trajectory of the center of mass of a neutral system of electrical charges can be deflected by an inhomogeneous magnetic field, even if its internal angular momentum is zero. This challenges the common view about the function of the Stern-Gerlach apparatus, as resolving the eigen-states of an intrinsic angular momentum. Doubts are cast also on the supposed failure of Schrodinger's theory to explain the properties of atoms in presence of magnetic fields without introducing spin variables.
