A diode-laser optical frequency standard based on laser-cooled Ca atoms: Sub-kilohertz spectroscopy by optical shelving detection

We report an optical frequency standard at 657 nm based on laser-cooled/trapped Ca atoms. The system consists of a novel, compact magneto-optic trap which uses 50 mW of frequency-doubled diode laser light at 423 nm and can trap >10⁷ Ca atoms in 20 ms. High resolution spectroscopy on this atomic sample using the narrow 657 nm intercombination line resolves linewidths (FWHM) as narrow as 400 Hz, the natural linewidth of the transition. The spectroscopic signal-to-noise ratio is enhanced by an order of magnitude with the implementation of a “shelving" detection scheme on the 423 nm transition. Our present apparatus achieves a fractional frequency instability of in 1 s with a potential atom shot-noise-limited performance of and excellent prospects for high accuracy. Received 2 November 1998     

Improved short-term stability of optical frequency standards: approaching 1 Hz in 1 s with the Ca standard at 657 nm

For a neutral (40)Ca-based optical frequency standard we report a fractional frequency instability of 4 x 10(-15) in 1 s, which represents a fivefold improvement over existing atomic frequency standards. Using the technique of optical Bordé-Ramsey spectroscopy with a sample of 10(7) trapped atoms, we have resolved linewidths as narrow as 200 Hz (FWHM). With colder atoms this system could potentially achieve an instability as low as 2 x 10(-16) in 1 s. Such low instabilities are important for frequency standards and precision tests of fundamental physics.     

Absolute frequency measurements of the Hg+ and Ca optical clock transitions with a femtosecond laser

The frequency comb created by a femtosecond mode-locked laser and a microstructured fiber is used to phase coherently measure the frequencies of both the Hg+ and Ca optical standards with respect to the SI second. We find the transition frequencies to be f(Hg) = 1 064 721 609 899 143(10) Hz and f(Ca) = 455 986 240 494 158(26) Hz, respectively. In addition to the unprecedented precision demonstrated here, this work is the precursor to all-optical atomic clocks based on the Hg+ and Ca standards. Furthermore, when combined with previous measurements, we find no time variations of these atomic frequencies within the uncertainties of the absolute value of( partial differential f(Ca)/ partial differential t)/f(Ca) < or =8 x 10(-14) yr(-1) and the absolute value of(partial differential f(Hg)/ partial differential t)/f(Hg) < or =30 x 10(-14) yr(-1).     

A Ca optical frequency standard: Frequency stabilization by means of nonlinear Ramsey resonances

An optical frequency standard based on frequency stabilization to Ramsey fringes observed in a Ca atomic beam is described. The important operation parameters influencing the uncertainty of such a standard are studied experimentally. Frequency shifts due to phase errors of separated traveling wave excitation can be strongly reduced by means of laser beam reversal. It is expected that the present fractional uncertainty of approximately 2.3×10^–12 to realize the true line center can be reduced below the 10^–14 level by applying atomic beam cooling and improved phase alignment.     

Absolute-frequency measurements with a stabilized near-infrared optical frequency comb from a Cr:forsterite laser

A frequency comb is generated with a chromium-doped forsterite femtosecond laser, spectrally broadened in a dispersion-shifted highly nonlinear fiber, and stabilized. The resultant evenly spaced comb of frequencies ranges from 1.1 to beyond 1.8 microm. The frequency comb was referenced simultaneously to the National Institute of Standards and Technology's optical frequency standard based on neutral calcium and to a hydrogen maser that is calibrated by a cesium atomic fountain clock. With this comb we measured two frequency references in the telecommunications band: one half of the frequency of the d/f crossover transition in 87Rb at 780 nm, and the methane v2 + 2v3 R(8) line at 1315 nm.     

Synthesis of two-species ion chains for a new optical frequency standard with an indium ion

Ion chains consisting of different species play an important role in new applications in quantum information processing as well as in optical frequency standards. We demonstrate generation and stabilization of ion chains consisting of Ca⁺ and In⁺. The Ca⁺ chains with In⁺ located at specified positions are synthesized using resonant photo-ionization, real-time imaging and trap field control techniques. A specific configuration of an ion chain is stabilized by destabilizing other configurations via selective excitation of vibrational modes using amplitude modulation on the cooling laser beam. New approaches to an indium ion optical clock are proposed using the ions chains.     

Multiple frequency radiofrequency-optical resonance in a four-level model of rubidium atoms with optical pumping

We consider a four-level model for alkali metal atoms with optical pumping by nonresonant light under conditions when magnetic dipole transitions are induced between energy sublevels of the hyperfine structure in the ground state. We present the dependences of the observed signal as a function of the frequency detuning of the applied rf fields relative to the resonant value, calculated in the density matrix formalism. We note the absence of a light shift in the radiofrequency-optical resonance signal, independent of the amplitude of the rf field and the optical and thermal relaxation rates. We show that when using a modulation technique for phase detection of the signal, its maximum discrimination ability is observed under conditions for simultaneous modulation of the pump light intensity and the frequency of the rf field, which in principle does not occur in the classical two-level model for optically oriented atoms in magnetic resonance. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 3, pp. 326–329, May–June, 2006.     

