Hyperfine Spectroscopy of Rubidium

Last Update April 2024

An oscilloscope trace, showing the raw spectrum (blue), the Doppler-free spectrum (yellow), their difference (red), and an interferometer showing the laser's frequency shift (pink)

In this experiment you will use a narrow bandwidth, tunable diode laser to probe the hyperfine structure of natural rubidium (Rb). The technique of Doppler-free saturated absorption spectroscopy will be used to resolve the hyperfine structure which is otherwise masked by the effect of Thermal Doppler broadening of the spectral lines.


In the lab, we provide you with everything you need to do the experiment. You will select from the optical components available, arrange them on the table to create the beam geometries that you need, and align the beams so that they all go precisely where they need to go.

The heart of the experiment is a Toptica DL100 laser which produces a very narrow bandwidth beam that can be tuned over an appropriate frequency range for the measurement you need to make. The laser operates at wavelengths near 780 nm and the power output can be as high as 120 mW. This power level makes it a Class 3B laser, which means the laser can cause permanent damage to the eye, but will not cause damage to skin or set objects on fire. In order to protect yourself, appropriately-rated eye goggles must be worn whenever the laser is on, and the laser must only be operated with the door to the room closed. (For this laser, “appropriately-rated” means that the goggle offers at least OD 3 protection at 780 nm.)

The mostly likely time for a laser accident is during alignment; when placing and adjusting components, laser beam paths can go in unexpected places, including being reflected upward out of the plane of the table and toward eye level. Therefore, as an added level of protection you will build and align your optics using a separate low power alignment light laser (which has a power of less than 5 mW and is roughly equivalent to the type of laser pointer used in presentations.) Nevertheless, you should still practice proper laser safety with the low power laser and avoid reflections and stray beams.

There are only one Topitica laser and two photodetectors available for the entire class. As such, you will need to share these components with other groups (who will be working on their own version of the experiment on days when you are not in lab). The laser will stay put on the main optical table (and should not be adjusted), but the rest of your optical setup will be built on a small 300 mm x 600 mm optical bread board which can be attached to the main optical table while you are working on it (and subsequently removed and stored at the end of the lab period). When you return to the lab, you simply reattach your optical setup to the main table and continue your work. (Do not take components off of other groups' boards.)

If you think you need something which is not provided, ask the lab staff.

  1. The same technique is used to measure hyperfine splitting in positronium, which may help resolve discrepancies between measurements and Quantum Electrodynamic(QED) calculations.
    1. Follow-up precision measurements seem to indicate that there may be agreement with theory after all

Teaching Points

From creating Bose Einstein condensates to quantum encryption, the techniques and optical components used to precisely control and align laser beams are a common element of current physics research. This lab aims to provide you with some hands on experience working with lasers and optics. It is the only lab in this course where you are provided with some tools, a laser and assorted optical components, which you have to use to design, build and run an experiment. The experimental goal is to measure the magnitude of the energy splitting due to the hyperfine effect in atomic Rubidium, using a technique known as Doppler Free Saturated Absorption Spectroscopy (DFSAS).

  • Laser beam conditioning and alignment
    • Understanding the function and how to use common optical components such as mirror mounts, irises, polarizers, and polarizing and non-polarizing beam splitters.
    • Learn how to safely align laser beams.
    • Learn how to design an optical layout to build a DFSAS experiment.
  • Measure the energy of the hyperfine splitting in atomic Rubidium.
    • Understanding atomic energy level structure and the Hyperfine interaction.
    • Understanding the effects of doppler broadening.
    • Understanding how the DFSAS technique works.

A note about uncertainties and fitting the data.

In this experiment most of your data will be from measurements which can be made straight from the scope. While you could attempt to fit the data from the scope, doing so is NOT recommended. The signals which you will be working with do not have simple functional forms and the uncertainties on the fit parameters are challenging to interpret and you can easily waste hours on this. Instead you are encouraged to make measurements directly off of the scope using its built in cursor features, and use your judgement to estimate the uncertainties.


Details about how to safely operate the laser will be given in the lab by the instructor.

