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 formidable challenge. Here we provide a review of our SG experiments over the last decade. We describe several novel configurations such as that giving rise to the first SG spatial interference fringes, and the first full-loop SGI realization. These devices are based on highly accurate magnetic fields, originating from an atom chip, that ensure coherent operation within strict constraints described by previous theoretical analyses. Achieving this high level of control over magnetic gradients is expected to facilitate technological applications such as probing of surfaces and currents, as well as metrology. Fundamental applications include the probing of the foundations of quantum theory, gravity, and the interface of quantum mechanics and gravity. We end with an outlook describing possible future experiments.

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We describe and characterize alternative configurations for Doppler-free polarization spectroscopy. The suggested apparatus enables complete pump/probe beam overlap and allows substantial miniaturization. Its utility and performance for narrow linewidth, high-stability frequency locking is discussed for the /5S(1/2)F=2>-->/5P(3/2)F(')>D(2) transition in (87)Rb.

We analyze theoretically and experimentally the existence of a magic frequency for which the absorption of a linearly polarized light beam by vapor alkali atoms is independent of the population distribution among the Zeeman sub-levels and the angle between the beam and a magnetic field. The phenomenon originates from a peculiar cancelation of the contributions of higher moments of the atomic density matrix, and is described using the Wigner-Eckart theorem and inherent properties of Clebsch-Gordan coefficients. One important application is the robust measurement of the hyperfine population.PACS numbers: 32.10. Fn,32.70.Cs, 42.25.Bs Interaction of light with alkali metal vapor has an important role both in the study of fundamental physics and in many technological applications. Macroscopic entanglement was demonstrated using cesium vapor cells [1]; Pulses of light, as well as images, were stored in rubidium vapor [2,3]; Rubidium vapor cells serve as a basis for chip-scale atomic clocks [4]; and alkali vapor cells are used for high sensitivity optical magnetometry [5,6]. More applications can be found in [7][8][9][10].The density matrix representing the state of an alkali vapor in a specific hyperfine state |F can be expanded in terms of polarization moments (PM). A PM ρ (κ) is an irreducible spherical tensor of rank κ (0 ≤ κ ≤ 2F + 1) whose components are given by [10]:where q = −κ...κ, m 1 and m 2 are the magnetic quantum numbers, ρ m1,m2 are the density matrix elements and F, m 2 , F, −m 1 |κ, q are the Clebsch-Gordan coefficients (CGC). The PMs of ranks κ = 0, 1 and 2 are proportional to the population, the dipole moment (or orientation), and the quadrupole moment (or alignment), of the relevant |F state, respectively [10][11][12][13]. For a full mapping of the density matrix it is essential to measure the hyperfine population ρ (0) . While unpolarized light from lamps [14][15][16] or polarized light from lasers [17] were previously used to optically pump atomic vapor and monitor its relaxation process, these measurements had limited accuracy in estimating the hyperfine population.Here we demonstrate for the first time the existence of a magic frequency for which the light absorption of linearly polarized laser radiation is independent of the population distribution among the Zeeman sub-levels and of the angles between the light and the magnetic field. At the magic frequency the absorption is proportional only to ρ (0) and can therefore serve as an accurate and robust measure of the hyperfine population.In general, different Zeeman sub-levels |F, m F have At these frequencies, the absorption from all Zeeman sublevels is equal, namely, the overall absorption depends only on the total population in the hyperfine state, and is independent of the internal population distribution. Plotted is a ∆ΓF surface, proportional to the differences of the absorption rates of light (D2 line) by 87 Rb atoms (T = 295K) in different Zeeman sub-levels of the |F = 2 hyperfine state [Eq. (7)], for a small external DC magnetic fiel...

We report two novel effects in an inhomogeneous ensemble of two-level systems driven by an external field. First, we observe a rigidity of the oscillation frequency: the dominant Rabi oscillation frequency does not change with the frequency of the driving field, in contrast to the well-known law of Rabi frequency increase with growing detuning of the driving field. Second, we observe a timedependent frequency shift of the ensemble-averaged oscillation. We show that these effects follow from the inhomogeneity of the two-level splitting across the ensemble, allowing for a distribution of local oscillations in which those with high frequencies interfere destructively and decay faster than those with a low frequency, which are the only to survive in the output signal. Hence, coherence emerges from long-lived oscillations in an inhomogeneous ensemble. We analyze the Fourier spectrum of the time-dependent oscillation signal and find a non-trivial spectral structure that is double peaked for certain parameters. We show that the effects observed in alkali vapor are universal and expected in any system with a moderate inhomogeneity driven by an external field. arXiv:1803.00797v2 [quant-ph]