Last Update Dec. 2023

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.)

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
2. Doppler-free spectroscopy may be used to non-invasively probe the temperature of a flame

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).

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

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?

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 description of the Hyperfine interaction as it applies to atomic rubidium: Rb Hyperfine
• A description of thermal doppler broadening of atomic emission/absorption lines for atoms in a gas: Thermal Doppler Broadening
• A description of the technique of Doppler Free Saturated Absorption Spectroscopy: Doppler Free Saturated Absorption Spectroscopy
• A description of using a Michelson Interferometer to calibrate the frequency sweep of a laser: Calibrating Frequency Sweep of Laser
• A description of the optical components available for your use in the lab: Description of Optical Components

For this experiment you will need to design, build and align your own optics in order to measure the hyperfine splitting in atomic Rb. This exercise 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.

Do the following:

Alignment task 1

Use a mirror, a 50/50 beamsplitter, and two photodetectors to build the optical setup shown in Fig 1. Turn on the photodetectors and connect them to the scope, making sure their Gain settings are the same.

Turn on the guide laser and use the scope to measure the intensity of the two beams coming out of the beam splitter. Sketch your optical path and record your measurements in your lab notebook.

Does the 50/50 beamsplitter do what its name suggests?

Figure 1: Alignment task 1

Alignment task 2

Insert a linear polarizer in the beam path somewhere before the beam enters the 50/50 beamsplitter. In principle, a 50/50 beamsplitter should be insensitive to the polarization of the incident beam. Is this the case? If not how close to being truly 50/50 is it?

Use this optical setup to determine the polarization state of the beam from the guide laser.

Figure 2: Alignment task 2

Alignment task 3

Now replace the 50/50 beamsplitter with a polarizing beam splitter (PBS). Determine which polarization state passes straight through the PBS and which is reflected. How efficient is the PBS at the wavelength of the alignment laser?

Figure 3: Alignment task 3

Alignment task 4

Insert a half-waveplate as show in Fig 4. Use the linear polarizer to ensure that the beam incident on the half-waveplate is as linearly polarized as possible.

Use the half-waveplate to create a vertically polarized beam incident on the PBS, a horizontally polarized beam incident on the PBS, and a beam which is in a 50/50 superposition of vertical and horizontal polarization states. Use measurements of the intensity of the transmitted and reflected beams to verify that you have properly set up these three configurations. Include sketches and measurements in your lab notebook.

Figure 4: Alignment task 4

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.

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.

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.

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.

You will do this by building a Michelson interferometer on the optical table. 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. Once you know the change in frequency, you can calculate the change in energy from the relationship $\Delta E = h \Delta\nu$.

At this point you should have useable data for the Doppler-broadened peaks, a DFSA spectrum for the Rb-87(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 Rb-85(F=3) peak, including the appropriate Doppler-broadened profile to subtract off of the DFSA spectrum. You should not have to make any major changes to your optical layout at this point. However, obtaining all six doppler free features for Rb-85(F=3) will require more careful optimization as they are more closely spaced and thus more difficult to resolve than was the case for Rb-87(F=2).

You have one week to perform a full and complete analysis of the data you collect in lab and submit the following assignments. You can score up to a maximum of 50 points total on these assignments, but you should notice that the pool of points available is actually 60 points. This means that you don't need to do everything perfectly to get full credit (though you should still try to do everything as well as possible, because we will not consider make-up or extra credit). If you score more than the maximum of 50 points… “hooray”! (But you will still only get a score of 50; you don't get extra credit.)

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:

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

Do the following:

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:

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:

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.

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.

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.

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

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.

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.

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.

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.