Doppler-free saturation spectroscopy

The saturated spectroscopy , often short saturation spectroscopy is, in the laser spectroscopy a high-resolution spectroscopic method for investigating atomic spectra , in which by appropriate experimental setup , the effects of Doppler broadening can be avoided. The method enables effects such as the hyperfine structure and the natural line width of atomic spectra to be measured.

Experimental setup

Basic measurement setup

The basic structure of saturation spectroscopy is that a tunable laser is split into two partial beams of different intensity by a beam splitter . Both partial beams are deflected via mirrors in such a way that they run parallel but in opposite directions (anti-collinear) through the sample to be measured (e.g. a gas ). The stronger beam is called the pump or saturation beam , the weaker test , query or trial beam . The sample beam is directed into a spectrometer , from which it can be read off which frequencies were absorbed in the sample .

Alternatively, it is possible to use two lasers with the same frequency without using a beam splitter. However, it must also be ensured that both lasers are actually operated at the same frequency, which requires greater effort.

The use of two opposing beams is the difference to “normal” spectroscopy, in which only a single beam is directed through the sample directly into the detector.

Physical explanation

Population density in saturation spectroscopy with the Bennet holes of the pump and interrogation beam.

For the description one uses the consideration of different velocity classes of the particles of the sample, which is given by the thermal movement according to the Maxwell-Boltzmann distribution . Due to the Doppler shift , absorption takes place at the absorption frequency for an incident laser beam of the frequency only for particles of the velocity class . Correspondingly for a laser beam running in the opposite direction . ${\displaystyle f_{0}}$ ${\displaystyle f}$ ${\displaystyle v_{z}=\lambda (f-f_{0})}$ ${\displaystyle v_{z}=-\lambda (f-f_{0})}$

Lamb dip in the absorption spectrum.

If both the pump and the interrogation beam have the same frequency , then only two cases can occur: ${\displaystyle f}$

• ${\displaystyle f\neq f_{0}}$: Due to the optical Doppler effect, both beams are absorbed by particles moving in opposite directions, i.e. different speed classes. In the population density of the lower level there are two minima ( Bennet hole , see animation on the right). The Doppler-broadened profile of the interrogation beam can be seen on the detector.

• ${\displaystyle f=f_{0}}$( Resonance ): Both beams are absorbed by the particles that are at rest relative to the direction of the beam or moving perpendicular to the beam, i.e. of the same velocity class . In this case, there is no longer any Doppler shift and the Bennet holes overlap. Due to the high intensity of the pump beam, a large number of excited states occur , with the lower level being depopulated and the upper level being saturated. The query beam is therefore hardly absorbed and in the absorption profile there is a strong incision in the originally Doppler-broadened curve, the so-called Lamb dip in the form of the natural line width. ${\displaystyle v_{z}=0}$

If, in the case of resonance, the difference between the absorption spectra with and without a saturation beam is formed with a lock-in amplifier, for example , an absorption profile without Doppler broadening is obtained. The width of the lines is now only given by their natural line width.

Cross-over signal

Cross-over signal between the lamb dips of the transitions and with a common level. ${\displaystyle f_{1}}$ ${\displaystyle f_{2}}$

In the absorption spectrum there is an additional crossover signal at the middle frequency between the lamb dips of two transitions and with a common upper or lower level: ${\displaystyle f_{1}}$ ${\displaystyle f_{2}}$

${\displaystyle f_{c}={\frac {f_{1}+f_{2}}{2}}}$

This can be explained by the fact that at this frequency the opposite Doppler shift of the pump and interrogation steel on the two transitions is the same, but opposite, so that both the depopulation by the pump beam and the absorption by the interrogation beam are at the same speed class occur, whereby the absorption is reduced analogous to the formation of the lamb dips.

In the case of a common lower level there is an additional absorption minimum, in the case of a common upper level there is an absorption maximum.

The half-width of the crossover results from the half-widths of the transitions involved:

${\displaystyle \gamma _{c}={\frac {\gamma _{1}+\gamma _{2}}{2}}}$

Other methods

Absorption spectra of the first excited state of rubidium : the hyperfine structure, which cannot be seen with conventional laser spectroscopy (blue), is only resolved by Doppler-free saturation spectroscopy (red).

Saturation spectroscopy

In addition to forming the difference between the absorption spectra with and without the saturation beam, the fluorescence can also be measured, whereby the Lamb dips are visible in the fluorescence spectrum . This is particularly useful for samples with a low density (and therefore low absorption).

If the sample is brought directly into the resonator of a laser, the losses due to absorption in the case of resonance are minimal, as a result of which the laser power has a sharp maximum here. If the laser frequency is actively regulated to this maximum, lasers can be built with a very precisely defined and stabilized wavelength.

Two-photon spectroscopy

In Doppler-free two-photon spectroscopy, the absorption is carried out by two different photons from the two opposing beams ( two-photon absorption ). In analogy to saturation spectroscopy, this is only possible for the case in which no Doppler shift takes place. ${\displaystyle f=f_{0}}$

literature

• W. Demtröder , Laser Spectroscopy 1 - Basics . 6th edition. Springer 2011, ISBN 978-3-642-21305-2 (especially chapters 3.2, 3.4, 3.5)
• W. Demtröder , Laser Spectroscopy 2 - Experimental Techniques. 6th edition. Springer 2013, ISBN 978-3-642-21446-2 (especially chapters 2.2, 2.3, 2.6)
• Lexicon of Physics . Spektrum Akademischer Verlag 1998, https://www.spektrum.de/lexikon/physik/saettigungsspektoskopie/12722
• Atomic Spectra Database