Laser Spectroscopy Experiments

Home , Nicolaas Bloembergen, Willis Lamb

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 spectroscopy 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 following 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 spectrum 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 comparing the gaps with the known frequency intervals (a good reference is Rao[10]). Estimate, roughly, the temperature 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 saturation effect, that is, to make visible the separate transitions between one hyperfine state in the ground state and one hyperfine 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 compared 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 detection, 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 saturation absorption spectroscopy. We’ll be using a lockin amplifier in the way that he describes. The money-shot for our purposes is figure 2, however, 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 absorption spectroscopy, made deep comparisons between 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 electric dipole transitions between (hyperfine-split) energy 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. Nonlinear spectroscopy of rubidium: an undergrad- hyperfine transitions? Yes! What are the extra notches? uate experiment, V Jacques, B Hingant, A Allafort, (See the discussion of crossover frequencies in the Pre- M Pigeard and J F Roch, Eur. J. Phys. 30 921 ston’s article[9]). Be sure of quantum numbers of the (2009). This paper reports the state of the art re- transitions you are exciting. Be sure to record the best sults for this experiment. spectra from each isotope, obtain hard copy and tape them into your lab notebook, along with the settings of all the instruments, so that you could in principle recre- 5. Demonstrating optical saturation and veloc- ate the data (one always has to do this!). Save the data ity selection in rubidium vapor, Razdan & file, and write down the path name in your lab notebook. Van Baak, Am. J. Phys. 67 832 (1999).

6. About Lock-in Ampliﬁers, Stanford Research Sys- B. References: read this stuﬀ AFAHP, which tems (SRS) technical applications note. There is obviously means as fast as humanly possible:), and an even more brief description of the technique in no, this doesn’t mean one can get away with really, Melessinos[8], in section 3.8. really long sub-heading titles in real research papers, but who knows... 7. Using Etalons, a very simple, very brief discussion 1. High Resolution Spectroscopy, Ch.6, section 6.6 in about Fabry-Perot etalons, composed as technical our text.[8] Our experiment relates directly to the applications document for Melles Griot, Inc. We discussion of saturation absorption spectroscopy will use an etalon as an optical ruler for frequency of Rubidium, however, the entire chapter lays changes of 300 MHz. And, of course, there is a dis- the necessary physics background for the experi- cussion of the Fabry-Perot etalons in Melessinos[8], ment, especially 6.3. The set up that I’ve imple- in section 4.6. 4

II. AN HISTORICAL PERSPECTIVE ON tion in technique and technology. LASER SPECTROSCOPY One of the common questions is this: how to observe transitions between states each of which are split by nuclear magnetism, especially when there are confounding effects that make observation difficult? High resolution There are several interwoven themes in this experi- optical spectroscopy, made possible with very coherent, ment, although I will choose just two: laser spectroscopy narrow bandwith laser light (along with a few important and nuclear spin. The former has proved to be a very experimental tricks) makes such observations possible, practical tool for a broad range of scientists, quite out- thus making manifest the effects of nuclear magnetism side the pale of physics even, and the latter, while even- upon atomic energy states. tually leading to enormously practical technologies (e.g., What are we attempting to observe? We want to see think MRI, even atomic clocks), was a remarkable quan- transitions between the ground state of Rb I to its sec- tum discovery. The substance of this discovery, so ob- 2 2 ond excited state, S1/2 −→ P3/2, given that within vious with a simple tunable diode laser, goes back to these two terms there is hyperfine structure, a very, very Rabi’s work[1] on the molecular beam method of measur- small energy perturbation compared with the energy gap ing nuclear magnetic moments before WWII, to Pauli’s between the two terms...and we want to see the underly- recognition[2] that there should be such things in na- ing structure, in order to confirm that it is really there. ture before that, and to Otto Stern’s discovery of the Without getting too philosophical about what ‘reality’ spin of the proton.[3] I say the themes are interwoven means here (admittedly, a deep discussion), we want to because the 1981 noble prize in physics was shared by demonstrate the reality of the hyperfine structure, that it the physicists who first developed laser spectroscopy, and is not simply a quantum theorist’s idea of what ought to who made spin-physics discoveries in nuclei and with elec- be true. According to first order (quantum) perturbation trons. One these physicists (Nicolaas Bloembergen) did theory, the perturbing Hamiltonian is given by both things,[4] and there is a line that runs from his work with nuclear resonance straight through Norman Ram- Hhf = A(I · J), (1) sey’s work, and Ed Purcell’s work,[5] to Rabi’s work. And Rabi learned the molecular beam method from Stern as where I is nuclear angular momentum, and J the spin his postdoc. Rabi’s creative contribution was improving plus orbital angular momentum of the spectroscopic the detection technique with nuclear magnetic resonance. term. The natural eigenstates or eigenkets maybe be la- Later, Willis Lamb Jr. came into close connection with beled, |FMF i, where F = I + J, which we met in the op- Rabi at Columbia, eventually using the beam-resonance tical pumping experiment. The energy corresponding the technique to measure the energy level shift between the each ket or state is a line on an energy diagram. We may 2 2 S1/2 and P1/2 terms of hydrogen’s n = 2 eigenstates. suppose two such lines exist if we can observe a transition This was one of the principal experiments that demon- between them. Oh, sorry, that’s backwards. We suppose strated the need to go beyond Dirac’s synthesis of rela- two such lines exist when we observe a spectral line! How tivity and quantum mechanics, and one the touchstones do we corroborate the real existence of the states? Let’s of reality that ’grounded’ the nascent[6] science of QED. leave this particular philosophy of physics question for Lamb’s work[7] was a seminal work (Noble prize-Physics a deeper truth. We want to remind ourselves how all 1955), as was everything else discussed above. The story physics, new physics in particular, becomes a trustable of scientific discovery has a great deal to do with innova- addition to ‘knowledge’ (whatever that is :).

