Method to investigate the symmetry of saturated absorption signals by means of laser frequency locking techniques

It is shown that the line shape of a saturated absorption signal — especially its symmetry — can be investigated by combining laser frequency locking methods. The laser frequencyv, modulated with a frequencyf, is stabilized alternatively to the zero crossings of the synchronously detected 2f and 3f absorption signals. In addition, almost any other part of the profile can be tested by locking the laser frequency to neighboruing points of the zero crossings by using an offset technique. With two prestabilized Ar⁺ lasers atv=582 THz the symmetry of different¹²⁷ I ₂ hfs signals was investigated with an uncertainty of typically 2×10^–12 v or 10^–3 halfwidths.     

Intrinsic point defects in niobium: Trapping at100Pd and111In impurities observed by PAC

Radiation-induced lattice defects in high-purity niobium have been investigated in the temperature range of 30K to 540 K by means of - perturbed angular correlation (PAC) measurements using the radioactive probes¹⁰⁰Pd/¹⁰⁰Rh and¹¹¹In/¹¹¹Cd. Both probes were produced within the niobium samples by means of heavy-ion nuclear reactions. At the Pd impurities trapping of defects occurred during heavy-ion irradiation at about 30 K in two defined configurations: defect 1(Pd) withv _Q1=e ² qQ/h=42(±2) MHz, ₁=0 and defect 2 (Pd) withv _Q2=(±2) MHz, ₂=1. Two defects were observed at the In impurities in annealing stage III (around 250 K) after heavy-ion as well as electron irradiations: defect 1(In) withv _Q1=87(±1) MHz, ₁=0 and defect 2(In) withv _Q2=105(±2) MHz, ₂=0.65(±0.02). A third defect (defect 3(In):v _Q3=177(±2) MHz, ₃0.2) appeared above 260 K after heavy-ion irradiation only. The data are interpreted in terms of interstitial trapping at the Pd impurities and vacancy trapping at the In impurities. Information on the microscopic structure of defect 1(In) and 2(In) is obtained from a PAC-single-crystal experiment. For defect 1(In) axial 111-symmetry is found, which leads us to identify this defect with a monovacancy as nearest neighbor with respect to the In probe. Defect 2(In) is the trapped divacancy for which an orientation is found that is consistent with both vacancies being nearest neighbor to the probe but second nearest neighbors to each other.     

The applications of the stark effect to the stabilization of the CO2 laser and the submillimeter laser

Methods based on the Stark effect are described for dither-free frequency stabilization of the optically pumped submm laser. The CO₂ pump laser was stabilized using a Stark Lamb dip signal of the submm lasant in an external Stark cell. An estimated frequency stability (f/f) better than ±1.4×10^–8, for one hour recording, was obtained by this method. The frequency of the submm laser was stabilized using the d.c. and a.c. Stark effects for a metal-dielectric rectangular waveguide laser. An estimated frequency stability of ±6×10^–8 was obtained for 119 m line of CH₃OH laser for one hour recording.     

Precision measurement of the electric quadrupole interaction in zinc metal

To decide on the validity of various values for the quadrupole coupling constant of Zn metal available in the literature, we have used the frequency modulation technique to the 93.3 keV Mössbauer resonance of⁶⁷Zn. We obtained for a⁶⁷Zn metal absorber: e²qQ/h =v _O = 12.34 ± 0.03 MHz. The asymmetry parameter was found to be =0.00 _–0 ^+0.06 . These precise values can be used as a calibration standard for⁶⁷Zn Doppler drives.This work has been supported by the Bundesministerium für Forschung und Technologie and by the Kernforschungszentrum Karlsruhe.     

Frequency of lamb-dip-stabilized 1.52 μm He-Ne lasers

A ³He-²⁰Ne and a ³He-²²Ne 1.52 m laser were frequency stabilized to the Lamb-dip of their respective gain curve and provided a resettability of 2 MHz. Using these lasers, absolute frequencies for the ²⁰Ne and ²²Ne laser transitions were measured by interferometric frequency comparison with an I₂-stabilized He-Ne laser at 0.633 m. A least-square analysis which accounts for the linear frequency dependence of the laser gas pressure yielded two parameters which can reproduce the measured frequencies within an accuracy of ±1.0·10^–8 at 1.52 m.     

