535 research outputs found
An Ultra-Stable Referenced Interrogation System in the Deep Ultraviolet for a Mercury Optical Lattice Clock
We have developed an ultra-stable source in the deep ultraviolet, suitable to
fulfill the interrogation requirements of a future fully-operational lattice
clock based on neutral mercury. At the core of the system is a Fabry-P\'erot
cavity which is highly impervious to temperature and vibrational perturbations.
The mirror substrate is made of fused silica in order to exploit the
comparatively low thermal noise limits associated with this material. By
stabilizing the frequency of a 1062.6 nm Yb-doped fiber laser to the cavity,
and including an additional link to LNE-SYRTE's fountain primary frequency
standards via an optical frequency comb, we produce a signal which is both
stable at the 1E-15 level in fractional terms and referenced to primary
frequency standards. The signal is subsequently amplified and frequency-doubled
twice to produce several milliwatts of interrogation signal at 265.6 nm in the
deep ultraviolet.Comment: 7 pages, 6 figure
Measurement of excited-state transitions in cold calcium atoms by direct femtosecond frequency-comb spectroscopy
We apply direct frequency-comb spectroscopy, in combination with precision cw
spectroscopy, to measure the transition
frequency in cold calcium atoms. A 657 nm ultrastable cw laser was used to
excite atoms on the narrow ( Hz) clock transition, and the direct output of the frequency comb was
used to excite those atoms from the state to the state. The resonance of this second stage was detected by observing a
decrease in population of the ground state as a result of atoms being optically
pumped to the metastable states. The transition frequency is measured to be kHz; which is an improvement by almost four orders of magnitude over
the previously measured value. In addition, we demonstrate spectroscopy on
magnetically trapped atoms in the state.Comment: 4 pages 5 figure
Kilohertz-resolution spectroscopy of cold atoms with an optical frequency comb
We have performed sub-Doppler spectroscopy on the narrow intercombination
line of cold calcium atoms using the amplified output of a femtosecond laser
frequency comb. Injection locking of a 657-nm diode laser with a femtosecond
comb allows for two regimes of amplification, one in which many lines of the
comb are amplified, and one where a single line is predominantly amplified. The
output of the laser in both regimes was used to perform kilohertz-level
spectroscopy. This experiment demonstrates the potential for high-resolution
absolute-frequency spectroscopy over the entire spectrum of the frequency comb
output using a single high-finesse optical reference cavity.Comment: 4 pages, 4 Figure
Ultrastable lasers based on vibration insensitive cavities
We present two ultra-stable lasers based on two vibration insensitive cavity
designs, one with vertical optical axis geometry, the other horizontal.
Ultra-stable cavities are constructed with fused silica mirror substrates,
shown to decrease the thermal noise limit, in order to improve the frequency
stability over previous designs. Vibration sensitivity components measured are
equal to or better than 1.5e-11 per m.s^-2 for each spatial direction, which
shows significant improvement over previous studies. We have tested the very
low dependence on the position of the cavity support points, in order to
establish that our designs eliminate the need for fine tuning to achieve
extremely low vibration sensitivity. Relative frequency measurements show that
at least one of the stabilized lasers has a stability better than 5.6e-16 at 1
second, which is the best result obtained for this length of cavity.Comment: 8 pages 12 figure
Ultra-low noise microwave generation with fiber-based optical frequency comb and application to atomic fountain clock
We demonstrate the use of a fiber-based femtosecond laser locked onto an
ultra-stable optical cavity to generate a low-noise microwave reference signal.
Comparison with both a liquid Helium cryogenic sapphire oscillator (CSO) and a
Ti:Sapphire-based optical frequency comb system exhibit a stability about
between 1 s and 10 s. The microwave signal from the fiber
system is used to perform Ramsey spectroscopy in a state-of-the-art Cesium
fountain clock. The resulting clock system is compared to the CSO and exhibits
a stability of . Our continuously operated
fiber-based system therefore demonstrates its potential to replace the CSO for
atomic clocks with high stability in both the optical and microwave domain,
most particularly for operational primary frequency standards.Comment: 3 pages, 3 figure
Atomic fountains and optical clocks at SYRTE: status and perspectives
In this article, we report on the work done with the LNE-SYRTE atomic clock
ensemble during the last 10 years. We cover progress made in atomic fountains
and in their application to timekeeping. We also cover the development of
optical lattice clocks based on strontium and on mercury. We report on tests of
fundamental physical laws made with these highly accurate atomic clocks. We
also report on work relevant to a future possible redefinition of the SI
second
A neutral atom frequency reference in the deep UV with 10^(-15) range uncertainty
We present an assessment of the (6s^{2})1S0 -> (6s7s)3P0 clock transition
frequency in 199Hg with an uncertainty reduction of nearly three orders of
magnitude and demonstrate an atomic quality factor, Q, of ~10^(14). The 199Hg
atoms are confined in a vertical lattice trap with light at the newly
determined magic wavelength of 362.5697 +/-0.0011 nm and at a lattice depth of
20Er. The atoms are loaded from a single stage magneto-optical trap with
cooling light at 253.7 nm. The high Q factor is obtained with an 80 ms Rabi
pulse at 265.6 nm. The frequency of the clock transition is found to be 1 128
575 290 808 162.0 +/-6.4 (sys.) +/-0.3 (stat.) Hz (fractional uncertainty =
5.7x10^(-15)). Neither an atom number nor second order Zeeman dependence have
yet to be detected. Only three laser wavelengths are used for the cooling,
lattice trapping, probing and detection.Comment: 5 pages, 6 figure
A Machine Checked Model of Idempotent MGU Axioms For Lists of Equational Constraints
We present formalized proofs verifying that the first-order unification
algorithm defined over lists of satisfiable constraints generates a most
general unifier (MGU), which also happens to be idempotent. All of our proofs
have been formalized in the Coq theorem prover. Our proofs show that finite
maps produced by the unification algorithm provide a model of the axioms
characterizing idempotent MGUs of lists of constraints. The axioms that serve
as the basis for our verification are derived from a standard set by extending
them to lists of constraints. For us, constraints are equalities between terms
in the language of simple types. Substitutions are formally modeled as finite
maps using the Coq library Coq.FSets.FMapInterface. Coq's method of functional
induction is the main proof technique used in proving many of the axioms.Comment: In Proceedings UNIF 2010, arXiv:1012.455
Generating Bijections between HOAS and the Natural Numbers
A provably correct bijection between higher-order abstract syntax (HOAS) and
the natural numbers enables one to define a "not equals" relationship between
terms and also to have an adequate encoding of sets of terms, and maps from one
term family to another. Sets and maps are useful in many situations and are
preferably provided in a library of some sort. I have released a map and set
library for use with Twelf which can be used with any type for which a
bijection to the natural numbers exists.
Since creating such bijections is tedious and error-prone, I have created a
"bijection generator" that generates such bijections automatically together
with proofs of correctness, all in the context of Twelf.Comment: In Proceedings LFMTP 2010, arXiv:1009.218
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