Hyperfine Spectrum of Rubidium: laser spectroscopy experiments Physics 480W (Dated: Sp19 Paper #4) I. OBJECTIVES FOR THESE EXPERIMENTS We wish to use the technique of absorption spec- troscopy to probe and detect the energy level structure of atomic Rubidium, Rb I, whose ground state is split by a tiny amount on account of nuclear magnetism. In effect, the spectroscopy we do today tells us about nuclear prop- erties and so combines atomic and nuclear physics. The main result of this experiment, the 4th of the semester, is to 1. measure the hyperfine splitting for each isotope, and compare with accepted values, with the fol- lowing details in mind: (a) what is the hyperfine splitting of the ground 2 state, S1=2 term? Do we need saturation- absorption techniques for this? (b) what are the hyperfine splittings of the ex- 2 cited state, P3=2 term, that can be reached with a nominal wavelength of 780nm from the ground state? Here we need saturation- absorption techniques to perform sub-Doppler FIG. 1. Note the four 'blobs'. Why are there four? Which spectroscopy, certainly. Help the reader un- 85 are associated with Rb37, and so on. If all goes swimm- derstand what is entailed in the technique, ingly, we'll get an absorption spectrum that looks much line both experimentally and theoretically. You the figure below the setup. The etalon data will be needed to will need to explain what `saturation' means. make the abscissa something proportional to frequency. The The saturation intensity is an important fig- accepted value of the gap between the 2 outermost dips is ure of merit. How might one use the mea- 6.8347 GHz. Note also the schematic for the Rb I absorp- surements of the cross-over resonances to help tion experiment of part 6. A neutral density filter (ND) can determine (and modestly reduce) the uncer- be placed before the beam enters the gas cell (ND-pre) or tainty in the gap spacings (energy gaps)? after the beam exits the gas cell (ND-post), allowing us to compare the absorption of laser beams of very different inten- 2. compare the ground state splittings with theory, sities within the gas cell which are nevertheless of the same following Melissinos, section 6.3. Using this de- intensity at the detector. A portion of the incident beam is velopment (cf. especially equation 6.24), estimate deflected to an etalon using a beamsplitter (70t,30r). The etalon provides frequency notches every 300 MHz. hBe(0)i. Compare this expectation value of known magnetic fields to get some perspective for its mag- nitude. Is it big or small? What do you expect (before you begin)? 3. measure the FWHM (full width half max) of the blobs (also called dips) to estimate the temperature A. Procedures of the Rb atoms in the vapor, consider exhibiting the Gaussian fit and ask: should it be Gaussian? 1. Absorption spectrum of Rb I Give physical arguments to support your work. Note that the deliverable concerning the 'pre' and 'post' This "simple" laser technique can resolve the ground- experiment with the Neutral Density filter is not required state hyperfine (hf) splitting of both isotopes which is for the 4th paper. The discussion of that experiment and possible since the laser line width is very small compared its relation to the concept of saturation intensity is left with the Doppler broadening of the spectral lines. Using in solely as an aid or a spur to understand the concept the simple technique, schematically diagrammed below of saturation. The intended main contributions of the in figure I A 1 we can see four big blobby dips. Try to get papers are given above. a complete spectrum showing all four blobs at different 2 intensities, say, one high, and one low. take the best spec- trum and get hard copy, and tape the figure into your lab notebook (along with all the settings). Compare theory and experiment. In this case, this means identifying the quantum numbers associated with each dip, and com- paring the gaps with the known frequency intervals (a good reference is Rao[10]). Estimate, roughly, the tem- perature of the Rb atoms from the Doppler broadening of the lines. Is there any difference in the spectra as the intensity of the laser is changed? Can you account for the differences? FIG. 3. Schematic for the Rb I absorption experiment. We use beam splitters and mirrors to try to demonstrate the sat- uration effect, that is, to make visible the separate transitions between one hyperfine state in the ground state and one hy- perfine state in the excited state (of the sort F ! F 0, where FIG. 2. Schematic (simple version) for the Rb I absorption ex- the prime indicates the excited state). periment. We can simply re-position the