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A theoretical model of semiconductor lasers mounted in external cavities is developed. The modes' frequencies and gains are calculated. We study the frequency of the oscillating mode versus the laser injection current. We explain its hysteresis behavior by introducing in the model the coupling between the semiconductor gain and its index of refraction induced by fluctuations in carrier density. We also determine the influence of the laser diode output facet reflection coefficient on mode hops and frequency tuning. Theoretical simulations coincide well with experimental observations.

An optical frequency/wavelength standard using the high line Q/sup 2/S/sub 1/2/-/sup 2/D/sub 5/2/ transition of Ca/sup +/ confined in a RF trap and laser cooled is discussed according to the following points: optical excitation scheme to cool the ions and probe the clock transition of an odd isotope of Ca/sup +/ and feasibility of the production of the optical excitations from laser diodes. >

Ultrahigh-resolution spectroscopy is limited by the spectral quality of lasers. We describe a servo system that stabilizes a dye laser by reflection in an optical resonator, which provides an error signal. We analyze the error signal to determine the spectral performance of the dye laser, which is shown to have a Gaussian-shaped spectrum with a width of less than 4 kHz.

High finesse optical cavities are used either in reflection or in transmission for the frequency stabilization of lasers. In this paper, we calculate the transient response of the Fabry–Perot cavity after a small frequency jump of the laser in both cases. We compare the static gains and the transfer functions for small frequency fluctuations, and explain partially the good experimental observed performances of the Fabry–Perot used in reflection.

We present a 729 nm laser diode placed in a self-aligned external cavity and stabilized on a high finesse Fabry-Perot cavity in order to probe the high Q /sup 2/S/sub 1/2 /-/sup 2/D/sub 5/2/ Ca ion transition.

A self-aligned cavity is presented which shows significant improvements, in particular much less sensitivity to mechanical perturbations. Among the two studied configurations, the unfolded cavity is the more suitable regarding beam quality and reliability. Continuous tunability depends greatly on the quality of the AR coating of the diode output facet.

Observation with an improved signal-to-noise ratio of the hyperfine resonance pattern of199Hg+ stored in a radiofrequency trap is reported. A frequency control loop which locks the frequency of a 5MHz quartz crystal oscillator to the hyperfine transition of stored mercury ions, close to 40.5 GHz, is described. In this system, pulses delivered by the photomultiplier are processed digitally. Optimal conditions for the interrogation of the hyperfine transition are specified. A fractional frequency stability σy(τ)=3.6×10−11τ−1/2 for 10s

We describe a laser-cooling experiment on Mg+ ions confined in an electromagnetic trap (Penning trap or rf trap) and give the preliminary experimental results. In particular, we have observed a laser cooling in the Penning trap configuration in which a measured temperature of about 1 K has been obtained.

The main features of the design of two hydrogen masers in operation at the Laboratoire de l'Horloge Atomique are described. They show a frequency stability (square root of the Allan variance) of 4 × 10-13 × 1/τ for 1 s < τ < 40 s and 5 × 10-15 for 200 s < τ < 1 h. Results of time comparisons with distant Cs clocks are also given. The oscillation frequency has been extrapolated to zero magnetic field and a frequency offset, which depends on the value of the applied field, has been measured.

A frequency control loop which locks the frequency of a 5-MHz quartz crystal oscillator to a value defined by the hyperfine transition of 199Hg+ ions is described. The properties of the closed loop are studied using the z-transform technique. The loop parameters are calculated in order to optimize the response time to some usual deterministic perturbations of the VCXO frequency. The results of this analysis can be applied to other digital control loops, such as the hydrogen-maser auto-tuning system.

The limitation to the density of an ion cloud confined in a Penning trap is not well understood till now. Our experiments show that this limitation results from the combined effect of the trap asymmetry and the space charge. The main features of this effect are described by a simplified calculation.

Measurements have been performed of wall effects (atomic loss rate, wall relaxation and wall shift for a FEP 120 coating) and spin exchange effects (spin exchange cross-section, spin exchange frequency shift) in a hydrogen maser for various temperatures of the wall and the atomic hydrogen gas in the range 77-363 K. These experimental results allow a discussion of the phenomena involved in atom-wall collisions. It is shown that the FEP wall behaviour is different according to the temperature range. When the temperature is smaller than 202 K, the wall behaves like a perfect solid and the H atoms are perturbed during weak physical adsorption. When the temperature is greater than 202 K, the wall is no longer a perfect solid: the adsorption sites are modified, or new sites appear, the effects of this change being stronger and stronger when the temperature rises. The phenomena responsible for the loss of atoms on the wall are not modified at 202 K. For temperatures above 296 K, new phenomena appear, which introduce strong positive wall shift and atomic loss, when the temperature rises. These changes of the wall behaviour are connected with second order transitions affecting FEP. The experimental results relative to spin exchange effects are in good agreement with theoretical calculations by Allison: at room temperature the experimental values for the spin exchange cross section is σ = 23.1 ± 2.8 A2 and for the spin exchange frequency shift is λ = 2.5 ± 2.5 A2 (the theoretical values are respectively σ = 23.5 ± 2.4 A2 and λ = 4.5 ± 0.45 A2). We observe small variations of σ in the considered temperature range and a change of the sign of λ at a temperature around 205 K, as predicted by the theoretical calculations.

