High Resolution Laser Spectroscopy: Rubidium Hyperfine SpectrumQuinn Pratt, John Prior, Brennan Campbella)

(Dated: 23 September 2015)

We illustrate a method for resolving the hyperfine spectrum of rubidium through saturation absorptionspectroscopy. Using a relatively simple setup, we excite rubidium atoms confined to a gas cell to a higherstate using a tunable diode laser. We observed the effect of doppler broadening on the absorption dips. Then,utilizing a counter-propagating laser beam and phase-sensitive detection, we were able to drastically reducethe effect of broadening. Ultimately we were able to improve the effective resolving power of our setup by afactor of 13, culminating in our ability to dissect the hyperfine spectrum of Rubidium within its excited state.

I. INTRODUCTION

Laser spectroscopy is a staple of modern physics, espe-cially since the introduction of the low-cost diode laser.We begin our journey to higher and higher resolvingpower by introducing some concepts surrounding the ori-gin of these absorption ‘dips’ as well as the theory back-ing the existence of this hyperfine spectrum of states. Wemust also address doppler broadening; one of the funda-mental qualities of laser spectroscopy.

After addressing these concepts we will examine theresults of our experiment and calculate the improvementin our resolving power.

A. Laser Spectroscopy: an Introduction

When laser light of variable frequency is incident on asample of a particular atom, there will exist a resonantfrequency for which the atom will absorb photons and beelevated to an excited state.

Naturally, it would be impossible to become perfectlyresonant with a given atom, and so thanks to the Heisen-berg uncertainty principal and the thermal velocities ofthe atoms as they ‘jiggle’ about their confinement, awider and wider range of frequencies will serve to excitethe atom.

It is upon this concept that we explore the energy levelsof rubidium. By hitting our sample with laser light ofvarying frequency we will excite atoms from the groundstates (shown in FIG. 1), to excited states. Ultimately,when it comes time to examine the hyperfine structureat the excited level, we must employ a more advancedmethod to sharpen our metaphorical dissecting scalpel,and peer into the once hidden transitions.

II. THEORY

The principal theoretical subjects we must address in-clude: Rubidium’s relevant energy levels, doppler broad-ening, and saturation absorption spectroscopy.

a)also at University of San Diego: Department of Physics & Bio-physics.

A. Energy Levels of Rubidium

The absorption spectrum for a given sample is analo-gous to its atomic fingerprint. In our experiment, we areinvestigating a very particular set of transitions withinRubidium’s ‘fingerprint’.

Specifically, we are concerned with the transition from5S1/2 → 5P3/2

FIG. 1. This energy diagram illustrates the relevant absorp-tion levels of both present isotopes of Rb. Note that thisdiagram is not to scale. The hyperfine spectra are enclosedwith the dotted line.

It is important to note the split-states between themain energy levels. These are the hyperfine spectra. Thetransitions we will observe directly are those labeled aand b from the diagram above.

The hyperfine spectra arise from the small interactionbetween the magnetic dipole of the nucleus (with non-zero spin) and the electrons. These interactions acts as asmall perturbation to the main energy level, and there-fore adds several new states to the energy spectrum.[1]

The other important note to make here is the separa-tion between the states. Naturally the main transitionfrom 5S1/2 → 5P3/2 is the furthest apart, meaning thatwe will easily be able to resolve the transitions labeleda and b, but to see the hyperfine spectra is a differentstory.

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B. Doppler Broadening

As noted before, the resonant frequency to cause ab-sorption could not possibly be one exact frequency, in-stead there is a range of frequencies (albeit very close toan exact frequency), which can cause excitation. Thisrange of frequencies is broadened even more by the ther-mal motion of the atoms with respect to the incidentlaser light.

For example, if an atom travels toward the laser, itwill experience the laser light ‘blue-shifted’ wherein thefrequency of the light increases. On the other hand, ifan atom happens to be traveling away from the laserlight it will experience the light ‘red-shifted’ such thatthe frequency appears to decrease.

If we imagine the laser operating at a frequency of383.5× 106 MHz (exactly 0.5× 106 MHz away from theresonant frequency), and an atom just so happens to betraveling toward the laser with sufficient velocity to causethe light to appear to be 0.5 × 106 MHz greater than itactually is, the atom will absorb the photon and undergoa transition to a higher energy level.

Macroscopically this effect drastically broadens the ab-sorption ‘dips’. Specifically, this effect makes the hyper-fine states invisible without using extra methods. (SeeFIG. 3).