  • Always wear the protective laser goggles provided when the high-power laser is on.
  • Note that the beam from the high-power laser will cause permanent damage if it strikes your eye. If the laser is on and you are in the room, you must wear the protective goggles provided. Additionally, anyone entering the room while the laser is on must be wearing goggles as well.
  • The laser beam is not harmful to the skin, so it is safe to operate with your hands in the beam. However, you should remove any reflective objects – such as watches and rings – from your hands and wrists before working on the optics table to prevent accidental deflection of the beam out of the plane of the table. 

Pre-lab research

Before coming to lab, it will be helpful if you can familiarize yourself with the following:

  • What is the hyperfine effect?
  • What is Thermal Doppler Broadening?
  • What is Doppler-Free Saturated Spectroscopy?

Theory and apparatus

The following are links to our wiki pages discussing some of the concepts that you need to be familiar with. Search the internet for additional information if you come across concepts or terms you are not familiar with.


A beamsplitter illuminated with a Helium-Neon (HeNe) laser

Basic optics and alignment

For this experiment you will need to design, build and align your own optics in order to measure the hyperfine splitting in atomic Rb. The following exercises will familiarize you with the optical components you will be using and provide hands on experience placing and aligning them.

The laser which you will use to measure the hyperfine splitting emits light at 780 nm, which is in the infrared part of the electromagnetic spectrum and is nearly invisible to the eye. It is also sufficiently high power that it will cause permanent damage to the eye if you are struck by the unattenuated beam. These two factors make beam alignment more challenging, so you will begin with a low power, visible light laser.

The optical layout that you need to build and align for this experiment does not require any special skills. However it is involved enough that jumping straight into building the final spectroscopy layout without prior experience working with these types of optical components can be very challenging.

The series of alignment exercises which you will work through are designed to build up your understanding of the optical components you will be working with, and give you helpful practice working with them in smaller, more accessible chunks. By the time you have finished all of the tasks you will have gained experience with all of the beam alignment and manipulation which you will have to do to assemble the full doppler free saturated spectroscopy setup.

Alignment task 1 (5 points)

This first task has you investigating how to use the combination of a linear polarizer ( ThorLabs LPVIS050) and a 1/2 waveplate ( ThorLabs WPH05M-633) and a polarizing beam splitter ( ThorLabs PBS122) to create two beams whose power ratio can be easily varied. This is a task you will need to be able to accomplish as part of the spectroscopy setup you will build later in the lab.

Additionally this exercise is designed to:

  • Provide an introduction to creating a simple beam path by placing optical components on the table and aligning them to get the laser light where it needs to go, without requiring particularly precise positioning of components.
  • Give you some practice using the photodetectors to make measurements of beam intensities.
  • Show you how to manipulate the polarization state of light.

The 1/2 waveplate is a material which has two different optical axes with different indices of refraction. This link takes you to a wikipedia page that explains how a waveplate does what it does. In practical terms, the 1/2 waveplate can be used to rotate the plane of polarization of linearly polarized light. The linear polarizer ensures that we have a highly polarized beam of light incident on the 1/2 waveplate. The combination of these two optical components can be used to prepare light in a specific polarization state and is a very common technique in laser optics.

Build the optical setup shown in Figure 1. In order to receive credit for this task you need to be able to demonstrate and explain the following to an instructor in the lab.

  • Determine what are the polarization states of the transmitted and reflected beams.
  • What happens to the intensity of the light transmitted vs reflected when you rotate the polarization of the state of the incident light using the 1/2 waveplate.
  • Create a state where all of the light is transmitted and no light is reflected.
  • Create a state where all of the light is reflected and no light is transmitted.
  • Create a state where 60% of the light is transmitted and 40% is reflected?

Note that you can use a DMM to display the output voltage of one of the photodiode detectors.

 Figure 1b.
Figure 1 - an optical setup allowing for the creation of various combinations of linear polarizations.

Alignment task 2 (5 points)

The first task was very straightforward and forgiving in terms of the degree of precision needed for the alignment of the beams. However building your DFSA spectroscopy experiment you will require much more precise alignment of multiple beams. This exercise separates out the most challenging component of the alignment you will need to do so that you can concentrate on mastering the skills required without having to concern yourself with other details.

