Version 1 as of April 17, 2013Primary author: Joshua C. Frechem

Doppler-Free Saturated Absorption Laser Spectroscopy of Rubidium 85Rb and 87Rb(Dated: April 17, 2013)

Using the two stable isotopes of Rubidium (85 and 87), an experiment was done to show moreaccurate methods of spectroscopy than traditional methods. Since there’s only one valance electronin Rubidium, it can be treated simply as Hydrogen in the case of this experiment. A beam from a780nm semiconductor laser was split into 2 weak beams and 1 strong beam with the weak beamsbeing probe beams and the strong beam the pump beam. The pump beam was shone anti-parallelto one of the probe lasers to induce the absorption of the laser energy to excite those valanceelectrons to transition to a higher state. To find the resonance frequency where these electrons willtransition, the voltage through a piezo-electric crystal was changed causing a frequency change inthe laser giving it a scanning effect. With the aid of a near IR sensitive camera to detect when thelaser was scanning, the places of these transitions were easily found. Using an oscilloscope thesetransitions were measured and then ratios of the real peaks were taken to compare to the expected.These ratios were the keys to naming the transitions by isotope and by hyperfine level. Althoughtwo of the ratios were almost identical to the expected, two were also nearly idenitical to eachother.To determine which was which, the spectra were visually compared to the expected and identified.All experimentally obtained spectra were classified correctly and as seen on figures 3-6 and table 1,the data was very close to the expected.

INTRODUCTION

Doppler-free saturated spectroscopy was developed bythe group of Arthur L Schawlow and actually won a jointNobel prize for this development in 1981. That discov-ery came out of the need for more accurate optical spec-troscopy. The Doppler widths of close to 500 MHz werecaused by random thermal motion of atoms thus leadingto the importance of Doppler-Free spectrocopy which hasa way of cancelling out this Doppler width.1 Rubidiumis often chosen for student labs because of the simplic-ity of its use in this experiment. Rubidium has a veryhigh vapor perssure which allows it to be used at roomtemperature for this experiment without the use of ovensallowing the setup to be much simpler. Rubidium alsoonly has one electron in the fifth (valence) shell allow-ing it to be looked at with the energy level structure ofHydrogen.3 Atoms have something called a fine struc-ture caused by the magnetic moments of electron spinand angular momentum while the hyperfine structure isdue to internally generated electric and magnetic fieldsinteracting with the momentum of the electrons. The finesplittings are under the Nuclear spin(I) which is I=5/2for 85Rb and I=3/2 for 87Rb.2 These numbers are de-termined by whether the atom is an odd-even, even-odd,even-even, or odd-odd nucleus talking about the num-ber of protons and neutrons respectively. The levels ofthe Rubidium isotops this valance electron is being ex-cited to are the 52P1/2 and the 52P3/2 fine levels fromthe 52S1/2 term. These are called Term States. Termstates are denoted by n2s+1lj and specified by the an-gular momentum quantum numbers s,l, and j which nbeing the principal quantum number or rather the or-bital shell number. In the previous equation s is thespin which in the case of stable Rubidium isotopes is 1/2

because there is only 1 valance electron and electronsare fermions with spin 1/2, l is the subshell ( s, p, d,f, g, h...), and j is the total angular momentum corre-sponding to |l-s| ≤j≤ l+s. The hyperfine structure is theinteraction between I (total nuclear angular momentumas stated before) and J as previously stated in the finestructure section. The total atomic angular momentumis denoted as F and are the labels for each level in thehyperfine structure and are calculated similarly to J asstated above. F is calculated as |J-I| ≤F≤ J+I in inter-vals of 1(j and J denote the same quantity just as i andI also do). For different atoms these transitions in thehyperfine structure are at different wavelengths (close to780nm in this lab).4 These wavelengths allow the electronto transition up an energy level and this can only happenat resonance frequences where the pump laser is in phasewith moving atoms. These facts can be exploited witha tuneable laser to scan a small stretch of wavelngthsto find these levels in a process called saturated spec-troscopy. The lab explained in this write-up explains amore accurate way of analyzing these transitions by can-celling out the Doppler Effect. The reason this saturatedabsorbtion spectroscopy is more accurate is because allof the transitions mentioned about require energy fromthe laser to excite the electron to the excited state. Thisloss in energy results in dips in the spectra allowing moredetail of the spectra to be shone. Six dips are shown inthe spectra but three of them are crossovers. Crossovershappen exactly half-way between the real transitions sothese can be calculated and used later on in the lab whenlabeling spectra. Additionally, due to the Doppler Effect,crossovers are caused when atoms are in resonance withboth the pump and the probe beams causing the pumpbeam to seem at a lower frequency giving a false positive.