Frequency- and wavelength-modulation spectroscopies: Comparison of experimental methods using an AlGaAs diode laser

Low-wavelength modulation (1 kHz), high-wavelength modulation (100 MHz) and two-tone frequency modulation (390±5 MHz) spectroscopies are systematically compared by measuring the minimum detectable absorption achieved using an AlGaAs diode laser tuned on a third-overtone methane transition at 886 nm. From the S/N behavior has been extrapolated a minimum relative absorption (1 Hz of bandwidth) of 4.5(1)×10^–7 for the LMW, 9.7(3)×10^–8 for the HWM and 6.4(2)×10^–8 for the TTFM. In the LWM case the detection-limit value is represented by the laser amplitude 1/f excess noise, while for the high-frequency detection techniques this contribution is negligible with respect to other noise sources. These detection limits well agree with the calculated quantum limited values based on measured laser power, modulation index, noise figure of the electronic components, and other parameters of the apparatus.     

Evolution of the homogeneous IR spectrum of a highly vibrationally excited molecule as a result of a change in its vibrational energy

Using a photodissociation technique, we have measured the IR spectrum of thev ₂₁ mode of the (CF₃)₃ CI molecule with a vibrational energy ofE ₂=42500±3500 cm^–1 which is more than two times the dissociation energy. The experimental spectrum of a Lorenzian shape with a halfwidth of ₂=10.8±1.5 cm^-1 has been analyzed simultaneously with the results of the preceding work (₁=8.6±0.6 cm^-1) that were obtained at a lower vibrational energy (E ₁=36500±2500 cm^–1).     

Narrow-band extreme-ultraviolet laser radiation tunable in the range 90.5–95 nm

Tunable, narrowband extreme ultraviolet radiation in the range 90.5–95 nm with only limited intensity variations is produced by frequency-tripling ultraviolet light from a frequency-doubled dye laser in a gas-jet of xenon. Acetylene gas is found to be an efficient medium for third-harmonic generation in this wavelength range as well. The extreme-ultraviolet radiation is applied in a spectroscopic study of the b ¹ II _u , v=6–8 and v=10–12, o ¹ II _u , v=0 and b¹ _u ⁺ , v=9 states of molecular nitrogen. From linewidth measurements a value k _p=6×10¹⁰ s^–1 for the predissociation rate of the b ¹ II _u , v=11 state is deduced.     

Critical exponents,hyperscaling, and universal amplitude ratios for two- and three-dimensional self-avoiding walks

We make a high-precision Monte Carlo study of two- and three-dimensional self-avoiding walks (SAWs) of length up to 80,000 steps, using the pivot algorithm and the Karp-Luby algorithm. We study the critical exponentsv and 2 ₄ – as well as several universal amplitude ratios; in particular, we make an extremely sensitive test of the hyperscaling relationdv = 2 ₄ –. In two dimensions, we confirm the predicted exponentv=3/4 and the hyperscaling relation; we estimate the universal ratios <R _g ² >/<R _e ² >=0.14026±0.00007, <R _m ² >/<R _e ² >=0.43961±0.00034, and ^*=0.66296±0.00043 (68% confidence limits). In three dimensions, we estimatev=0.5877±0.0006 with a correctionto-scaling exponent ₁=0.56±0.03 (subjective 68% confidence limits). This value forv agrees excellently with the field-theoretic renormalization-group prediction, but there is some discrepancy for ₁. Earlier Monte Carlo estimates ofv, which were 0.592, are now seen to be biased by corrections to scaling. We estimate the universal ratios <R _g ² >/<R _e ² >=0.1599±0.0002 and ^*=0.2471±0.0003; since ^*>0, hyperscaling holds. The approach to ^* is from above, contrary to the prediction of the two-parameter renormalization-group theory. We critically reexamine this theory, and explain where the error lies. In an appendix, we prove rigorously (modulo some standard scaling assumptions) the hyperscaling relationdv = 2 ₄ – for two-dimensional SAWs.     

