615 research outputs found
Ultrastable Optical Clock with Neutral Atoms in an Engineered Light Shift Trap
An ultrastable optical clock based on neutral atoms trapped in an optical
lattice is proposed. Complete control over the light shift is achieved by
employing the transition of
atoms as a "clock transition". Calculations of ac multipole polarizabilities
and dipole hyperpolarizabilities for the clock transition indicate that the
contribution of the higher-order light shifts can be reduced to less than 1
mHz, allowing for a projected accuracy of better than .Comment: 4 pages, 2 figures, accepted for publication in Phys. Rev. Let
System of Complex Brownian Motions Associated with the O'Connell Process
The O'Connell process is a softened version (a geometric lifting with a
parameter ) of the noncolliding Brownian motion such that neighboring
particles can change the order of positions in one dimension within the
characteristic length . This process is not determinantal. Under a special
entrance law, however, Borodin and Corwin gave a Fredholm determinant
expression for the expectation of an observable, which is a softening of an
indicator of a particle position. We rewrite their integral kernel to a form
similar to the correlation kernels of determinantal processes and show, if the
number of particles is , the rank of the matrix of the Fredholm determinant
is . Then we give a representation for the quantity by using an -particle
system of complex Brownian motions (CBMs). The complex function, which gives
the determinantal expression to the weight of CBM paths, is not entire, but in
the combinatorial limit it becomes an entire function providing
conformal martingales and the CBM representation for the noncolliding Brownian
motion is recovered.Comment: v3: AMS_LaTeX, 25 pages, no figure, minor corrections made for
publication in J. Stat. Phy
Two Bessel Bridges Conditioned Never to Collide, Double Dirichlet Series, and Jacobi Theta Function
It is known that the moments of the maximum value of a one-dimensional
conditional Brownian motion, the three-dimensional Bessel bridge with duration
1 started from the origin, are expressed using the Riemann zeta function. We
consider a system of two Bessel bridges, in which noncolliding condition is
imposed. We show that the moments of the maximum value is then expressed using
the double Dirichlet series, or using the integrals of products of the Jacobi
theta functions and its derivatives. Since the present system will be provided
as a diffusion scaling limit of a version of vicious walker model, the ensemble
of 2-watermelons with a wall, the dominant terms in long-time asymptotics of
moments of height of 2-watermelons are completely determined. For the height of
2-watermelons with a wall, the average value was recently studied by Fulmek by
a method of enumerative combinatorics.Comment: v2: LaTeX, 19 pages, 2 figures, minor corrections made for
publication in J. Stat. Phy
Cooling of Sr to high phase-space density by laser and sympathetic cooling in isotopic mixtures
Based on an experimental study of two-body and three-body collisions in
ultracold strontium samples, a novel optical-sympathetic cooling method in
isotopic mixtures is demonstrated. Without evaporative cooling, a phase-space
density of is obtained with a high spatial density that should
allow to overcome the difficulties encountered so far to reach quantum
degeneracy for Sr atoms.Comment: 5 pages, 4 figure
Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics
Cellular automata are widely used to model real-world dynamics. We show using
the Domany-Kinzel probabilistic cellular automata that alternating two
supercritical dynamics can result in subcritical dynamics in which the
population dies out. The analysis of the original and reduced models reveals
generality of this paradoxical behavior, which suggests that autonomous or
man-made periodic or random environmental changes can cause extinction in
otherwise safe population dynamics. Our model also realizes another scenario
for the Parrondo's paradox to occur, namely, spatial extensions.Comment: 8 figure
Optical clocks based on ultra-narrow three-photon resonances in alkaline earth atoms
A sharp resonance line that appears in three-photon transitions between the
and states of alkaline earth and Yb atoms is proposed
as an optical frequency standard. This proposal permits the use of the even
isotopes, in which the clock transition is narrower than in proposed clocks
using the odd isotopes and the energy interval is not affected by external
magnetic fields or the polarization of trapping light. The method has the
unique feature that the width and rate of the clock transition can be
continuously adjusted from the level to sub- without loss of signal
amplitude by varying the intensities of the three optical beams. Doppler and
recoil effects can be eliminated by proper alignment of the three optical beams
or by point confinement in a lattice trap. The three beams can be mixed to
produce the optical frequency corresponding to the -
clock interval.Comment: 10 pages, 4 figures, submitted to PR
Functional central limit theorems for vicious walkers
We consider the diffusion scaling limit of the vicious walker model that is a
system of nonintersecting random walks. We prove a functional central limit
theorem for the model and derive two types of nonintersecting Brownian motions,
in which the nonintersecting condition is imposed in a finite time interval
for the first type and in an infinite time interval for
the second type, respectively. The limit process of the first type is a
temporally inhomogeneous diffusion, and that of the second type is a temporally
homogeneous diffusion that is identified with a Dyson's model of Brownian
motions studied in the random matrix theory. We show that these two types of
processes are related to each other by a multi-dimensional generalization of
Imhof's relation, whose original form relates the Brownian meander and the
three-dimensional Bessel process. We also study the vicious walkers with wall
restriction and prove a functional central limit theorem in the diffusion
scaling limit.Comment: AMS-LaTeX, 20 pages, 2 figures, v6: minor corrections made for
publicatio
Studies of the S--P transition in atomic ytterbium for optical clocks and qubit arrays
We report an observation of the weak S-P transition in
Yb as an important step to establish Yb as a primary candidate for
future optical frequency standards, and to open up a new approach for qubits
using the S and P states of Yb atoms in an optical lattice.Comment: 5 pages, 3 figure
Critical behavior for mixed site-bond directed percolation
We study mixed site-bond directed percolation on 2D and 3D lattices by using
time-dependent simulations. Our results are compared with rigorous bounds
recently obtained by Liggett and by Katori and Tsukahara. The critical
fractions and of sites and bonds are extremely well
approximated by a relationship reported earlier for isotropic percolation,
, where and are the critical fractions in
pure site and bond directed percolation.Comment: 10 pages, figures available on request from [email protected]
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