258 research outputs found
Computing A Glimpse of Randomness
A Chaitin Omega number is the halting probability of a universal Chaitin
(self-delimiting Turing) machine. Every Omega number is both computably
enumerable (the limit of a computable, increasing, converging sequence of
rationals) and random (its binary expansion is an algorithmic random sequence).
In particular, every Omega number is strongly non-computable. The aim of this
paper is to describe a procedure, which combines Java programming and
mathematical proofs, for computing the exact values of the first 64 bits of a
Chaitin Omega:
0000001000000100000110001000011010001111110010111011101000010000. Full
description of programs and proofs will be given elsewhere.Comment: 16 pages; Experimental Mathematics (accepted
Collisions of cold magnesium atoms in a weak laser field
We use quantum scattering methods to calculate the light-induced collisional
loss of laser-cooled and trapped magnesium atoms for detunings up to 30 atomic
linewidths to the red of the 1S_0-1P_1 cooling transition. Magnesium has no
hyperfine structure to complicate the theoretical studies. We evaluate both the
radiative and nonradiative mechanisms of trap loss. The radiative escape
mechanism via allowed 1Sigma_u excitation is dominant for more than about one
atomic linewidth detuning. Molecular vibrational structure due to
photoassociative transitions to bound states begins to appear beyond about ten
linewidths detuning.Comment: 4 pages with 3 embedded figure
On the feasibility of cooling and trapping metastable alkaline-earth atoms
Metastability and long-range interactions of Mg, Ca, and Sr in the
lowest-energy metastable state are investigated. The calculated
lifetimes are 38 minutes for Mg*, 118 minutes for Ca*, and 17 minutes for Sr*,
supporting feasibility of cooling and trapping experiments. The
quadrupole-quadrupole long-range interactions of two metastable atoms are
evaluated for various molecular symmetries. Hund's case (c) 4_g potential
possesses a large 100-1000 K potential barrier. Therefore magnetic trap losses
can possibly be reduced using cold metastable atoms in a stretched M=2 state.
Calculations were performed in the framework of ab initio relativistic
configuration interaction method coupled with the random-phase approximation.Comment: 8 pages, 2 figures; to appear in PR
Magnetic trapping of metastable atomic strontium
We report the magnetic trapping of metastable atomic strontium. Atoms
are cooled in a magneto-optical trap (MOT) operating on the dipole allowed
transition at 461 nm. Decay via
continuously loads a magnetic trap formed by the quadrupole magnetic field of
the MOT. Over atoms at a density of cm 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
Calculations of collisions between cold alkaline earth atoms in a weak laser field
We calculate the light-induced collisional loss of laser-cooled and trapped
magnesium atoms for detunings up to 50 atomic linewidths to the red of the
^1S_0-^1P_1 cooling transition. We evaluate loss rate coefficients due to both
radiative and nonradiative state-changing mechanisms for temperatures at and
below the Doppler cooling temperature. We solve the Schrodinger equation with a
complex potential to represent spontaneous decay, but also give analytic models
for various limits. Vibrational structure due to molecular photoassociation is
present in the trap loss spectrum. Relatively broad structure due to absorption
to the Mg_2 ^1Sigma_u state occurs for detunings larger than about 10 atomic
linewidths. Much sharper structure, especially evident at low temperature,
occurs even at smaller detunings due to of Mg_2 ^1Pi_g absorption, which is
weakly allowed due to relativistic retardation corrections to the forbidden
dipole transition strength. We also perform model studies for the other
alkaline earth species Ca, Sr, and Ba and for Yb, and find similar qualitative
behavior as for Mg.Comment: 20 pages, RevTex, 13 eps figures embedde
High-accuracy relativistic many-body calculations of van der Waals coefficients C_6 for alkaline-earth atoms
Relativistic many-body calculations of van der Waals coefficients C_6 for
dimers correlating to two ground state alkaline-earth atoms at large
internuclear separations are reported. The following values and uncertainties
were determined : C_6 = 214(3) for Be, 627(12) for Mg, 2221(15) for Ca,
3170(196) for Sr, and 5160(74) for Ba in atomic units.Comment: 5 pages, submitted to Phys. Rev.
Photoionization of ultracold and Bose-Einstein condensed Rb atoms
Photoionization of a cold atomic sample offers intriguing possibilities to
observe collective effects at extremely low temperatures. Irradiation of a
rubidium condensate and of cold rubidium atoms within a magneto-optical trap
with laser pulses ionizing through 1-photon and 2-photon absorption processes
has been performed. Losses and modifications in the density profile of the
remaining trapped cold cloud or the remaining condensate sample have been
examined as function of the ionizing laser parameters. Ionization
cross-sections were measured for atoms in a MOT, while in magnetic traps losses
larger than those expected for ionization process were measured.Comment: 9 pages, 7 figure
Doppler cooling and trapping on forbidden transitions
Ultracold atoms at temperatures close to the recoil limit have been achieved
by extending Doppler cooling to forbidden transitions. A cloud of ^40Ca atoms
has been cooled and trapped to a temperature as low as 6 \mu K by operating a
magneto-optical trap on the spin-forbidden intercombination transition.
Quenching the long-lived excited state with an additional laser enhanced the
scattering rate by a factor of 15, while a high selectivity in velocity was
preserved. With this method more than 10% of pre-cooled atoms from a standard
magneto-optical trap have been transferred to the ultracold trap. Monte-Carlo
simulations of the cooling process are in good agreement with the experiments
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