Octave-spanning Ti:sapphire laser with a repetition rate >1 ghz for optical frequency measurements and comparisons

We demonstrate a self-referenced, octave-spanning, mode-locked Ti:sapphire laser with a scalable repetition rate (550 MHz - 1.35 GHz). We use the frequency comb output of the laser, without additional broadening in optical fiber, for simultaneous measurements against atomic optical standards at 534, 578, 563, and 657 nm and to stabilize the laser offset frequency.     

Induction of a radio-optical dark resonance for a four-level models of alkaline atoms with optical pumping

The phenomenon of coherent population trapping for a four-level model of alkaline atoms with optical pumping by nonresonant light is analytically investigated. Expressions for experimentally observed signals are derived for different variants of induced magnetodipole transitions in the hyperfine structure of the ground state of atoms within the density matrix formalism. No light-induced frequency shift of the signal of radio-optical resonance is observed irrespective of the radio field amplitude and optical and thermal relaxation rates. It is demonstrated that with the use of modulation technique of phase detection of experimentally observed signal, its discrimination power reaches a maximum under conditions of simultaneous modulation of the pumping light intensity and radio-field frequency, which in principle is not observed in the classical two-level model of optically oriented atoms in the magnetic resonance. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 12–16, August, 2006.     

Absolute frequency measurement in the 28-THz spectral region with a femtosecond laser comb and a long-distance optical link to a primary standard

A new frequency chain was demonstrated to measure an optical frequency standard based on a rovibrational molecular transition in the 28-THz spectral region accessible to a CO₂ laser. It uses a femtosecond-laser frequency comb generator and two laser diodes at 852 nm and 788 nm as intermediate oscillators, with their frequency difference phase locked to the CO₂ laser. The rf repetition rate of the femtosecond laser was compared with a 100-MHz signal from a hydrogen maser, located at BNM-SYRTE. The 100-MHz signal is transmitted by amplitude modulation of a 1.55-m laser diode through a 43-km telecommunication optical fibre. As a first example, the absolute measurement of a saturation line of OsO₄ in the vicinity of the P(16) laser line of CO₂ is reported with a relative uncertainty of 10^-12, limited by the CO₂/OsO₄ frequency day-to-day reproducibility. The current limit on the stability of the frequency measurement is 4×10^-13 at 1 s. PACS 06.20.-f; 42.62.Eh; 06.30.Ft     

Towards a determination of absolute cross sections for projectile excitation of hydrogen-like uranium in collisions with neutral atoms

Recently, the contribution of the generalized Breit interaction to electron impact ionization was identified for the first time in a high-Z system, namely, hydrogen-like uranium. This study employed a measurement of the relative population of the j = 1/2 and j = 3/2 states of the L shell by projectile excitation in collision of U⁹¹⁺ with hydrogen and nitrogen targets. However, for a rigorous test of ion–atom collision theory, also the absolute excitation cross sections are of great importance. In the present work, we report on our efforts to extend the previous study to a determination of the absolute projectile excitation cross sections by normalization to the well-known radiative electron capture process.     

Magnetization plateaus for spin-one bosons in optical lattices: Stern-Gerlach experiments with strongly correlated atoms

We consider insulating states of spin-one bosons in optical lattices in the presence of a weak magnetic field. For the states with more than one atom per lattice site we find a series of quantum phase transitions between states with fixed magnetization and a canted nematic phase. In the presence of a global confining potential, this unusual phase diagram leads to several novel phenomena, including the formation of magnetization plateaus. We discuss how these effects can be observed using spatially resolved spin polarization measurements.     

Overall values of conventional discrepancy indices for crystals with heavy atoms. Part I—Results for a triclinic crystal when the model consists of the heavy atoms and a part of light atoms

The joint probability density functions of the normalized structure amplitudes of the structure and the model (i.e.,y _N andy _p ^c ) are derived for triclinic crystals containing heavy atoms (1, 2 and many) by taking the model to consist of the heavy atoms and a part of the light atoms in the unit cell. These functions are derived for the two cases where the model is completely correct (i.e., the related case) and where the model is completely wrong (i.e., the unrelated case) in terms of the fractional contributions to the local mean intensity from the heavy atoms and all known atoms (i.e., σ _1h ^/2 and σ ₁ ² ) as parameters. These functions are then used to obtain the theoretical local values of 〈y _N〉 and 〈|y _N ⁿ − σ ₁ ⁿ (y _P ^c ) ⁿ |〉,n=1, 2. A method of using these results to compute the theoretical overall values ofR(F) andR(I) for the related and unrelated cases is briefly described. A comparison of the observed values of these indices with their theoretical values for the related and unrelated cases would help in determining the correctness of the proposed trial structure. Contribution No. 548     

