Magnetic trapping of metastable 3P2^3P_2 atomic strontium

We report the magnetic trapping of metastable $^3P_2$ atomic strontium. Atoms are cooled in a magneto-optical trap (MOT) operating on the dipole allowed $^1S_0-^1P_1$ transition at 461 nm. Decay via $^1P_1\to {^1D_2}\to {^3P_2}$ continuously loads a magnetic trap formed by the quadrupole magnetic field of the MOT. Over $10^8$ atoms at a density of $8 \times 10^9$ cm$^{-3}$ and temperature of 1 mK are trapped. The atom temperature is significantly lower than what would be expected from the kinetic and potential energy of atoms as they are transferred from the MOT. This suggests that thermalization and evaporative cooling are occurring in the magnetic trap.Comment: This paper has been accepted by PR

Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality

The Fourier transform is often used to connect the Lorentzian energy distribution for resonance scattering to the exponential time dependence for decaying states. However, to apply the Fourier transform, one has to bend the rules of standard quantum mechanics; the Lorentzian energy distribution must be extended to the full real axis $-\infty<E<\infty$ instead of being bounded from below $0\leq E <\infty$ (``Fermi's approximation''). Then the Fourier transform of the extended Lorentzian becomes the exponential, but only for times $t\geq 0$, a time asymmetry which is in conflict with the unitary group time evolution of standard quantum mechanics. Extending the Fourier transform from distributions to generalized vectors, we are led to Gamow kets, which possess a Lorentzian energy distribution with $-\infty<E<\infty$ and have exponential time evolution for $t\geq t_0 =0$ only. This leads to probability predictions that do not violate causality.Comment: 23 pages, no figures, accepted by Phys. Rev.

High-resolution Spectroscopy With Femtosecond Optical Combs

A stabilized femtosecond frequency comb has ∼106 stable optical modes spanning hundreds of terahertz, making it an ideal tool for high-resolution spectroscopy. We demonstrate some features of frequency-comb spectroscopy using experiments involving calcium and cesium. © OSA.Oskay, W.H., Diddams, S.A., Donley, E.A., Fortier, T.M., Heavner, T.P., Hollberg, L., Itano, W.M., Bergquist, J.C., Single-atom optical clock with high accuracy (2006) Phys. Rev. Lett, 97, pp. 020801/1-020801/4Fortier, T.M., Bartels, A., Diddams, S.A., Octave-spanning Ti:sapphire laser with a repetition rate >1 GHz for optical frequency measurements and comparisons (2006) Opt. Lett, 31, pp. 1011-1013Jones, D.J., Diddams, S.A., Ranka, J.K., Stentz, A., Windeler, R.S., Hall, J.L., Cundiff, S.T., Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis (2000) Science, 288, pp. 635-639Fortier, T.M., Le Coq, Y., Stalnaker, J.E., Ortega, D., Diddams, S.A., Oates, C.W., Hollberg, L., Kilohertz-resolution spectroscopy of cold atoms with an optical frequency comb (2006) Phys. Rev. Lett, 97, pp. 163905/1-163905/4Oates, C.W., Bondu, F., Fox, R.W., Hollberg, L., A diode-laser optical frequency standard based on laser-cooled Ca atoms: Sub-kilohertz spectroscopy by optical shelving detection (1999) Eur. Phys. J. D, 7, pp. 449-460Degenhardt, C., Stoehr, H., Lisdat, C., Wilpers, G., Schnatz, H., Lipphardt, B., Nazarova, T., Riehle, F., Calcium optical frequency standard with ultracold atoms: Approaching 10-15 relative uncertainty (2005) Phys. Rev. A, 72, pp. 062111/1-062111/1