Two-photon Doppler-free

Laser spectroscopy of the 1S-2S transition has been performed by Mills and coworkers at Bell Laboratories (Chu, Mills and Hall, 1984 Fee et al, 1993a, b) following the first excitation of this transition by Chu and Mills (1982). Apart from various technicalities, the main difference between the 1984 and 1993 measurements was that in the latter a pulse created from a tuned 486 nm continuous-wave laser with a Fabry-Perot power build-up cavity, was used to excite the transition by two-photon Doppler-free absorption, followed by photoionization from the 2S level using an intense pulsed YAG laser doubled to 532 nm. Chu, Mills and Hall (1984), however, employed an intense pulsed 486 nm laser to photoionize the positronium directly by three-photon absorption from the ground state in tuning through the resonance. For reasons outlined by Fee et al. (1993b), it was hoped that the use of a continuous-wave laser to excite the transition would lead to a more accurate determination of the frequency interval than the value 1233 607 218.9 10.7 MHz obtained in the pulsed 486 nm laser experiment (after correction by Danzmann, Fee and Chu, 1989, and adjustment consequent on a recalibration of the Te2 reference line by McIntyre and Hansch, 1986). 

The interval 235i — l3,S i has been measured by the method of two-photon, Doppler-free excitation in two experiments [13] [14], We will detail the latter experiment, which employs continuous-wave excitation. 

In Fig. 1 a schematic diagram of a two-photon Doppler-free experiment is shown. It is taken from the ASACUSA proposal [13] for the higher precision measurements of the transition lines between (36,35) and (34,33) metastable states, which are expected to be carried out in the nearest future. In what follows results of theoretical consideration for this particular transition are presented. 

In the NBS work, the transition of interest for a frequency standard is the Hg+ 5d 6s Si 5d 6s 5/2 quadrupole transition at 281.5 nm shown in Fig. 1. The 5/2 level has a lifetime of 86 ms, corresponding to a natural width of 1.8 Hz. Use of the single photon quadrupole transition has an advantage over two-photon Doppler free transitions because ac Stark shifts are negligible. 

The 1S-2S transition in muonium has also been measured by laser spectroscopy. The transition is induced by a two-photon Doppler-free process and detected through the subsequent photoionization of the 2S state in the laser field. The key to success in this experiment was the production of muonium into vacuum from the surface of heated W or of Si02 powder. The discovery experiment(33) was done at the KEK facility in Japan with a pulsed muon beam and an intense pulsed laser system. A subsequent experiment(34) done with the pulsed beam at RAL and a similar pulsed laser has improved the signal substantially and has achieved a a precision of about lO" in the 1S- 2S interval, thus determining the Lamb shift in the IS state to about 1% accuracy (Fig. 22). The precision of this experiment should be greatly improved in a new experiment now underway at RAL. This experiment will provide a precise... 

FIGURE 35 Example of high-resolution spectrum in sodium vapor obtained with two-photon Doppler-free spectroscopy. [Reproduced from Bloembergen, N., and Levenson, M. D. (1976). Doppler-free two-photon absorption spectroscopy. In High Resolution Laser Spectroscopy (K. Shimoda, ed.), p. 355, Springer, New York.l... 

Also, the residual Doppler effect has not been considered in the theoretical calculations for the nonlinear dispersion. Although two-photon Doppler-free configuration [19] has been used in all the experiments described in this Chapter, it can only cancel the first-order Doppler effect. To consider the residual Doppler effect due to the ground-state frequency difference, integration over the veloeity distribution for the hot atoms should be carried out [19], which was not done in our simple treatments [16,17]. 

Multiphoton Absorption and Ionization. High laser powers can induce the simultaneous absorption of two or more photons that together provide the energy necessary to excite a transition this transition may be one that is forbidden as a single-photon process (8,297). Such absorption can be made Doppler-free by propagating two laser beams of frequency V in opposite directions, so the Doppler shifts cancel and a two-photon transition occurs at 2v for any absorber velocity. The signal is strong because aU absorbers contribute, and peak ampHtudes are enhanced by, which may... 

Doppler-free two-photon spectroscopy spect A version of Doppler free spectroscopy in which the wavelength of a transition Induced by the simultaneous absorption of two photons is measured by placing a sample In the path of a laser beam reflected on itself, so that the Doppler shifts of the Incident and reflected beams cancel. dap-lor fre tu fO,tan spek tras-ka-pe j... 