C. Saturation Absorption Spectroscopy

Our ability to resolve the hyperfine spectrum comesdirectly from this method. By using two, counter-propagating beams we are able to achieve a doppler-freeabsorption spectrum.[2]The key concept here is that aswe sweep a range of frequencies, the two beams (of theexact same frequency) will interact with different groupsof atoms. However, once they sweep over the resonantfrequency, the two beams interact with the same groupof atoms, those effectively not moving with respect to thelaser light.

Ultimately this means that the stronger of the twobeams (called the ‘pump’ beam), is absorbed and theweaker beam (called ‘probe’) passes through the cell withlow absorption.

The other key to resolving the hyperfine spectrum isto use a method called ‘phase-sensitive detection’. Thisinvolves using a chopper to disrupt the beam at a givenfrequency, then coupled with a lock-in amplifier, we areable to sample the detector at a specific frequency, andamplify the signal. This rids us of all the irradiant lightwhich isn’t part of our narrow sweep of frequencies.

III. EXPERIMENTAL DESIGN

The experiment is conducted as follows:

1. The Diode laser can be controlled to sweep a range

of frequencies. The user can adjust a variety ofparameters including the voltage to the piezoelec-tric stack which, in turn, adjusts the frequency, thecurrent to the system, the speed at which the lasersweeps and amplitude of the sweep which effectivelybroadens or sharpens the range of frequencies overwhich we sweep.

2. The laser beam then passes through a beam splitterwhich produces one intense beam and one weakerbeam, the weaker beam is then sent to the etalonfor reference.

3. Then, the more intense beam is split once more intothe ‘pump’ and ‘probe’ beams. The pump beampasses through the chopper, which is a central partof phase-sensitive detection. The two beams arethen crossed through the rubidium gas cell.

4. Lastly we collect absorption data through the de-tector which is connected to a DSO, and a computerconsole.

The experiment setup is best displayed in the schematicbelow:

FIG. 2. This diagram highlights the essential parts of theexperiment. All solid angled lines represent mirrors, whereasthe dotted lines represent beam splitters. The primary diodelaser beam is split several times by beam splitters. One beamis directed to the etalon for frequency reference, the other twoare the aforementioned ‘probe’ and ‘pump’ beams.

Ultimately we collect data from the etalon and thePIN diode detector. The etalon data gives us a referencefor the change in frequency between subsequent ‘dips’,given that we know the free spectral range (FSR) for ouretalon.

IV. FINDINGS

We successfully collected a series of absorption spec-tra corresponding to various energy levels for Rubidium.The principal result of this experiment was our ability todrastically improve our effective resolving power throughthe method of saturation absorption spectroscopy.

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We can see the improvement in our resolving power byanalyzing the absorption data with respect to the etalon.

First we must take a macroscopic view of the energylevels we will be examining in detail. The following imagedisplays all four readily resolvable absorption dips. Oneshould consult FIG: 1 in conjunction with this diagram:

FIG. 3. Here we see four of the principal absorption dips ofboth isotopes of Rubidium present in the gas cell. The boxeddips correspond to those which we will be examining in detail.

This data was taken without employing the techniqueof saturation absorption, therefore these peaks are notdoppler-free. In fact, they are doppler broadened to thepoint which we cannot see the hyperfine spectra at thenadir of each dip. This is our starting point. We can usethe etalon to calculate the effective resolving power.

We know that the FSR of our etalon is 300MHz, thismeans that the gap between subsequent peaks in theetalon corresponds to a gap of 300MHz. Then, we usethe following equation to calculate the resolving power:

R =λ

∆λ(1)

Or similarly:

R =f

∆f(2)

Note that each absorption dip corresponds to a gap ofapproximately 600MHz, thus we can calculate our resolv-ing power to be,

R =384× 1012Hz

600× 106Hz(3)

R = 6.4× 105 (4)

Now we will make use of saturation absorption spec-troscopy to peer into the hyperfine spectra which lie atthe nadir of each of these ‘dips’.

FIG. 4. We can use the following technique to measure thegap in frequency between each dip.

First we will examine the transition from 87Rb: b, thatis: F = 1→ F′.

It is very important to note that there are 6 peaks vis-ible in FIG. 5, if we consult the energy level diagram inFIG. 1, we would expect to see only three peaks, the rea-son for this discrepancy is a phenomenon called ‘crossovertransitions’ which we will discuss later in detail.

Additionally we can examine the hyperfine spectrumof the transition 85Rb: b, that is F = 2→ F′.