PIN diode detector to block the probe beam (or the pump beam, for that matter) to collect the absorption spectrum without using Doppler-free techniques. dips with a series of notches in it, as shown in figures 6.25 and 6.26 in our text[8]. The number of notches depends on actual hyperfine structure of the terms participating in the electric dipole transitions. The energy level structure of Rb is shown below. Ex- perimentally, one sees two spectral lines for each isotope 2. Which arrangement (`pre' or `post') creates the deepest of Rb, transitions which are designated "a" and "b" on absorption dips the energy level diagrams in figure I A 3. Please look at figure 1 again. Which arrangement leads to the deepest absorption dips? Why would there be any difference at all? This is the question to be addressed. The actual measurement that this question is meant to highlight of course is the measurement of the intensity of the input laser beam into the optical cavity (that part containing the gas cell in figure 2), which is to be com- pared with the saturation intensity of the transition. 3. Saturation absorption spectroscopy We use a tunable diode laser to sweep the frequency of a beam of photons though an energy interval that can excite Rb I atoms from the ground state to one of the low lying excited states. Instead of an interference filter guaranteeing that only certain transitions are possible, the wavelength and `detuning' range of the laser itself will guarantee which transitions (electric dipole!) are FIG. 4. Partial energy level diagram for Rb I, showing the possible. The set-up for the first experiment is shown 2 2 schematically in figure 1. split ground state S1=2 and an excited state, P3=2, for the two naturally occurring isotopes of Rb I. The frequency swept laser light is passed through a cell containing rubidium vapor and the transmitted light is Doppler broadening, however, obscures the far smaller detected using a PIN diode. The fond hope is to obtain a hyperfine splitting of the exited state. To see the separate 85 signal that looks like (for the one of the Rb37 dips) like a transitions from one hyperfine-split (ground) state to the 3 excited hyperfine-split states, the ones `allowed' by selec- mented differs somewhat from everyone else's, (e.g. tion rules for electric dipole transitions, one must some- Melissino's set up is like many one can find in the how get around the confounding nature of Doppler broad- `literature', two papers of which will be useful for ening. One technique which has proved to be very pow- us; my set up is most like the one they use at cal- erful in this regard is saturation absorption spectroscopy, tech; I will include their `manual' for reference as described in the references above. We will need to add a well) second, far older technique, called phase sensitive detec- tion, which typically involves the use of some means of signal modulation and the lock-in amplifier, as shown in 2. Arthur Schawlow's nobel prize address[4] gives a figure I A 3. These are powerful and proven techniques in good overview of `sub-Doppler' spectroscopy, which modern physics research. is what we'll be doing, using the technique of sat- uration absorption spectroscopy. We'll be using a lockin amplifier in the way that he describes. The money-shot for our purposes is figure 2, how- ever, from the point of view of his contribution to physics, that would be (in my opinion, just my opinion) figure 7. Sub-Doppler spectroscopy, made possible by the technique of saturation ab- sorption spectroscopy, made deep comparisons be- tween quantum theory and atomic (and molecular) physics possible. There was also a kind of curious artifact of the technique. Question: how to account for all those peaks? Do they all correspond to elec- tric dipole transitions between (hyperfine-split) en- ergy levels? Answer: no. There is something new FIG. 5. In this application, a single optical beam is chopped here. It is called a `cross over resonance'. by the outer row of slots, and the reference output from the right BNC is used to lock the lock-in amplifier to the chop frequency. This text is shamelessly lifted from SRS technical 3. Doppler-free saturated absorption: Laser note on optical choppers spectroscopy[9] a very good `tutorial' paper published in the American Journal of Physics that describes the techniques referred to in the above references, and which address `the curious artifact For both isotopes, obtain the so-called Doppler-free referenced above. spectrum of one of the absorption dips, and account for all of its features, comparing theory with experiment. Question: are there more notches or lines than pairs of 4.