[1] NobelPrize-Physics 1944. No Nobel lecture was given for [3] I. ESTERMANN, O. C. SIMPSON, AND O. STERN, obvious reasons. The seminal citation is a brief note in the ’The Magnetic Moment of the Proton’, PHYSICAL RE- physical review, just two columns of one page (how cool VIEW, 52, 535 (1937); this was the first notice of the is that). I.I. Rabi, J.R. Zacharias, S. Millman, P. Kusch result in US journals. See Stern’s Nobel Prize address at Phys Rev., 53 318, (1938). How many of his students www.nobelprize.org, Physics-1943. were Noble Prize winners!? Why were they so honored? [4] The Nobel Prize in Physics 1981 was divided, one half How did it happen? jointly to Nicolaas Bloembergen and Arthur Leonard [2] A. Pais, ”Inward Bound, of matter and forces in the Schawlow ”for their contribution to the development of physical world”, (OUP, NY 1986), see especially p. 315. laser spectroscopy” and the other half to Kai M. Sieg- Pauli’s solution to the ’nuclear energy crisis’, a missing bahn ”for his contribution to the development of high- particle which he predicted to exist, much like the predic- resolution electron spectroscopy”. tion of the Higgs (by Higgs and others), was eventually [5] see the Nobel Prize addresses of Ramsey, Purcell, called the neutrino (although he calls it the neutron, it- Bloembergen, and for all the other physics prizes at self not yet discovered). I bring it up because Pauli is the www.nobelprize.org first to recognize (predict) that the constituents of the [6] A. Pais, Op. cit. See p.447ff. Pais was a young theorist nucleus may have spin. who actually joined Feynman, Bethe, and Schwinger, and 5

Rabii, et al., at the Shelter Island conference in 1947. [8] A.C. Melissinos Jim Napolitano, Experiments in Modern Lamb presented his work there and Rabii reported Nafe’s Physics, 2nd. Ed. work on the hyperﬁne structure of the ground state of [9] D.W. Preston, Doppler-free saturated absorption: Laser hydrogen. spectroscopy, Am. J. Phys. 64, 1432, (1996). [7] W. E. Lamb, Jr. and R. C. Retherford, Phys Rev., 72 [10] G. N. Rao, M. N. Reddy, and E. Hecht, Atomic hyper- (1947) 241; 79 (1950) 549; 81 (1951) 222. W. E. Lamb, ﬁne structure studies using temperature/current tuning of Jr., Phys. Rev., 85 (1952) 259. W. E. Lamb, Jr. and R. diode lasers: An undergraduate experiment, Am. J. Phys. C. Retherford, Phys. Rev., 86 (1952) 1014. 66, (1998).