Take two of your iris's, make sure that they are set to precisely the same height above the table and place them as shown in Figure 2a. Use mirrors to direct the alignment laser beam around and through the center of the two iris's. The iris's should be closed down to match the diameter of the beams. You will find that directing the beam through one iris is not too difficult, however getting it to go through the very center of two iris's is much more challenging. Do not be surprised or discouraged if this task takes more time than the others, you also may well have to try more than one configuration of optical components to accomplish it.

To aid you in getting the beam to pass through both Irises, there is an iterative technique that is referred to as “walking the beam”. Referring to Figure 2a this technique works as follows:

  1. Begin by positioning Mirrors #1 and #2 on the table so that the beam hits the center of Iris #2. It is best to open Iris #1 all the way for this first step.
  2. With the beam centered on Iris #2, close Iris #1 until its opening is about the same size as the beam diameter. Now adjust Mirror #1 to put the beam at the center of Iris #1.
  3. Open up Iris #1 and check the position of the beam on Iris #2. You will notice that in centering the beam on Iris #1 in step 2 you have moved it away from the center of Iris #2.
  4. With Iris #1 opened up, adjust Mirror #2 to get the beam centered on Iris #2.
  5. Return to step 2.

As you loop over steps 2 through 5 you will find that each iteration gets incrementally closer to having the beam centered on both Irises. At some point in this procedure you may have to reposition one of the two mirrors, which is fine. Keep in mind that you always adjust Mirror #1 to center the beam on Iris #1, and Mirror #2 to center the beam on Iris #2.

Figure 2a

Now use two beamsplitters as shown to create a second beam which passes through the two iris's from the opposite direction as the first beam. This simulates the alignment needed to create the counter propagating beams through the vapor cell which are needed for DFSA spectroscopy. Keep in mind that the first beam still needs to reach the photodetector.

Figure 2b

Alignment task 3 (5 points)

For this task we are not going to show you what arrangement of components to use. It is up to you to decide how best to accomplish the objective.

Design an optical setup which will create two beams passing through the pair of iris's in opposite directions. However this time each beam has to go to a separate photodetector. Additionally you need to be able to control the intensity of the two beams independently of one another. Accomplishing this can be done in multiple ways, but will require the use of polarizing optics.

  • Sketch out your optical design on the blackboard and have an instructor check it to verify that it will work as intended. Once you have received instructor approval on your design, draw it in your lab notebook.
  • Build the optical setup and demonstrate that the two beams pass through the centers of the two iris's.
  • Demonstrate to an instructor that you can set the intensities of the two beams to be equal.
  • Demonstrate to an instructor that you can set the intensities so that the signal at one PD is 5 times larger than the signal at the other PD.
Figure 3

Task 4 - Observe the Doppler-broadened spectrum (5 points)

Now that you have had some practice with placing optics and beam alignment, it is time to start learning how to work with the Toptica laser and view the absorption spectrum from the Rb vapor cell.

Remove the optical components you used for the previous exercise with the low power alignment laser.

Use the optics at your disposal to send the beam through the vapor cell and into one of the photo-detectors.

Note that the full power of the Toptica laser will saturate the detector. There is a half-waveplate and PBS in the beam path from the Toptica laser; you should now understand how to use this combination to control how much of this laser light passes through the two guide irises and across your removable optical breadboard. You can also make use of a linear polarizer to control the intensity of the beam.

Be sure to use the low power alignment laser for the initial placement and alignment of the optical components. Once you are happy with your initial setup you can switch over the the Toptica laser beam which should follow the same path as the alignment laser beam.

Once you have the optics set up, find one of the lab staff to instruct you on how to safely work with the beam from the Toptica laser.

Tune the Toptica laser onto resonance with the Rb atoms in the vapor cell, find the signal on the scope, and record the doppler-broadened absorption spectra. Save the digitized waveform from the scope so that you can fully analyze it later. In your notebook, you should sketch the spectrum you see on the scope. Identify the different features in the spectrum and measure the peak spacings relative to the first peak in the spectrum using the cursors on the scope. Also, measure the full-width half-maximum (FWHM) of each peak.