Simultaneous phase-lock of five CO2 lasers to a primary Cs frequency standard

The output of a CO₂ laser, operating on theP _I(18) transition of¹³C¹⁶O₂ at 26941 GHz (11.128 m) was phase-locked to a 5 MHz signal from a primary Cs frequency standard by means of a frequency chain having only CO₂ lasers as infrared sources. Simultaneously, four other CO₂ lasers in the chain were phase-locked to the 26941 GHz output. This provided CO₂ laser frequencies at 26 450 305, 26 940 815, 28 694 625, 29 442 480, and 33 185 715 MHz having zero long-term-average frequency error relative to the Cs standard, and the ±10^–13 (3 Hz) long-term absolute uncertainty of the standard.     

Self-avoiding random walks on the hexagonal lattice

We use the algorithm recently introduce by A. Berretti and A. D. Sokal to compute numerically the critical exponents for the self-avoiding random walk on the hexagonal lattice. We find=1.3509±0.0057±0.0023v=0.7580±0.0049±0.0046=0.519±0.082±0.077 where the first error is the systematic one due to corrections to scaling and the second is the statistical error. For the effective coordination number we find=1.84779±0.00006±0.0017 The results support the Nienhuis conjecture=43/32 and provide a rough numerical check of the hyperscaling relationdv=2–. An additional analysis, taking the Nienhuis value of=(2+2^1/2)^1/2 for granted, gives=1.3459±0.0040±0.0008     

The CO fundamental-band laser as secondary frequency standard at 5 µm

We present a very high-resolution heterodyne spectrometer based on a CO laser which operates down to fundamental-band transitions of the molecule. This allows us to detect saturated absorption signals on these transitions at very low pressure (0.4 Pa) and laser intensity (< 1 mW/cm²), yielding a linewidth of about 250 kHz. With the CO fundamental-band laser stabilized to these saturation signals we have measured the transition frequencies of the fundamental bands of three isotopic species to an accuracy of typically 20 kHz (v/v 3 × 10^–10), referenced to the CO₂ frequency standard. Together with additional frequency measurements of the first hot bands, these provide the first heterodyne frequency data of sub-Doppler accuracy for transitions in low lying bands of CO. They now represent the most accurate secondary frequency standard in the spectral region around 5 µm (60 THz).     

Spectroscopy of excited state positronium

Electric dipole transitions in the microwave range have been induced between the fine-structure levels of positronium in the excited staten=2. As an indication of the transitions, we used the increase in Lyman- radiation when the metastable 2³S₁-level is depopulated. The results for the transitions 2³S₁2³P_0,1,2 are ₀=18499.65±1.20±4.00 MHz, ₁=13012.42 ±0.65±1.54 MHz and ₂=8624.38±0.54±1.40 MHz. The first error is statistical and the second systematic. The precision of the present measurement has improved by a factor of 3, compared to previous data. Recent bound state QED-calculations have been extended to the orderR _t8 ⁴ln ^–1. The not yet completely calculated orderR _t8 ⁴ is estimated to contribute less than 1 MHz. Our experimental results are in good agreement with theory. By applying a weak magnetic field, we were able to observe the transition 2³S₁2¹P₁ which is strictly forbidden byC-invariance in zero field. Our result, corrected for Zeeman- and motional Starkeffect, is ₃=11180.0±5.0±4.0 MHz. An upper limit for theC-violating matrix element of MHz could be deduced. Our experiment used moderated slow positrons from the bremsstrahlung and pair production of a pulsed electron linear accelerator (TEPOS facility at the university of Giessen).     

Difference-frequency source for very low optical frequencies spectroscopy: CO2 induced spectra

In a previous paper [1] the manufacturing, development and testing of a coherent submillimetric source was exposed. This source was obtained by difference frequency mixing of two CO₂ TEA lasers.In this present work, are presented the first results obtained with this mounting and concerning the collision induced spectrum of gaseous carbon dioxide at room temperature in the 4–40 cm^–1 region.The absorption coefficient is calculated together with the first coefficients of its development as a function of density.The curves ₂/v ²=f(v) and ₃/v ²=f(v), wherev is the frequency, are presented. They permit the calculation of the virial coefficients.The results are then compared with those determined by an extrapolation in this frequency range, of measurements already made in CO₂ in higher (optical) or lower (microwaves) frequencies.     

