1. Chapter 8 Doppler-free laser spectroscopy

2. Contents 8.1 Doppler broadening of spectral lines 8.2 The crossed-beam method 8.3 Saturated absorption spectroscopy 8.4 Two-photon spectroscopy 8.5 Cablibration in laser spectroscopy

3. 8.1 Doppler broadening of spectral lines The Doppler effect on the observed frequency of radiation. Radiation that has an angular frequency of ω in the laboratory frame of reference has the frequencies indicated in a reference frame moving with a speedν e.g.the rest frame of an atom. Only the component of the velocity along the wavevector k contributes to the first-order Doppler shift.

4. 8.2 The crossed-beam method

5. α Atoms Laser beam Slit Over is the Doppler width of a gas at the same temperature as the beam.

6. 8.3 Saturated absorption spectroscopy Integration of the contributions from all the velocity classes gives the absorption coefficient as

7. 8.3.1 Principle of saturated absorption spectroscopy For all intensities, the integral of the number densities in each velocity class equals the total number density in that level, i.e. and similarly for ． The total number density

8. The hole burnt into the lower-level population by a beam of intensity I has a width ω ω

9. A saturated absorption spectroscopy experiment Laser BS Pump beam Probe beam M1 sampleDetector

10. A plot of the probe intensity transmitted through the sample as a function of the laser frequency. With the pump beam blocked the experiment gives a simple Doppler- broadened absorption, but in the presence of the pump beam a narrow peak appears at the atomic resonance frequency. ω ω ω0ω0 Signal withoutPump beam Signal withpump beam

11. The population densities of the two levels and as a function of velocity for three different laser frequencies: below, equal to, and above the atomic resonance, showing the effect of the pump and probe beams.

12. 8.3.2 Cross-over resonances in saturation spectroscopy E3E3 E2E2 E1E1 ħω 12 ħω 13

13. ω 12 ω 13 Intensity of probebeam at detector ω Cross-over

14. 8.4 Two-photon spectroscopy Laser Beam splittter sends light to calibration Filter Detector Sample Lens Mirror If the atom absorbs one photon from each of the counter-propagating beams then the Doppler shifts cancel in the rest frame of the atom

15. 1 2 Laboratoey frame ωω Atom frame When twice the laser frequency equals the atomic resonance frequency all the atoms can absorb two photons; whereas in saturation spectroscopy the Doppler-free signal comes only from those atoms with zero velocity.

16. F'=1 F=0 F'=0 F=1 Intensity of Lyman-aradiaion Relative frequency of ultraviolet radiation(MHZ) 0 200800 Lyman-a collisions Transit time Collision broadening Laser bandwith Secood-order Doppler effect Light shift

17. 8.5 Cablibration in laser spectroscopy Laser spectroscopy experiments use tunable lasers, i.e. laser systems whose frequency can be tuned over a wide range to find the atomic, or molecular, resonances.For example,dye lasers(early experiments ), solid lasers (nowdays ),semiconductor diode lasers and so on.But the method of calibrating the laser frequency depends on whether the experiment requires absolute or relative measurements.

18. 8.5.1 Calibration of the relative frequency Detector Etalon Molecules Laser Beam splitter Na vapour 1 2 3 1.Spectrum to be calibrated 2.Molecular 3.Etalon transmission

19. 8.5.2 Absolute calibration (a)A two-photon spectrum of the 1s-2s transition in atomic hydrogen as in Fig.8.11 but on a different scale. (b)(b) The saturated absorption spectrum of molecular tellurium used for calibration. The absolute frequency of the line labeled i was determined with an uncertainty of (by auxiliary measurements). Adapted from Mclntyre et al.(1989). Copyright 1989 by the American physical Society.

20. A frequency chain Helium-neon laser =260THZ (1.15μm ) colour centre laser =260THZ (2.3μm ) Molecalar iodine =520THZ (0.576μm ) =48020 22 2 5 Carbon dioxide laser =26THZ 11.5μm ) Methanol laser =3.72THZ Methanol laser =525GHZ Microwave source =75.1GHZ Microwave source =10.7GHZ Counter Cs frequency standard

21. 8.5.3 Optical frequency combs Recently, a new method of measuring optical frequencies has been invented that has revolutionized optical metrology. The new method relies on the ability to generate frequency combs using laser techniques, i.e. laser radiation that contains a set of regularly-spaced frequencies.

22. The experimental arrangement for the measurement of an optical frequency using a frequency comb from a femtosecond laser.

23. The signal from this detector contains the frequencies The light from the calibrated frequency comb is mixed with some of the output of the continuous-wave laser whose frequency is to be measured, whilst the remaining light from this second laser is used for experiments, e. g.

24. Further reading This chapter has focused on just a few examples of Doppler-free lase : spectroscopy and calibration to illustrate the important principles. Such measurements of the transition frequencies in atomic hydrogen give a precise value for the Rdberg constant and the QED shift. Nowadays, laser spectroscopy is very widely used more complex situations, e. g. liquids and solids. The monogragh by Series ( 1988 ) on the spectrum of atomic hydrogen gives a comprehensive description that includes Lamb and Retherford’s historic experiment and later refinements of the radio-frequency techniques, as well as laser spectroscopy. The measurement of the absolute frequency of light using optical frequency combs is a relatively new technique but already it has had an important impact on optical frequency metrology ( Udem et al. 2002 ).