Interferometer task 5 (5 points)

The final alignment task is to construct and align a Michelson Interferometer. You will need to do this as part of your DFSAS setup in order to calibrate the frequency sweep of the laser. Aligning an interferometer can be tricky, trying to do it for the first time as part of your DFSAS setup, with a lot of other optics on the table, makes it even more challenging. This exercise provides hands on experience while working with the low power alignment laser.

Construct the interferometer as shown in Figure 4. Keep in mind that it is necessary for the two beams entering the detector to be parallel and overlapping, it is not sufficient to get the two spots to overlap at the detector. You will need to use a lens at the output of the interferometer in order to view the interference fringes.

In order to receive credit for this task you need to show an instructor the interference fringes at the output. The fringes should look something like this.

Figure 4

Once you have this aligned to the point where you can see interference fringes, you are ready to switch to the beam from the Toptica laser and collect your frequency sweep calibration data for your full analysis. It will be helpful to get an instructor to help you with the final fine tuning of the interferometer with the infrared beam.

Full data set

This is a good point at which to go over the Doppler Free Saturated Spectroscopy technique, and why it is needed to measure the energy of the Hyperfine states in the first excited state of Rb, with an instructor.

Obtain a Doppler-free spectrum

Design and build a Doppler-Free Saturated Absorption (DFSA) spectroscopy layout and optimize it until you can see six doppler-free dips in the ${}^{87}$Rb(F=2) peak and in the ${}^{85}$Rb(F=3) peak.

At this point you should have useable data for the Doppler-broadened peaks, a DFSA spectrum for the ${}^{87}$Rb(F=2) peak, and a set of calibration data. All that remains to obtain a full data set is to obtain a DFSA spectrum for the ${}^{85}$Rb(F=3) peak. You should not have to make any major changes to your optical layout at this point. However, obtaining all six doppler free features for ${}^{85}Rb$(F=3) will require more careful optimization as they are more closely spaced and thus more difficult to resolve than was the case for ${}^{87}$Rb(F=2).

Laser frequency sweep calibration

Once you have obtained an absorption spectrum of the Doppler-broadened peaks of Rb, it is time to think about how to measure energy differences from the data. Note the the x-axis of the scope is time. Since the laser sweeps back and forth over a range of frequencies, the time axis of the scope is related to the frequency sweep of the laser. To calibrate the time sweep of the scope you need to measure constant of proportionality which tells you how fast the laser frequency changes.

When you send light of a fixed frequency (i.e. wavelength) into a Michelson interferometer, there will be some degree of destructive interference at the output which depends on the frequency ($\nu$) of the light and the path length difference ($\Delta L$) between the two arms of the interferometer. If $\nu$ and $\Delta L$ are constant in time, the interference condition is also constant. However, the light from the Toptica laser is sweeping over some range of frequencies, and as a result the interference condition at the output will change in time – producing interference maxima and minima which change with time. From knowledge of the path length difference of your interferometer, you can calculate how much $\nu$ has to change to go from one interference maxima to the next.

By recording the interferometer output on the scope while the laser sweeps in frequency, you can measure the time required to sweep from one maxima to the next, thus allowing you to calibrate the time difference between any two features on the scope trace of a source spectrum in terms of the change in frequency of the laser.

$\phi_1 - \phi_2 = \Delta \phi = \dfrac{4\pi f}{c}(L_1 - L_2)$

Once you know the change in frequency, you can calculate the change in energy from the relationship $\Delta E = h \Delta\nu$.

Final data analysis

You have one week to perform a full and complete analysis of the data you collect in lab and submit the following assignments.

Laser frequency calibration (25 points)

Show all of your data, plots, calculations and uncertainties for the calibration of the laser frequency sweep. Include data and analysis related to systematic effects which you evaluated. Plots should be publication quality with properly labeled and scaled axes and annotations.

Do the following:

  • Calculate the laser frequency sweep calibration, with uncertainties, from your interferometer.
  • Determine whether or not the rate of change of the frequency over the scan is linear or not. Be quantitative and include measurements and or plots which clearly demonstrate how linear the calibration actually is.
  • Include a diagram or photo of your interferometer setup along with measured arm lengths with uncertainties.
  • Include plots of the scope traces used in your calibration.
  • Show how you determined values of maxima locations from the scope data. If you fit sections of the scope data to obtain these values, the fit functions and plots of all fits should be included.
  • Include all measured values from the scope traces including uncertainties.
  • Show details of calculations, including error propagation. If the same calculation is performed multiple times, it is sufficient to detail one example.