Recent progress with the CO-overtone Δv=2 laser

We report the recent progress in the performance of the CO-overtone v=2 laser. We were able to increase both the number of lines and the output power by a significant amount. This laser is now a reliable source for spectroscopic applications in the spectral region from 2500–3800 cm^–1. The typical parameters of the laser plasma and a table with the observed laser transitions and their frequencies are given.     

Frequency-stabilized seed laser system for dial applications around 0.94 μm

Absolute frequency stabilization of an extended-cavity diode laser at 0.94 μm is reported. The diode laser was frequency locked against rovibrational absorption lines of water vapour by using the frequency modulation spectroscopy technique. The stabilized oscillator shows a short-term frequency stability level of 40 kHz for integration times of 1 s and a long-term frequency drift lower than 10 MHz for observation times longer than 10³ s. The frequency-stabilized oscillator system is mounted on a compact breadboard (75 cm×50 cm) and constitutes the seed laser system for the injection of a high-energy DIAL laser transmitter operating in the 0.94-μm spectral region.     

Test of special relativity in an ion storage ring

An accurate measurement of the Doppler effect in collinear laser spectroscopy has been performed at the TSR storage ring with electron cooled⁷Li⁺ ions at=0.064. This experiment is a sensitive test of the=(1– ²)^–1/2 factor(=v/c) in the special theory of relativity. The Doppler shifted frequencies of the moving⁷Li⁺ ions are compared with calibrated molecular lines at rest. The frequencies at rest for the⁷Li⁺ ions are known from independent measurements. The Doppler shifted frequencies in the collinear experiment have been measured with a precision ofv/v=6×10^–9, mainly limited by the signal width of the resonance. A corresponding upper limit of 8×10^–7 is deduced for any deviation of the time dilatation factor in special theory of relativity. A still higher accuracy is expected with a laser cooled ion beam. If such a beam is simultaneously subjected to RF bunching, the particle velocity and phase are exactly known. With an additional high resolution laser frequency measurement an improvement of at least one order of magnitude may be achieved.     

73Ge: a new high resolution PAC probe

Long lens electron spectrometers were used to make electron-gamma and electron-electron PAC measurements for the 5/2⁺ 13.3 keV state of⁷³Ge. Sources of⁷³As were produced in the decay of⁷³Se implanted at the CERN/ISOLDE facility. The magnetic interaction in nickel was determined as _L=74.2(7) Mrad s^–1 and the quadrupolar frequency in antimony asv _Q =19.7(2) MHz. The nuclear moments derived are =–1.08(3) _N and |Q|=0.70(8) b.     

Magnetic and electric hyperfine interactions in the system EuSm

Magnetic and electric hyperfine interactions in the system EuSm were investigated with the isomeric 11/2^– state in¹⁴⁵Eu by applying the time-differential perturbed angular distribution (TDPAD) method. The temperature dependence of paramagnetism was studied between 90 K and 1000 K by measuring the magnetic hyperfine interaction frequency _L=g_NN¹ (T)B_ext. The paramagnetic correction factor strictly follows the Curie-Weiss relation =1+C/(T-), withC=–50(2) K and =–29(5) K. This is compatible with a hyperfine field ofB _int(0)=–25(1) T, a valence of two for Eu in Sm, and antiferromagnetic order at low temperatures.The temperature dependence of the electric quandrupole coupling constant v_Q, investigated between 100 K and 400 K, can be reproduced by a linear temperature variation v_Q(T)=v_Q(0) (1-AT), with v_Q(0)=16.2(4) MHz andA=7.2(8)·10^–4 K^–1.The paramagnetic relaxation time _rel of the nuclear alignment is proportional to the temperature of the sample, with _rel T^–1=3.7(2) ·10^–9s K^–1.This leads to the Korringa relation _J T=const=5.1(5)·10^–11s K for the relaxation time of the 4f electronic spinJ. Assuming that the relaxation ofJ is mainly caused by exchange interaction between conduction electrons and localized 4f electrons at the Eu site, an exchange integral of |J _eff|=0.10(2) eV can be deduced.