Abstract:

I measured the hyperfine structure of Rubidium in its first excited state by use of Saturated Absorption Spectroscopy with an Open Cavity Tunable Diode Laser.

Theory:

Atomic spectral lines are the result of electrons jumping between different atomic levels. Typically, each atomic level is actually made up of many different states that have the same energy. Spectral lines are split when the energy of one of these states is altered by some force. In atoms under normal conditions, there are two types of splitting present, fine and hyperfine.

Fine structure splitting occurs because of the electromagnetic interaction between an electron and the nucleus. From the point of view of the electron, the nucleus is spinning around it, and hence its moving charge sets up a magnetic field. This field interacts with the intrinsic magnetic moment of the electron. Thus its energy is changed based on the orientation of its spin relative to its orbit as well on the angular momentum of the orbit. A well-known example of this splitting is the sodium doublet, and typically it is not difficult to observe in other atoms because the splitting is often on the order of a nanometer.

Hyperfine splitting occurs because of the interaction between an electron and the nucleus. However, this effect is due to the interaction of the spins of the electron and the nucleus. Essentially the splitting is just due to the energy of two magnetic dipoles in different orientations. The magnetic moment of the nucleus is not simple, however, like that of the electron, and in fact depends critically on nuclear structure, making it an interesting phenomenon to study. Unfortunately the hyperfine splitting is very small; according to theory it should be smaller by the ratio of the mass of an electron to the mass of a nucleon, or about 1 part in 2000. In practice, this is smaller than the Doppler broadened spectrum of a single line, and hence special means are necessary to observe this type of splitting.

Rubidium is a convenient atom to study because it is an alkali metal. This means it has several full shells of electrons and one electron in an empty shell by itself. Thus, its interactions are simple, roughly similar to that of hydrogen because the closed shell electrons can be ignored for many purposes, and predictions about its behavior are far simpler to make than with other many-electron atoms. I will be looking at the excitations from the ground state, 5S_1/2, to the first two excited states, 5P_1/2 and 5P_3/2 (fig. 1). The fine structure splitting between the first two excited states is about 15 nm. (The so-called D1-transitions (5S_1/2 to 5P_1/2) occur at ~795 nm and the D2-transitions (5S_1/2 to 5P_3/2) at ~780 nm.) I will only be observing the D2-transitions, both because of its wavelength is close to that of a widely available diode laser, and because it has more hyperfine levels.

Hyperfine splitting of the ground state, 5S_1/2, splits the D2-transitions into two groups. In addition, there is also splitting of the excited state, 5P_3/2, into four different levels because of the larger number of available spin configurations. Although this appears to leave a total of 8 states, two are not allowed because of selection rules. (Specifically, the orbital angular momentum cannot change by more than one unit.) Thus there are a total of 6 transitions that are divided into two main groups because the ground state splitting is far stronger than that of the excited state. (This is because the ground state is much closer to the nucleus.) Although the splitting within each main group is fairly small, the groups themselves are split enough that their Doppler spectrums do not overlap at room temperature. The 3 lines in each group, however, have to be observed using a special method, such as saturated absorption spectroscopy.

What makes rubidium a good candidate for study, in addition to it being an alkali metal, is that it has two naturally occurring isotopes in reasonable abundances. It is known that ⁸⁵Rb (72% natural abundance) has a total nuclear spin of 5/2, while ⁸⁷Rb (28%) has a total spin of 3/2. This should have significant effects on the magnetic moment of the nucleus and thus on the hyperfine splitting. This means that instead of observing 2 groups of transitions, there should be 4, for a total of 12 different D2-transitions. In addition, the relative abundances mean that one should be able to determine which transitions are due to which isotope simply by observing the absorption strengths of the different lines.

Open Cavity Tunable Diode Lasers: Diode lasers are cheap and widely available with moderately powerful outputs, however they suffer from numerous drawbacks for scientific applications. Their extremely small oscillation cavities produce a large line width (on the order of a nm), and their wavelengths are not precisely controlled in the way that they are with other types of lasers. Furthermore, their output frequency is a altered by both the temperature of the diode and the current flowing through it, but in a way that is not easily controllable or continuous. However, they can fairly easily be improved by use of external feedback. To do this, a large portion of the laser light is fed back into the laser cavity. This essentially creates a new laser cavity, and the electromagnetic waves are allowed to oscillate along a longer path and the light makes more passes through the laser cavity.

One simple way of doing this is by employing a feedback grating. The setup I used is shown as fig. 2. The grating is placed so that only a specific wavelength of light is directly reflected back into diode junction (which is extremely small). Since different wavelengths of light are refracted at different angles by the diffraction grating, this means that changing the angle of the grating slightly also changes which wavelength of light makes it back to the laser diode. The wavelengths of light that are reflected back into the cavity then stimulate more emission of light at the same frequency, and almost instantly that wavelength of light overrides all other emission. Since the laser can only lase at one very specific frequency, the line width is drastically reduced, in theory down to the 100 KHz range, although in practice it is typically larger (in my experiment, it was ~30 MHz). By placing a piezo element behind one edge of the grating it becomes possible to very accurately and stably control the output frequency of the laser for use in fine studies of spectra.

Saturated Absorption Spectroscopy: Spectral lines do not have an infinitesimally small width; rather the line width is usually determined by Doppler broadening. This effect is due to the thermal motions of the individual molecules in the gas being observed. This motion causes a slight shift in the observed absorption wavelength due to the Doppler effect. Thus when one observes the absorption spectrum of an entire gas, there appears a smooth curve around the true absorption frequency as opposed to a sharp spike. Usually this is not a problem as the width is relatively small in comparison to the distance between different atomic levels. However, when very fine features are being observed, such as the hyperfine structure, this Doppler-width can be significantly greater than the separation between the individual lines and it becomes impossible to separate them. Fortunately, there are several methods to overcome this problem; the one we will employ is known as saturation spectroscopy.

To implement saturation spectroscopy we will use two laser beams, a strong saturation beam and a weak probe beam. My setup is shown as fig. 3. The probe beam passes through the gas being studied in the same location as the saturation beam, which is traveling in approximately the opposite direction, before being detected by a photodiode. The beams are both split from the same source, in this case a tunable diode laser, so that they all have the same wavelength.

If the laser is not tuned to the center of a spectral line, the two beams should be absorbed in equal amounts by the vapor and no differential signal is observed. The saturation beam has no effect on the probe beam because the two excite different atoms in the Doppler profile. For example, if the laser wavelength is slightly below the center of the absorption peak, the probe beam will excite only atoms moving towards it with some speed, v, which is enough to red-shift the beam from the atom’s point of view so that it coincides with the transition frequency. Conversely, the absorption beam will excite only atoms moving with the same speed in the opposite direction, namely –v. Since the two beams affect different individual atoms in the vapor, they do not interfere. However, in the case that the laser wavelength is exactly at the transition frequency the affected atoms are not moving, i.e. v = 0, and the two lasers are exciting the same group in the Doppler profile. If the saturation beam is significantly intense, the probe beam does not have as many atoms available to be excited because the saturation beam has already excited them. In this case the probe beam is attenuated less than the reference beam as it travels through the vapor, and a differential signal is measured. Consequently, the width of the differential signal as it is scanned across different frequencies is determined only by the fundamental properties of the transition (typically the excited lifetime) and the spectral width of the laser.