Hyperfine splitting analysis (25 points)

Show all of your data, plots, calculations and uncertainties for your analysis of the hyperfine splitting for ${}^{87}$Rb(F=2) and ${}^{85}$Rb(F=3).

Do the following:

  • Calculate the energy differences between hyperfine states for both isotopes of Rb.
  • Include plots of the spectra from the scope. Relevant features such doppler free transitions and crossover dips should be identified.
  • Show detailed examples of relevant calculations including frequency calibrations, error propagation, etc.
  • Show how you determined values of peak locations, peak widths, etc. from the scope data. If you fit sections of the scope data to obtain these values, the fit functions and plots of all fits should be included.

Conclusions and comparison with literature (25 points)

You will need to write a complete and persuasive conclusion that includes a comparison of your results to expectations/literature and puts the results in proper context. Even more than in the assignments above, this assignment leans heavily on your ability to write clearly and correctly. You may want to look over our page on Drawing Conclusions.

Do the following:

  • Compare your measured values for the energy difference between hyperfine states for all both isotopes with literature values.
  • Discuss the impact of the linearity of the laser frequency sweep calibration on the final results.

Notes on experimental procedure

Main optical table

The above photo shows the main optical table on which you will be working; it is shared by all groups working on the experiment.

Mounted on this table are the main 780 nm laser which will be used to perform the spectroscopy experiment. Two mirrors are used to direct the beam from this laser through a pair of irises. Your group's smaller optical table will bolt to the main optical table in the location shown, and then you can place and align all of your components on your table which can then be removed from the main table and stored in between lab sessions. The two optical tables are made with sufficient precision that you can easily return your table to the main table and all of your previous optical alignment will still be intact. The two irises are there to ensure that the laser beam always passes over the same path across the main table.

There is also a low power HeNe laser which will you can use to align your optics. You do not want to build your optical setup using the main laser for the following two reasons:

  1. The beam from the main laser is hazardous and can cause serious eye injury. Most accidents with laser beams occur during alignment work when you are moving optical around on the table.
  2. The beam from the main laser is almost invisible to the human eye and is difficult to see without the aid of beam cards and CCD cameras which are sensitive in the near infrared part of the spectrum.

The beam from the alignment laser is also directed through the same two irises that the main beam passes through. This is accomplished by using a flip mirror which can be flipped in and out of the beam path without changing its alignment. Using the flip mirror you can determine whether the main laser beam or the alignment beam is going through the irises.

Only one of the two lasers should ever be on at any given time – either the main laser or the alignment laser. The main laser should only be turned on after you have completely aligned the optics using the alignment laser and you are ready to take data.

There are three photodiodes on in moveable mounts which can be positioned to detect the beams.

There is an inexpensive CCD camera which can be used to view the beam from the main laser.

There will also be a set of bolts and an Allen wrench for attaching your optical table to the main table.

Other apparatus shown in the photo but now actually on the optical table include:

  • The electronics for controlling the main laser.
  • A computer.
  • A couple of scopes.
  • A monitor connected to the CCD camera.

Individual group components

The photo below shows four smaller optical tables, each with a complete set of optics. Each lab group will use one of these tables and optics sets. Each group has an identical set of optical components which are more than sufficient to do the experiment.

Use only your optics, do not borrow or use components from any other groups set… even if they are not using them. If you think you need additional components, or if one of yours is damaged, talk to a member of the lab staff about obtaining what you need.

Under no circumstances should you disturb any of the other optical setups with belong to other groups. Be careful when retrieving and returning your table to the storage area so as not to bump someone else's setup.

Do not work on your table in the setup area. Take your table to the main optical table or to the free standing table at the far wall to work on it.

Each group has the following optical components to work with in designing and building your experiment:

Component Qty
Silver Mirror 5
50/50 Cube Beam Splitter 2
Linear Polarizer 2
780nm Half-Waveplate 1
Iris 2


Aligning optics is a skill which requires practice to get good at. If this is your first time working with laser optics, you may find it a frustrating experience at times. Here are some tips to keep in mind while you work.

