UChicago Instructional Physics Laboratories

A simple linear absorption spectroscopy experiment is shown at the top of Fig. 3a. The intensity of a monochromatic beam of laser light, passing through a vapor cell, is measured as a function of the laser frequency. When the frequency of the laser matches the frequency of an allowed atomic transition, the photons will excite the atoms in the vapor and the intensity of the transmitted beam will be diminished. A plot of beam absorption as a function of laser frequency will show Doppler broadened absorption features like those seen in the bottom of Fig. 3a.

Figure 3: Comparison of (a) linear saturated absorption spectroscopy to (b) Doppler-free saturated absorption spectroscopy.

For the case of rubidium atoms at room temperature, Doppler broadening of the spectral lines makes the hyperfine features un-resolvable using linear absorption spectroscopy. However, Doppler-free saturated absorption spectroscopy, as illustrated in Fig. 3b, allows one to resolve features normally obscured by the effect of thermal Doppler broadening.

Doppler free saturated absorption spectroscopy uses two overlapping, counter-propagating beams – from the same laser in our case – which we call the probe beam and the pump beam. The intensity of the probe beam is monitored as a function of laser frequency just as is done in linear absorption spectroscopy. In the absence of a pump beam, the probe beam would produce a Doppler broadened linear absorption spectrum. The effect of the pump beam depends on the velocity of the atom along the $z$-axis.

Figure 4: Doppler shifting of probe and pump beams.

First consider the case illustrated in Fig. 4a, where an atom has non-zero velocity relative to the laser, along the z-axis. Since the two beams are counter-propagating one beam will always appear, to the atom, to be red-shifted and the other blue-shifted. Thus, any given transition cannot simultaneously be in resonance with both the probe and pump beams.

Now consider the case in which the atom has zero velocity relative to the laser, along the $z$-axis as illustrated in Fig. 4b. Since there is no Doppler shift, the atom sees both probe and pump beam photons at the same frequency. Thus, it is possible for a given transition to be simultaneously in resonance with both beams. If the laser is tuned to the frequency of a transition and the pump beam is intense enough, it will keep most of the atoms in the vapor in the excited state. (I.e. the pump beam saturates the vapor.) This saturation reduces the number of atoms available to absorb photons from the probe beam and so there is less attenuation of the probe beam than there would be in the absence of a pump beam.

Finally let us examine how both of these cases affect the absorption of the probe beam as the laser frequency is scanned across a Doppler-broadened transition as shown in Fig. 3b. As the laser frequency approaches the atomic transition frequency, the probe beam will be absorbed only by that fraction of the atoms in the vapor whose velocity along the $z$-axis Doppler shifts the probe beam onto resonance. These atoms cannot simultaneously be in resonance with both beams, and so the probe beam will measure the Doppler broadened absorption profile until the laser matches the frequency of an atomic transition. At that point, $f^\prime = f^{\prime\prime}$  and both beams can excite the same population of atoms having zero velocity parallel to the beams. The more intense pump beam will saturate the vapor and the absorption of the probe beam will decrease. As the laser frequency continues past the transition frequency the probe beam will again return to sampling the Doppler broadened spectrum. The result is a dip in the Doppler-broadened spectrum at the Doppler free frequency of the transition. The width of the Doppler free line is just the natural line width of the transition. Recall that the natural line width is related to the lifetime of the excited state by the uncertainty principle as

where $\tau$ is the lifetime of the excited state and $\Gamma$ is the natural line width (in units of energy).

Consider the case when the frequency of the laser $f_L$ is tuned to the midpoint between two transitions with frequencies $a$ and $b$ so that $f_L = \frac{1}{2} (f_a + f_b)$. There will be a subset of atoms whose velocity Doppler shifts the photons in one beam (pump or probe) into resonance with transition $a$ while shifting the photons in the other beam (probe or pump) into resonance with transition $b$. At these frequencies referred to as crossover frequencies, a dip in the Doppler broadened absorption spectra will appear. Thus, an atom with two transitions will exhibit three Doppler-free features, two transitions and one crossover. An atom with 3 transitions will have 3 crossover frequencies as illustrated in Fig. 5.

Figure 5: Energy level diagram for 85Rb showing allowed transitions to the $F = 3$ ground state (solid lines) along with the associated crossover frequencies (dashed lines).