Note that the entirety of this hyperfine spectrum dis-played in FIG. 6 appears to fit within 300Hz. This isas we would expect, if we consult FIG. 1, we can seethat the hyperfine states (F′) for 85Rb are much moreclosely packed than those of 87Rb. The entirety of the F′

states for Rubidium-85 only span 213MHz, whereas theF′ states for Rubidium-87 span 516MHz (see FIG. 5).

This shows that our experiment is in agreement withthe theory concerning the distribution of these hyperfinestates.

We must also determine the effective resolving powerof our spectroscopy after implementing phase-sensitivedetection and saturation absorption.

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FIG. 5. The top portion of this figure is data from the Lock-in amplifier used during phase-sensitive detection. The lowerportion shows how much more resolution we attain throughthese extra techniques.

If we examine FIG. 5, we can see that the averagewidth of each peak corresponds to approximately 150samples. Simultaneously, the etalon spread of 300 MHzcorresponds to approximately 1000 samples. This means150 samples has a frequency spread of 45 MHz. Ourresolving power is therefore:

R =384× 1012Hz

45× 106Hz(5)

R = 8.5× 106 (6)

This is factor of 13 times better than our previous re-solving power.

However, we must address the fact that there are 6peaks visible in the hyperfine spectrum of 87Rb eventhough there are only three transitions within the 5P3/2

level.This comes from an effect called Crossover Transitions.

These crossover transitions add an interesting feature tothe graphical results of our experiment. In an ideal casewe would only see the exact hyperfine frequencies at theirnatural linewidth. Instead, we see all 6 peaks, only threeof which correspond to actual hyperfine spectrum, theother three are crossover transitions. These arise whenthe frequency of the pump laser happens to be reso-nant with two groups of atoms at once. This occurs

FIG. 6. Once again the top portion of this figure was at-tained through the extra methods of saturation absorptionspectroscopy and phase-sensitive detection.

halfway between the actual resonant frequencies.[2]Thepeaks which are a result of this effect and are not actu-ally part of the atomic spectrum are best representing inthe following diagram:

FIG. 7. Here we indicate which of the absorption peaks ac-tually correspond to the atomic spectrum, and which wereside-effects of our methodology.

To reiterate, the peak labeled (6) in the 87Rb hyperfinespectrum corresponds to the transition from F = 1 → F’= 1, the peak labeled (4) corresponds to the transitionfrom F = 1 → F′ = 2, and lastly, (1) corresponds to F

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= 1 → F′ = 3. Meanwhile, (5), (3), and (2) correspondto the halfway points between F′ = 1 and F′ = 2; F′ =2 and F′ = 3; and lastly F′ = 1 and F′ = 3.

V. DISCUSSION

It is clear that our efforts to boost the resolving powerof our spectroscopic experiment through the method ofsaturated absorption were successful.

Theory tells us that at the nadir of each of these ab-sorption dips there should exist a myriad of smaller ab-sorption dips, known as the hyperfine spectrum.

Although this hyperfine spectrum was not visible withthe initial method. We were able to capture spectroscopicimages of the hyperfine spectrum which, after some anal-ysis, match the corresponding energy diagram in FIG. 1.

We are also able to verify other attributes of the en-ergy diagram. We can see that the spacing between thehyperfine states for 85Rb are more close together thanthose of 87Rb. This can be seen in our findings as wewere able to fully resolve all of the peaks for Rubidum-87, but we were unable to resolve at least 3 peaks in theRubidium-85 dip.

Furthermore we confronted the problem of crossovertransitions by noting their influence on our findings, aswell as noting which peaks correspond to the actual

atomic spectrum.Lastly we quantitatively addressed the improvement

in our resolving power thanks to saturation absorptionspectroscopy, we saw an improvement by a factor of 13from our initial setup. Our ability to pick out individ-ual transitions in the hyperfine spectrum is an extremelyvaluable technique for high resolution spectroscopy.

VI. REFERENCES

1G. N. Rao, M. N. Reddy, and E. Hecht ‘Atomic hyperfine struc-ture studies using temperature/current tuning of diode lasers: Anundergraduate experiment’ Am. J. Phys., Vol. 66, No. 8, August1998

2Daryl W Preston ‘Doppler-free saturated absorption: Laser spec-troscopy’ Am. J. Phys., Vol. 64, No. 11, November 1996.

A. Figures

• FIG.1: Taken from the course document ‘HyperfineSpectrum of Rubidium: laser spectroscopy exper-iments’ on http://home.sandiego.edu/~severn/p480w/sat_abs_spec_Rb_f15.pdf

• FIG. 2: The general idea of this image was alsofound on the course document.