A method is described which makes it possible to measure the relaxation time constants of mercury ions. They are confined in a radio-frequency trap and optically pumped in order to observe the hyperfine transition in their ground state. This method is based on the study of the fluorescence signal emitted by the ions in various steady- and transient-state experiments. The storage time, longitudinal and transverse relaxation times, and the optical pumping time are measured.

We measure the lifetime of the 5 2 D 5 2 metastable level of Ba + ions confined in a cylindrical radiofrequency trap as well as some parameters which characterize the confining properties of the trap. This is accomplished by studying the ion response to a short pulsed optical excitation saturating the 6 2 S 1 2 –6 2 P 3 2 transition. The measured lifetime of the 5 2 D 5 2 metastable level is 47 ± 16 s. The storage voltages for which the ion number shows a maximum are experimentally investigated. Their change when a light buffer gas is added is observed. The effect of this gas on the storage time is also specified.

The lineshape for resonant mechanical energy absorption by ions confined in an RF quadrupole trap is studied theoretically and experimentally. A low sweep rate of the excitation frequency is considered, the trapping parameters being kept constant. It is shown that the total number of confined ions can be deduced from the resulting lineshape. The limitations of this method of measurement are discussed and some applications given.

A mercury ion frequency standard has been built and operated at Orsay. It is briefly described and the results obtained for its stability are given. Measurement of various physical parameters and calculation of their effect on the short and medium term stability allow to discuss possible improvements. Systematic effects are studied and a method of measurement is given. It is shown that good stability and accuracy can be achieved.

RF traps are widely used nowadays in high resolution hyperfine spectroscopy. The spectrum of the microwave hyperfine transition at 40.5 GHz of the fundamental level2S1/2 of199Hg+ is phase modulated at the secular frequency of the stored ions and it consists of a narrow central line and lateral bands broadened by the ion trajectory and velocity distribution. The central line itself is shifted by the second-order Doppler effect which is the most important systematic error of stored ions frequency standards. In this paper the relativistic Doppler effect in the case of199Hg+ stored ions is deduced applying a mathematical formalism and using physical parameters that we have measured experimentally.

The effects of transitions excited within the F = 1 multiplet of the ground state hydrogen atoms while radiating on the ΔmF = 0 transition are analyzed theoretically. The results are valid for low transition rates and unrestricted maser power. The predictions are: (a) an important modification of the well-known spin-exchange frequency shift of a hydrogen maser, due to the imaginary part of the spin-exchange cross section, (b) a frequency shift proportional to the asymmetry parameter between the 2-Zeeman frequencies in the upper multiplet F = 1, and (c) a frequency shift proportional to the polarization of the atoms in the storage bulb.Also shown is a displacement of the zero crossing of the maser detuning vs. the low frequency coherent transition frequency with respect to the dip of the maser absorption. This effect is visible for a maser tuned by spin-exchange and operated at a relatively high magnetic field and nonuniform Zeeman populations.An experimental verification of the theory is presented. A new method for tuning the hydrogen maser is suggested, and a proposal is made to measure the collisional frequency shift proportional to the average duration of hydrogen atom spin-exchange collisions.

The use of a stored ion cloud in an rf quadrupole trap has shown its possibilities as a high-performance frequency standard. The most important source of systematic error of such a standard is the second-order Doppler shift, an effect of special relativity, which produces a relative frequency shift approximated by the ratio of the mean kinetic energy to the rest mass energy of an ion. Assuming that the ion cloud can be characterized by a temperatureT, the determination ofT is of paramount importance in evaluating the second-order Doppler shift. In this paper, an analytical expression of the ion-cloud temperature is established taking space-charge effects into account and involving only physical parameters which can be easily measured. The validity of this approximate expression is discussed and it is compared to numerically established results published elsewhere.

Possible ways to improve the hydrogen maser accuracy are stated. Use of a special bulb, made of quartz, allowing simulation of two different mean diameters is proposed. It is experimentally proved that it allows one to achieve very good operating conditions in the temperature range 300-395 K. Measurement, with this bulb, of the temperature dependence of a FEP 120 teflon coating is reported. A change of FEP 120 properties is observed at a temperature of 360 K. This is confirmed by operating a hydrogen maser with a classical spherical bulb. A null of the mean phase shift per collisions occurs at a temperature of 385 K. Good precision of wall shift measurements made with the special bulb, in the temperature range 300-360 K allowed one to achieve an accuracy of 6 × 10-13 and to determine the unperturbed hydrogen hyperfine transition frequency fH with a precision of 7 × 10-13. The result is fH = 1420405 751.773 ± 0.001 Hz.