Entropic uncertainty for two atoms interacting with a cavity field under the influence of two photons (off-resonance case)

In this paper, we introduce a Hamiltonian model describing the interaction of two photons with two two-level atoms and a degenerate parametric amplifier. In the near-resonance case, we obtain an analytic solution of the evolution equation for the wave function in the Schr¨odinger picture and use the obtained result for discussing the atomic inversion, the purity, and the phenomenon of squeezing. We show that the phenomenon of superstructure appears in the atomic inversion in the presence of detuning (with parameter ??) and coupling (with parameter ??₃). Our study of the purity shows that the system is always in a mixed state, and the maximum value of entanglement occurs around ~0.6. Also we show that detuning leads to a reduction in the value of squeezing for all quadrature variances. In contrast, the coupling parameter leads to an increase in the value of squeezing. However, for the usual single-mode squeezing (of quadratures) the effect of detuning consists in increase in the squeezing period.     

Formant frequency estimates for abruptly changing area functions: a comparison between calculations and measurements.

Vocal tract area functions may contain quite abrupt changes in cross-sectional area. In formant frequency calculations for such area functions, an inner length correction (ILC) should be applied. The relevance of this correction was investigated by comparing acoustic measurements obtained from a physical model of the vocal tract with data gathered by means of computer simulations. Calculating formant frequencies without applying internal length corrections caused substantial errors, particularly for area functions representing apical stops just anterior to occlusion. Decentering and axial symmetry in the arrangement of the area elements of the physical model were briefly studied and found to have effects on the formant frequency values.     

Complexity out of a simple structure: The intricate multistable behaviour of an optical resonator filled with sodium atoms

A Fabry-Perot resonator containing sodium atoms displays a variety of switching phenomena even in the simplified case of homogeneous broadening. The processes are shown to arise from the combined effects of Zeeman pumping and electronic excitation. A simple model can clarify the dazzling complexity of the observed phenomena.Dedicated to Prof. Dr. Herbert Welling on the occasion of his 60th birthday     

Searching for a molecule with a wide frequency domain for non-resonant two-photon ionization to measure the ultrashort optical pulse width

The frequency domain of non-resonant two-photon ionization, defined as a frequency separation from half of the ionization energy to the excitation energy, was investigated using density functional theory calculations. Several organic compounds have the potential for use in the measurement of the ultrashort optical pulse width in the ultraviolet region using an autocorrelator consisting of a mass spectrometer as a two-photon-response detector.     

Transfer of a weakly bound electron in collisions of Rydberg atoms with neutral particles. II. Ion-pair formation and resonant quenching of the Rb(nl) and Ne(nl) States by Ca, Sr, and Ba atoms

Electron-transfer processes are studied in thermal collisions of Rydberg atoms with alkaline-earth Ca(4s ²), Sr(5s ²), and Ba(6s ²) atoms capable of forming negative ions with a weakly bound outermost p-electron. We consider the ion-pair formation and resonant quenching of highly excited atomic states caused by transitions between Rydberg covalent and ionic terms of a quasi-molecule produced in collisions of particles. The contributions of these reaction channels to the total depopulation cross section of Rydberg states of Rb(nl) and Ne(nl) atoms as functions of the principal quantum number n are compared for selectively excited nl-levels with l ? n and for states with large orbital quantum numbers l = n ? 1, n ? 2. It is shown that the contribution from resonant quenching dominates at small values of n, and the ion-pair formation process begins to dominate with increasing n. The values and positions of the maxima of cross sections for both processes strongly depend on the electron affinity of an alkaline-earth atom and on the orbital angular momentum l of a highly excited atom. It is shown that in the case of Rydberg atoms in states with large l ～ n ? 1, the rate constants of ion-pair formation and collisional quenching are considerably lower than those for nl-levels with l ? n.     

500-Hz two-photon Ramsey fringes with a SF6 beam: towards a new frequency standard in the 30-THz spectral region

A two-photon Ramsey-fringe experiment with a supersonic beam of SF₆ has been performed with an interzone distance of up to 50 cm. Using a He-seeded beam with 50% of SF₆, the two-photon transition P(4)E⁰ in the 2ν₃ band reveals its magnetic hyperfine structure and the periodicity of the fringes is 500 Hz. The strength of the central fringe of the main hyperfine component corresponds to a flux of 10¹⁰–10¹¹useful molecules/s, which is very promising for a new frequency standard in the 30-THz spectral region. Received: 27 April 2001 / Revised version: 18 June 2001 / Published online: 18 July 2001