Doppler-free

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)). 

Determination of Excited-State Rotational Constants and Structures by Doppler-Free Picosecond Spectroscopy, J. S. Baskin and A. H. Zewail, J. Phys. Chem. 93, 5701 (1989). 

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... 

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). 

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. 

The data recorded as the laser frequency is scanned consists of the fluorscence signal from the PMT, a Doppler-free I2 spectrum and frequency markers from the etalon. The etalon provides a calibration of the frequency scan. The Doppler-free I2 spectra provides an absolute frequency reference used to correct for small laser frequency drifts, separator voltage drifts and to determine the absolute acceleration voltage of the separator for the Doppler shift corrections. We are thus able to record data over long periods of time, e.g. 3 hours, and maintain a reasonable resolution of 100 MHz. Some of the first online data recorded with this system is shown in Figure 2. The overall detection efficiency has been measured to be 1/1000, i.e. one detected photon per 1000 atoms, for the largest transition in the nuclear spin 1/2 isotopes. 

Wieman, C. and Hansch, T.W. (1976). Doppler-free laser polarization spectroscopy, Phys. Rev. Lett., 36, 1170-1173. 

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...

Fig. 2. Schematic diagram of the apparatus. The superconducting magnetic coils create trapping potential that confines atoms near the focus of the 243 nm laser beam. The beam is focused to a 50 pm waist radius and retro-reflected to allow for Doppler-free excitation. After excitation, fluorescence is induced by an applied electric field. A small fraction of the 122 nm fluorescence photons are counted on a microchannel plate detector. Not shown is the trapping cell which surrounds the sample and is thermally anchored to a dilution refrigerator. The actual trap is longer and narrower than indicated in the diagram...

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]. 

When the transition temperature is achieved, a finite fraction of the atoms fall into the lowest energy quantum state of the trap. The spatial extent of the condensate is much smaller than the thermal radius of the cloud. Only a small fraction of the atoms are required to create a narrow region of very high density at the bottom of the trap. This high density region is readily observed because of its large cold collision frequency shift. The spectrum arising from the condensate can be seen in (Fig. 5), red-shifted up to 0.5 MHz from the Doppler free line. 

The Doppler-sensitive line gives a second clear signature for Bose-Einstein condensation. Because the lowest energy state is the lowest momentum state, the condensate appears as a relatively narrow peak at the center of the Gaussian spectrum. Its width is given by the cold collision frequency shift and is the same as in the case of Doppler free spectrum. 

Because of the large density contrast between the condensed and noncondensed fraction, we are able to study the density of the noncondensed fraction even in the presence of the condensate. We determine the peak density from the cold collision shift of the Doppler free line. Reducing the trap depth by lowering the rf-frequency reduces the temperature while increasing the density. However, when the critical density is achieved, as observed by the onset of the far red-shifted signal, the peak density in the noncondensed cloud decreases with... 

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