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EXPERIMENTAL SETUP AND PROCEDURE

This experiment started off with a tunable 780nmsemiconductor diode laser that was tunable with a piezo-electric crystal that changed lengths as a voltage between0 and 100 volts was run across it. The change in piezolength corresponded to a change in the angle of a grating.As the laser hit this grating the main beam reflected outas the experimental beam while some was reflected ontoa mirror which in turn was reflected back at the grating.This reflection back at the grating allowed for the laserto actually function because it caused the laser light tobe in phase which built up the beam of the laser withthe correct light which in turn came out as the experi-mental laser. The mirror used to reflect the secondarybeam back to the grating was set to tune the laser at 780nm and by changing the voltage of the piezo, the beamcould be minutely changed to scan a wide enough rangeof wavelengths to observe the transitions up to the 52P3/2

hyperfine levels which would allow characterization of thespectrums obtained. With the laser at 780 nm, the beamwent out to a beam splitting glass that was thick enoughto have reflections off the from and back surface of theglass to give two weak beams that reflected towards thisexperiment while the transmitted beam would have goneto another experiment. Of these two weak beams onewas blocked while the other went to another beam split-ter. This time the two even weaker beams (probe beams)reflected into a vacuum tube containing the two isotopesof Rubidium 85Rb and 87Rb. The transmitted beam (thepump beam) was reflected around to enter the vacuumtube and cross only one of the probe beams. Then twothin pieces of glass were used to reflect parts of eachbeam (the probe beam and the newly corrected beam) toa photo-detector. The expectation of this was to get theDoppler-broadened profile from the probe beam and sub-tract it from the Doppler-broadened profile that includedthe hyperfine absorbtions and what would be left wasthe spectra of these hyperfine transitions. Due to uncali-brated instruments the only outcomes possible were clas-sifying the spectra to their respective isotope and transi-tion. However, with calibrated instruments, more stepscould have been taken to get data for things such as theFull-Width-Half-Max of the Doppler-broadened lines aswell as obtaining acual values for the frequency distancesin the transitions rather than just comparisons.

EXPERIMENTAL RESULTS

Upon having done several trials with little success infinding all four spectra, the last time all four were foundand the spectra used were the cleanest spectra manage-able. Averages were not taken due to the discrepanciesof measurement placement having varying effects on thecalculated ratios. The single cleanest image for each spec-

trum was chosen and printed as a small image ( all fourfit on one side of a printed page). This was done soonly the peaks could be measurable. If the images wereprinted too large, measurement errors grew considerablydue to different placings for measurement marks. Forwide peaks, the mid-point of the peak was chosen as themeasurement point with measurements being accurate tohalf a millimeter. The known values are shown in figures1 and 2 for 85Rb and 87Rb respectively. The 85Rb F=2to F’=1,2 the ratio of frequencies was calculated to be.316 leaving F=2 to F’=2,3 to be .684. 85Rb F=3 toF’=2,3 had a calculated ratio of .344 while the F=3 toF’=3,4 ratio was .656. The calculated ratio for 87Rb F=1to F’=0,1 was .315 with the F=1 to F’=1,2 ratio being.685. Then, for 87Rb, the F=2 to F’=1,2 ratio was cal-culated as .37 and F=2 to F’=2,3 as .63.

Using the clear, smooth images of the spectra, the ex-perimental frequency ratios were found to be for 85RbF=2 to F’=1,2,3 as .317 and .683 having only a 0.3% er-ror. 85Rb F=3 to F=2,3,4 the experiment yielded ratiosof .347 and .653 with an error of 0.8%. 87Rb transitionfrom F=1 to F’=0,1,2 yielded an error of 1.6% with ra-tios of .32 and .68 while the largest error yield was for87Rb F=2 to F’=1,2,3 with ratios of .384 and .616. Theseresults and comparisons can be seen in table 1 while thespectra can be seen in figures 3 through 6.