Accuracy of the radiofrequency measurements of the classic 2S — 2P Lamb shift [15, 16, 23, 24, 25] is limited by the large (about 100 MHz) natural width of the 2P state, and cannot be significantly improved. New perspectives in reducing the experimental error bars of the classic 2S — 2P Lamb shift were opened with the development of the Doppler-free two-photon laser spectroscopy for measurements of the transitions between the energy levels with different principal quantum numbers. Narrow linewidth of such transi-... 

The methods of Doppler-free two-photon laser spectroscopy allow very precise comparison of the frequencies of the IS — 2S transitions in hydrogen and deuterium. The frequency difference... 

Starting with the pioneering work [52] Doppler-free two-photon laser spectroscopy was also applied for measurements of the gross structure interval in mnoninm. Experimental results [52, 53, 54, 55] are collected in Table 12.5, where the error in the first brackets is due to statistics and the second error is due to systematic effects. The highest accuracy was achieved in the latest experiment [55]... 

For many years, this hydrogen maser measurement remained the most accurate experiment in modern physics. Only recently the accuracy of the Doppler-free two-photon spectroscopy achieved comparable precision [34] (see the result for the IS — 2S transition frequency in (12.7)). 

Even in a molecule the size of benzene the resolution achieved in this way is sufficient to investigate the dynamic behavior of individual rotational states. For this it is necessary to eliminate the Doppler broadening of the rovibronic transitions. Two methods have been applied (i) the elimination of Doppler broadening in a Doppler-free two-photon-transition and (ii) the reduction of Doppler broadening in a molecular beam. Measurements of the dynamic behavior have been performed in the frequency [3] and time domain [4]. We will briefly summarize the results from high-resolution measurements and discuss the conclusions on the intramolecular decay mechanism. Then it will be discussed how the intramolecular dynamics is influenced by the attachment of an Ar or Kr atom to the benzene molecule, leading to a weakly bound van der Waals complex. 

Figure 1. Linewidlhs of different rotational transitions in the 14q1q vibronic band of benzene measured with Doppler-free two-photon absorption. The observed strong dependence on the quantum number J of the rotational angular momentum is evidence for a rotationally dependent intramolecular coupling process. (Taken from Ref. 3.)...

As shown by Fig. 14.15, the resonances occur near zero field, and it is easy to calculate the small Stark shifts with an accuracy greater than the linewidths of the collisional resonances. As a result it is straightforward to use the locations of the collisional resonances to determine the zero field energies of the p states relative to the energies of the s and d states. Since the energies of the ns and nd states have been measured by Doppler free, two photon spectroscopy,22 these resonant collision measurements for n = 27, 28, and 29 allow the same precision to be transferred to the np states. If we write the quantum defect dp of the K np states as... 

Chu, S., Mills Jr., A.P. and Hall, J.S. (1984). Measurement of the positronium 13Si-23Si interval by Doppler-free two-photon spectroscopy. Phys. Rev. Lett. 52 1689-1692. 

Fig. 1. Setup for Doppler-free two-photon spectroscopy of the hydrogen IS — 2S transition...

Fig. 2. Doppler-free spectra of the 15 — 2S two-photon transition (F = 1 —> F = 1) in atomic hydrogen, a) Spectra for three different nozzle temperatures and no delay time, b) Time resolved spectrum (nozzle temperature 6.5 K). This plot gives the 2S count rate as a function of the absolute optical frequency for different delay times. The inset shows the spectra with longer delay times on a magnified scale...

At low density (< 1012 cm-3) and temperatures > 100 /jK the two-photon lineshape is a double exponential, exp(- p /<5p0) [3], as expected for Doppler-free two-photon excitation by a Gaussian laser beam of a thermal gas [29]. Here v is the laser detuning from resonance and 8v0 is the linewidth due to the finite interaction time of the atom with the laser beam. At low temperature, lines as narrow as 3 kHz (FWHM at 243 nm) have been observed. A detailed discussion of this lineshape in the trap and the appearance of sidebands due to coherence effects for repeated crossing of the laser beam can be found in [30]. 

Fig. 5. Composite 15-2,S two-photon spectrum of trapped hydrogen after condensation. o-spectrum of sample without a condensate -spectrum emphasizing features due to a condensate. The high density in the condensate shifts a portion of the Doppler-free line to the red. The condensate s narrow momentum distribution gives rise to a similar feature near the center of the Doppler-sensitive line...

Abstract. The current experimental situation regarding tests of fundamental physics using positronium is reviewed. Five measurements are discussed and compared with theoretical predictions the singlet and triplet annihilation decay rates, the ground state and the n = 2 energy intervals, and the Doppler-free two-photon excitation of the IS to 2S transition. Previous results, recent progress (where appropriate), and the outlook for future improvements in these measurements are discussed. 

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