Beat signal

Figure 7.8 Pump-control-probe quantum beat signal obtained at various probe wavelengths from 378 (bottom) to 390 (top) nm. The delay between the pump and control pulses was set around timing. Each panel shows the different relative phase condition between the pump and control pulses. Reproduced with permission from the supplement of Ref. [39]. Copyright 2009 by the American Physical Society. (See color plate section for the color representation of this figure)...

The beat signal is first nulled with a glass slide in the sample position by moving the prism along the optical bench. The slide is then replaced by the fluorescent sample and the prism is again moved to a null. If X is the distance the prism must move, the lifetime T may be expressed as... 

The nature of the radiative decay in the resonance and in the statistical limits was considered by Berry and Jortner,7 who examined the interference effects in the radiative decay of coherently excited states. Quantum beat signals can be observed and used to analyze close-lying molecular... 

Level crossing spectroscopy has been used by Fredriksson and Svanberg44 to measure the fine structure intervals of several alkali atoms. Level crossing spectroscopy, the Hanle effect, and quantum beat spectroscopy are intimately related. In the above description of quantum beat spectroscopy we implicitly assumed the beat frequency to be high compared to the radiative decay rate T. We show schematically in Fig. 16.11(a) the fluorescent beat signals obtained by... 

Fig. 16.10 Quantum beat signals of high lying 2D states of Na obtained by time resolved selective field ionization. The variation of the beat frequency with principal quantum number is shown. Several quantum beat frequencies appear due to a Zeeman splitting of the fine structure levels in the earth s magnetic field (from ref. 43).

The problem of determining the set u>mfmf, from the observed quantum beat signal is solved with the aid of Fourier transformation. It is more difficult to interpret the signals of magnetic quantum beats in the case of polyatomic molecules, such as in [389] with SO2 and in [90] with N02(i2 2), where, as a general rule, one observes many perturbations between different states. 

Fig. 7. Allan variance

The results (3) - (5) were confirmed by an independent measurement using both iodine spectrometers, locked to the same HFS components of the P(54) line. While the ILP laser frequency was counted in the manner described above, the PTB laser frequency - shifted by an AOM - was determined by additionally counting the beat signal between the two oscillators. The pressure in the cells was kept equal, setting the temperature of the cold fingers of both cells to T = -5 °C. After extrapolating to cell number 16/89 and to an iodine pressure at -20 °C, the results for the PTB laser system agree with the outcomes (3) - (5) but uncertainty bars were now increased due to the lower reproducibility of the PTB laser. 

In 1986, R. BEAUSOLEIL and D. McINTYRE completed their thesis research at Stanford with an absolute frequency measurement of the F = 1 component of hydrogen 1S-2S [11,20], As frequency reference they employed a 486 nm cw dye laser, locked to a narrow absorption line of 1J Te2 vapor. This line was chosen near a reference line, calibrated to within 4 parts in 1010 by A. FERGUSON et al. [21]. Its second harmonic coincides very nearly with the resonance frequency of the hydrogen two-photon transition, so that the frequencies can be precisely compared by observing a radio frequency beat signal. 

An alternative, proposed by R. Kallenbach, employs two tunable dye lasers, operating at the fourth and sixth harmonic of the 3.39 pm helium neon laser frequency f. The frequency ratio of 3 2 is assured by comparing the second harmonic of the laser at 6f with the third harmonic of the laser at 4f. The frequency difference is simultaneously maintained at 2f by monitoring a beat signal between the sum frequency 4f+f and the difference frequency 6f-f. Summing the frequencies 6f and f finally produces 0.485 pm radiation at 7f. 

The spectrum of lattice-trapped atoms is recorded using a heterodyne technique. Light fluoresced by the trapped atoms is combined with light (frequency shifted by a modulator) from the laser forming the lattice. When the beams mix on a photodiode they create a beat signal at the difference frequency between the fluorescence and the frequency-shifted laser. The power spectrum of the photocurrent is identical to the fluorescence power spectrum, but centered at radio frequency. This heterodyne technique is not sensitive to the frequency jitter of the laser because the jitter is common between the fluorescence and the laser, which acts as a local oscillator. 

Research in textile electrodes has led to encouraging findings globally and to some product launches. Investigating textile electrodes for medical purposes, Hertleer et al. (2004) demonstrated that heart beat signals obtained from conventional electrodes with electrogel are comparable with knitted textile electrodes made with yams of metallic fibres. No gel was needed for the textile electrode, which can be a benefit in terms of convenience and user comfort. De Rossi et al. (2003) also found that their... 

The phase modulation has an additional advantage the first two sidebands at frequencies modulation frequency therefore receives the superposition of two beat signals between the carrier and the two sidebands, which cancel to zero if no absorption is present. Any fluctuation of the laser intensity appears equally on both signals and is therefore also cancelled. If the laser wavelength is tuned over an absorption line, one sideband is absorbed, if - X2 coincides with the absorption frequency coq (Fig. 1.8). This perturbs the balance and... 

If several resonator modes within the bandwidth of the laser pulse are excited, beat signals are superimposed onto the exponential decay curve. These beats are due to interference between the different modes with differing frequencies. They depend on the relative phases between the excited resonator modes. Since these phase differences vary from pulse to pulse when the cavity is excited by a train of input pulses, averaging over many excitation pulses smears out the interference pattern, and again a pure exponential decay curve is obtained. 

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