CONCLUSION

While the results were very close for 85Rb the resultswere considerably higher, although still well within rea-son, for 87Rb. While classifying each spectrum withits appropriate transition, the lower energy transitions(transitions from the lower hyperfine level of the groundstate for each isotope to the lower hyperfine levels of theexcited electron) proved difficult to distinguish from oneanother. The 85Rb F=2 transition and the 87Rb F=1transition had ratios almost identical. That closenessmade it a guess as to which spectrum was which and ul-timately the decision was made by observing previouslytaken spectra of the two and comparing. Magnetic fields,ambient light and ambient noise all contributed to thedifficulty of getting a smooth spectrum and seeing moredetail but the spectrum came out beautifully for the mostpart and despite the occasional mode hop it was fairlyconsistent. Getting a perfectly matching spectrum for85Rb F=2 proved too difficult with the environment andequipment given but the obtained spectrum contains allof the same characteristics minus a dip in the spectrumat the first crossover. Errors in measuring the ratios werecut down by decreasing the image size allowing only mea-surements of the peaks to be considered however it wasstill an as close as possible scenario. Another source oferror could have been nonlinear stretching of the piezoin the tuner of the laser. This would cause the ratio to

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be off and depending on how nonlinear the stretch of thepiezo is results in a change in the ratios away from theexpected.

[1] Background and Theory Reference1:Doppler-Free Saturated Absorption Spectroscopy:Laser Spectroscopy, lab handout, Swarthmore College,2001

[2] Background and Theory Reference2:Doppler-Free Spectroscopy, lab handout, MIT, 2000

<http://web.mit.edu/afs/athena/course/8/8.13/JLExperiments/JLExp 48.pdf>

[3] Background and Theory Reference3:Doppler-Free Saturated Absorption: Laser Spec-troscopy, Daryl Preston, Department of Physics, Cali-fornia State University, 22 July 1996

[4] Background and Theory Reference4:A study of the Hyperfine Structure of Rubidium,Beth Denius, Thomas Haynie, and AndrewBorleske, Davidson College Department of Physics,<http://webphysics.davidson.edu/Alumni/bedenius/rubidium/ title.htm>

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FIG. 1: This image shows the energy levels and wavelengths ofthe transitions from 52S1/2 to the 52P3/2 fine level with all of

the hyperfine levels of each for 85Rb

FIG. 2: This image shows the energy levels and wavelengthsof the transitions from 52S1/2 to the 52P3/2 fine level with all

of the hyperfine levels of each for 87Rb.

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Ground State 85Rb F=2 to 85Rb F=3 to 87Rb F=1 to 87Rb F=2 toHyperfine level F’= 1,2 F’= 2,3 F’= 2,3 F’= 3,4 F’= 0,1 F’= 1,2 F’=1,2 F’= 2,3

Expected 0.316 0.684 0.344 0.656 0.315 0.685 0.370 0.630Experimental 0.317 0.683 0.347 0.653 0.320 0.680 0.384 0.616

TABLE I: This table shows all expected and experimental data for the transition frequency ratios going from the ground 52S1/2

to the excited 52P3/2 state. The first row shows the ground state of which isotope of Rubidium it represents and breaks intotwo columns each in the second row that represents the ratio of both transitions the electron can undergo.

FIG. 3: This image shows the spectrum of the85Rb 52S1/2 F=3 to 52P3/2 F’=2,3,4 transition.The yellow line is the Doppler Broadened line withhyperfine saturations, the blue line is the Dopplerprofile, and red is the Doppler-free spectrum ofthe transition observed.

FIG. 4: This image shows the spectrum of the85Rb 52S1/2 F=2 to 52P3/2 F’=1,2,3 transition.The yellow line is the Doppler Broadened line withhyperfine saturations, the blue line is the Dopplerprofile, and red is the Doppler-free spectrum ofthe transition observed.

FIG. 5: This image shows the spectrum of the87Rb 52S1/2 F=2 to 52P3/2 F’=1,2,3 transition.The yellow line is the Doppler Broadened line withhyperfine saturations, the blue line is the Dopplerprofile, and red is the Doppler-free spectrum ofthe transition observed.

FIG. 6: This image shows the spectrum of the 87Rb52S1/2 F=1 to 52P3/2 F’=0,1,2 transition. The yel-low line is the Doppler Broadened line with hyperfinesaturations, the blue line is the Doppler profile, andred is the Doppler-free spectrum of the transition ob-served.