  • Beam alignment in three dimensions is more challenging that doing it in two dimensions (and is unnecessary for this experiment). Keep all of your beams the same height off the table to simplify things.
  • Have a detailed sketch of your optical layout on hand before you start placing components on the optical table. It is a lot easier to make changes on paper than it is to repeatedly tear down and rebuild parts of your setup.
  • Work front to back. Start with the first component which the beam will encounter on your portable optics table. Once that component is in place and properly aligned, move on to the second component, then the third, etc. Remember, making even a slight adjustment to the alignment of a component will throw off everything “downstream”.
  • Watch for unwanted reflections of the beam off of vertical surfaces. (For example, when the beam enters your vapor cell some of it will be reflected at the air to glass surface.) Pay attention to where that reflected beam is going to go and make sure it is not going to interfere with anything else, or create a dangerous situation where it might scatter into someone's face.

Video on Aligning Optics.

Once you have your optical paths setup and aligned, it is time to turn on the Toptica laser and use the flip mirror as shown in the video to switch from the guide laser to the main beam. Remember, everyone in the room must be wearing goggles appropriate for the 120 mW 780 nm laser before the beam is turned on. The door should be closed and anyone entering the room will need to put on goggles before entering or the beam should be shutoff. You should also have all of the detectors on and connected to the scope and the scope should be on and triggering on the sync pulse from the Toptica laser before turning its beam on.

Use the IR card to follow the Topica beam and make sure that it is aligned the same as your guide beam was. At this point, you should not have to do more than minor tweaking to the Toptica beam in order to have its alignment in good order.

Now you should find the signals from the photodetectors on the scope and tune the laser onto resonance with the Rb hyperfine transitions as shown in the video. Don't spend more than 20 minutes trying to tune the laser onto resonance. If you cannot get it to the point where you see at least three of the four doppler broadened peaks you should find the TA or one of the lab staff. Sometimes the laser itself needs a slight adjustment which is not something you can do yourself.

Video on tuning the laser onto resonance.

Once you have the Toptica laser sweeping over the hyperfine transitions you can begin the process of optimizing the signal and and recording spectra. Part of the optimization process involves maximizing the overlap of the probe and pump beams. Another significant part of the process involves setting the power in the probe and pump beams.

Finding the correct beam powers is accomplished through the process of trial and error. To help you in this process we provide a power meter with which you can measure the approximate power in the laser beam at any point on the table. In order to control how much of the laser power passes through the first iris on the main table we have placed a combination of a half-waveplate and a polarizing beam splitter (PBS) in the main laser beam as shown in the following image. The PBS has been aligned to pass horizontally polarized light and reflect vertically polarized light. The half-waveplate in front of the PBS allows you to rotate the plane of polarization of the light incident on the PBS, thus you can control how much of the laser light is horizontally polarized so that it passes through the PBS.

To get the beam powers in the correct range, use the half-waveplate and the power meter to set the power of the pump beam to be somewhere between 0.5mW and 1.5mW. The intensity of the probe beam should be about a factor of 5 or 6 less than the pump beam.

When you leave the lab

Since there will be other groups working on the apparatus, it is your responsibility to ensure that everything in the lab is in order with the next group arrives. The room should be tidy and everything should be either put away or reset to its default. If the lab room was in disarray when you arrived, you are still responsible for leaving it in the appropriate state for the next group.

Here are some general tips on things to check before you leave.

  • The lasers should off and the Toptica electronics rack should be off as well.
  • Your optical breadboard should be removed from the main optical table, labeled, and stored in its proper location.
  • Any and all optical components which are in use on your breadboard or permanently mounted on the main optical table should be put back where they belong.
  • The IR sensor cards should be laid out on the main optical table.
  • Photodetectors should be turned off and IR filters should be in place if you removed them.
  • All tools should be returned to the tool box.
  • The CCD camera and monitor should be turned off.
  • Scopes should be turned off and their inputs disconnected.
  • Any applications on the computer should be closed. Be sure to sign out of any accounts you may have logged into.
  • The computer can be allowed to go into sleep mode and does not have to be shut down.