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.

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

Before your preparation meeting with your TA, your and your lab partner(s) need to do some background research.  The purpose of this is so that you can go into your first meeting with the TA with a picture of what you need to measure, how those measurements will be made, what complications you are likely to encounter, and how you might deal with them. Then, at your first meeting you can focus on the details of what you need to do to start getting data to work with. Remember that you are expected to come to this meeting prepared to participate and demonstrate your understanding of these concepts.

Questions that your group should be prepared to answer are the following:

What are you measuring?

• What is the hyperfine effect?
• What is the predicted magnitude of the hyperfine splitting for the first excited state of atomic Rb-87?

What is the experimental technique that you will use?

• What is absorption spectroscopy?
• What is thermal doppler broadening and why does it prevent direct observation of the hyperfine splitting in Rb?
• What is Doppler-free saturated spectroscopy?

Some other useful concepts.

• What does bandwidth mean when used to describe a laser beam?
• What is a natural linewidth when used to describe an atomic transition and how is it calculated?

The following are links to our wiki pages discussing some of the concepts that you need to be familiar with. Outside of these links Google and Wikipedia are good sources of information if you come across concepts or terms you are not familiar with.

A description of the Hyperfine interaction as it applies to atomic Rb. 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

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

By the time you get to the lab you should understand what it is that you will be measuring and have a plan for how you are going to do the experiment.

In the lab we provide you with everything you need to do the experiment. You have to select 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 which can be tuned over an appropriate frequency range for the measurement you need to make. The laser operates at wavelengths near 780nm. The power output can be as high as 120mW which makes it a class IIIB laser which can cause permanent damage to the eye. The process of placing and aligning optical components is when you are most likely to struck in the eye by a stray beam. In addition to the safety measures already discussed, you will do build and align your optics using a separate low power alignment light laser which is equivalent to a laser pointer used in presentations. Nevertheless you should still practice proper laser safety, even while working with the lower power alignment laser. You will also be sharing the laser and photo detectors other groups which will be working on their own version of the experiment on days when you are not in lab. To accommodate this you will arrange your optical components on a small 300mm x 600mm optical bread board which can be attached to the main optical table while you are working on it, and then 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. The other groups sharing the laser will be doing the same.

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 780nm 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 groups 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 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 photo diodes 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 basic procedure can be summarized as follows:

• Take your optical table and bolt it to the main table in between the pair of irises.
• Turn on the alignment laser and gently place the flip mirror in the up position.
• Verify that the beam is passing through the center of the two irises.
• Begin placing your optical components on your table and aligning the beams.
• Position the detectors, turn them on and connect them to the scope.
• Once you are satisfied that everything is placed and aligned correctly unplug the alignment laser and gently put the flip mirror in the down position.
• Put your IR laser safety goggles on.
• Close the door to the lab room.
• Turn on the main laser and use the IR card and CCD camera to verify that the beam is passing through the center of both irises.
• Check the alignment of your optics. You might have to do some fine tuning to some of the components.
• Start looking at your signals on the scope and make final adjustments to the optics as needed to obtain the best possible absorption spectra.

This is likely to be an iterative process. You may have to go through the entire procedure outlined above more than once before you obtain acceptable results. This can be frustrating at times, but it is a part of lab work.

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.

When drawing your optical layout you can use the following symbols to represent the different components on the table.

Mirror	50/50 Beam Splitter	Linear Polarizer	Photo Detector	Rb Vapor Cell

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. Keeping all of your beams the same height off the table will 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 “down stream”.
• 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 120mW 180nm 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 photo-detectors 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 1/2 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 1/2 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 it's 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 it's 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.

Your analysis is due 4 days after your second day in lab. The analysis is not a lab report, rather it is all of the data reduction, number crunching, calculations, curve fitting, error propagation etc. which is necessary for you to establish your final conclusions. Think of it as being more like an extended homework set where you have to show how you got your final results.

Three days after your analysis submission your group will have a meeting with the TA to go over your analysis and make sure you are prepared to write your final report.

The final report is due three days after the analysis meeting.

Your graded analysis will be returned along with your graded final report.

Three days after your analysis is due your group will meet with the TA to discuss the overall analysis and make clear what needs to go into your final report. Note that this meeting is not for the purpose of discussing your grade on the analysis, you will receive the grade on the analysis along with the graded final report. Instead this is an opportunity for the TA to have reviewed your analysis to identify where you may have short comings or misconceptions in your understanding of the experiment with the goal of improving what goes into your final report. It is also an opportunity for you to make sure that you understand what your TA is looking for in your report.

You are expected to bring a detailed outline for your final report to this meeting. The outline should consist of section and sub-section headings which make clear what information you will put into the report as well as the order in which that information will appear. This should literally be a single page document. Having a meaningfully thought out outline will count towards your participation grade for the meeting.

The expectation is that between feedback on your analysis and your outline you should leave this meeting with a clear idea of how you will write up your final report.

Your analysis, like your reports, should be submitted as a single PDF. It is not expected that you will write narrative descriptions as you will in your final report. For the analysis it is acceptable to organize it into sections with one or two brief sentences of description. Things should be put in a sensible order so that the TA can follow what you are doing. For example plots, fits and calculations related to your energy calibration should be grouped together into a section, and that section should be placed before you apply the calibration to your data. For cases such as fitting and extracting peak locations for all of your scattering data it is sufficient to show one representative plot of a fit to the data along with a table containing all of the values. Scans or photographs of calculations done on paper or in your lab notebook are acceptable but absolutely MUST be clear and readable.

Each item below is graded on a 0-4 point scale:

• (4) - Good (A): Work is done correctly and covers everything in adequate detail.
• (3) - Adequate (B): Minor mistakes were made. Misses one or more minor elements.
• (2) - Needs improvement (C): Work is incomplete or incorrect in some significant way.
• (1) - Inadequate (D): Work is mostly incomplete or incorrect.
• (0) - Missing (F): omits all elements or makes no meaningful attempt.

All rubric items carry the same weight. The final grade for the analysis will be assigned based on the average (on a 4.0 scale) over all rubric items.

The final report is due three days after your scheduled analysis meeting with the TA.

Your final report will be evaluated based on the following rubric. The rubric is not a format for your analysis, you are not expected to have a specific section on Data Handling or Presentation of Data. Elements of the different rubric categories will appear at different points through out your analysis writeup. For example you will be presenting data in your discussion of the calibration, your discussion of determining peak locations, and likely in your final results. Your writeup of your analysis should be structured in a way that is clear and readable, there should be a logic to the flow of it.

Each item below is graded on a 0-4 point scale:

• 4 – Good (A): completes all listed tasks and provides appropriate context; thinks carefully about data and analysis; addresses all concerns raised by the results (where appropriate).
• 3 – Adequate (B): misses one or more minor element or lacks appropriate context; leaves a problem or ambiguity unaddressed; does not present analysis clearly enough.
• 2 – Needs improvement (C): omits or mishandles one or more item which renders the analysis fundamentally incorrect or incomplete; presents results in an incorrect or unclear way.
• 1 – Inadequate (D): omits or mishandles multiple items or treats them at an insufficient level; presentation is overall muddled or inaccurate; flaws in logic or process.
• 0 – Missing (F): omits all elements or makes no meaningful attempt.

All rubric items carry the same weight. The final grade for the analysis will be assigned based on the average (on a 4.0 scale) over all rubric items.