Recoil-free spectroscopy of neutral Sr atoms in the Lamb-Dicke regime

We have demonstrated a recoil-free spectroscopy on the ${}^1S_0-{}^3P_1$ transition of strontium atoms confined in a one-dimensional optical lattice. By investigating the wavelength and polarization dependence of the ac Stark shift acting on the ${}^1S_0$ and ${}^3P_1(m_J=0)$ states, we determined the {\it magic wavelength} where the Stark shifts for both states coincide. The Lamb-Dicke confinement provided by this Stark-free optical lattice enabled the measurement of the atomic spectrum free from Doppler as well as recoil shifts.Comment: 5pages, 4figure

Elliptic Determinantal Process of Type A

We introduce an elliptic extension of Dyson's Brownian motion model, which is a temporally inhomogeneous diffusion process of noncolliding particles defined on a circle. Using elliptic determinant evaluations related to the reduced affine root system of types $A$, we give determinantal martingale representation (DMR) for the process, when it is started at the configuration with equidistant spacing on the circle. DMR proves that the process is determinantal and the spatio-temporal correlation kernel is determined. By taking temporally homogeneous limits of the present elliptic determinantal process, trigonometric and hyperbolic versions of noncolliding diffusion processes are studied.Comment: v5: AMS-LaTeX, 35 pages, no figure, references updated for publication in Probab. Theory Relat. Field