Spin-exchange relaxation rates are measured, as a function of the atomic hydrogen density, in the storage bulb of a hydrogen maser of special design. The values of the hydrogen-hydrogen spin exchange cross section in the temperature 77--363 K result. These experimental values are in very good agreement with the result of a theoretical calculation by Allison. For ambient temperature, the experimental value is sigma = 23.1 +- 2.8 A/sup 2/ (the theoretical value is 23.5 +- 2.4 A/sup 2/) and varies slowly with temperature. (AIP)

We use the phase-space method for the calculation of the beam intensity of neutral particles, when a force proportional to the distance from the beam-symmetry axis is applied. We discuss in detail the focalization and the separation of hydrogen atoms according to their hyperfine levels, by means of a hexapolar magnet. The effect of the diaphragms on the beam intensity is shown. We demonstrate the velocity-selection properties of the system. Several examples are given.

The hyperfine transitions of atoms in the ground state are split when RF fields, whose frequencies correspond to the energy differences between the Zeeman sublevels, are applied. It is shown that the measurement of the intensities of these lines provides a very good determination of the populations of the different states. The calculation is made in the two extreme conditions of adiabatic or sudden application of the RE perturbation. The triplet splitting of the \Deltam = 0 transition of a hydrogen maser used as an amplifier is studied experimentally under the sudden passage condition and this method is used to measure the efficiency of a state selector that improves the atomic beam composition of a H maser.

Stored ions temperature is deduced using an analytical model with experimentally measured physical parameters.

Publisher Summary This chapter discusses two-photon transition between the fundamental state 5d106s2S1/2 and the metastable state 5d96s22S5/2 in mercury ions confined in a radiofrequency trap. The lifetime of the metastable state is about 0,1s, and so this transition is attractive as an optical frequency standard. The chapter describes the energetic properties of the confined particles. It illustrates the calculated profile of the line, broadened and red shifted by second order Doppler effect, for different temperatures of the ions in the trap with a monochromatic laser. The chapter further illustrates width at half maximum of the observed signal in function of the temperature of the ions for different linewidths of the laser.

The purpose of our experiment is to observe the two-photon transition between the fundamental state 5d106s2S1/2 and the metastable state 5d96s22D5/2 in stored Hg+. This transition is attractive as an optical frequency standard for two reasons. First, the radiative lifetime of the 2D5/2 state is about 0.1s and second, the first-order Doppler effect cancels for a two-photon absorption. Thus the transition line consists of a very narrow carrier and we can study the second-order Doppler effect (red shift and broadening, which is estimated to be a few kHz).

Summary A laboratory experiment which is aimed to evaluate the properties of a frequency standard using the hyperfine transition of stored mercury ions is descr i bed. 6 About 10 ions of 199 mercury isotope are confined in a cylindrical radiofrequency trap, The hyperfine transition at a frequency of about 40.5 Ghz is observed via optical pumping produced by the ultraviolet ligh t 194 nm which is emitted by an e I ectrode less 'Os Hg' I amp.

This experiment has been designed for the study of laser cooling of ions in either a rf or a Penning trap, and to understand the thermalization processes which the ions undergo in such a trap.

We give a simple model to calculate the trajectory of an ion in a Penning trap, submitted to a space charge potential. This model shows the effect of electric field asymmetries and misalignment of the magnetic ω z ’ field : the ion trajectory expands in the cases where the axial frequency is equal to some multiples of the magnetron frequency ω m ’ (Fig. 1), leading to a limitation of the density. These frequencies are modified by space-charge effect and evaluated in the simple case of a uniform distribution of the ions: $$\omega _{m}^{\prime } = \sqrt {{\omega _{z}^{2} - 1/3\omega _{p}^{2}}}$$ $$\omega _{m}^{\prime } = \frac{{{{\Omega }_{c}}}}{2}\left[ {1 - \sqrt {{1 - \frac{4}{{\Omega _{c}^{2}}}\left( {\frac{{\omega _{z}^{2}}}{2} + \frac{{\omega _{p}^{2}}}{3}} \right)}} } \right]$$ Where ωz is the axial frequency of a single ion in the trap, ωp the plasma frequency and Ωc the cyclotron frequency.

The coupling, due to relaxation mechanisms, between the hyperfine differences of population and the atomic polarization, introduces a lengthening of the dynamical time constants of the hydrogen maser.

The influence of the beam composition on the long-term stability of the hydrogen maser is considered. A device which removes 85% of the atoms in the undesirable state F = 1 mF = 1, and does not affect the atoms involved in the clock transition, is described. The operating conditions are given.