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.)

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, and is the only lab where you have to design, build and run an experiment yourself. 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).

The teaching goals are as follows:

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

You will be using the technique of Doppler Free Saturated Absorption Spectroscopy (DFSAS) to measure the energy splitting of the hyperfine effect in natural rubidium. That sentence contains a mouthful of technical terms and physics concepts which you would not likely be familiar with unless you had worked in an atomic and molecular optics (AMO) research lab. You are, however, likely familiar with the underlying physics concepts. The prelab question and subsequent in-lab exercises will walk you through the the processes of understanding the physics involved in the DFSAS technique as well as how to use a laser and some common optical components to build an experiment to perform the measurement.

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 the optical components available for your use in the lab: Description of Optical Components

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

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 figure above shows the layout of the optical table you will be working with for this lab.

There is a large optics table with two lasers, a pair of mirrors and a pair of irises already mounted to it. With the exception of the area labeled Photodetector Area, you should not move or add optical components to this table. The mirrors and lasers have been prealigned to direct the beam from either the IR Laser or the Alignment Laser through the center of the two irises.

The Photodetector Area is where you will place the photodetectors for making measurements.

Your group has its own smaller optical table and a set of optical components which an instructor will point out during your initial introduction to the lab. Your optical table can be placed and bolted on top of the larger optical table. This is where you will build your own optical setup for the various parts of the lab. The two irises define a precise beam path across your smaller optical table that you will use as a starting point for building your own optical setups.

Place your optical table on the larger one as shown in the above diagram. You will notice that there are 4 through holes in your optical table, one near each corner, which will line up with the tapped holes in the larger optical table.

• Place your optical table to the main board in the location shown above. Make sure that the beam path will pass over your table.
• Attach your table to the main table using the hex head bolts and allen wrench provided. Note that while you can secure all 4 corners of your board to the main one, using 2 will suffice. Make a note of which holes on the main board you used so that you can return your setup to the same location on the main board on days 2 and 3 in the lab.

Before proceeding you should check with an instructor that your table is properly positioned.

The goal is to send a pair of slightly diverging beams from the laser through a Rb vaporcell and into a pair of photodetectors. The outputs from the detectors will be observed on the scope while you tune the IR laser onto resonance with the Rb D1 transitions.

Use the 1º 9:1 wedge beam splitter to direct the beam from the laser through the vaporcell and into the two photodetectors as shown in the figure above. The 1º 9:1 wedge beam splitter is labeled and should be sitting in the Photodetector Area of the main board when you arrive to lab. If you cannot find it ask an instructor for assitance.

For todays tasks you will be working with a stand alone vaporcell of natural Rb. However, the next two days in lab will make use of a different vaporcell and Helmholtz coil assembly which is physically much larger than the stand alone vaporcell. The optical path you will build today will be used for the next two days of the lab. We provide a template of the boundary of the vaporcell and Helmholtz coil assembly which you can use to make sure that the components you place today will not be blocked when you switch vaporcells.

Perform the initial alignment using the alignment laser. Once you have the wedge beamsplitter, vaporcell and photodetectors in position and aligned using the alignment laser, have an instructor inspect it and provide instructions on how to use the IR laser.

Once you have switched to the IR laser, use the IR detection cards and the video monitor to verify that the IR beams are correctly passing through the vaporcell and into the photodetectors.

An instructor will assist you with this task.

Tuning the IR laser onto resonance with the Rb D1 transition is not difficult once you have seen it done, but it would be very difficult to explain in the Wiki.

Once you have been shown how to operate the laser and photodetectors, fine tune the laser diode current to obtain a clear and smooth spectrum which shows the absorption peaks for all four of the expected Rb D1 transitions. Use the USB connection between the scope and the lab computer to transfer a screenshot of the scope trace and/or the digitized data. You will need this for your day 1 out of lab assignment, so have an instructor verify that your spectrum is good.

You now need to build a Michelson Interferometer in order to calibrate the frequency sweep of the IR laser. Why we need to perform this calibration should have been covered when you were shown how to operate the laser. To recap…

Using your set of optics, place mirrors M1, M2, M3, M4, a beam splitter and a third photodetector to create the beam path shown in the figure below.

Aligning an interferometer to the degree of precision needed to see fringes is the most challenging alignment task you will need to perform for this lab. It is not trivial and can be frustrating. This step must be completed before you leave lab on day 1 in order to do your out of lab assignment. After completing all of the other day 1 tasks you should have at least 2 hours for this part. Keep an eye on the clock, if you are not at the point of taking data by the last half hour of the period, find an instructor to assist you. It is suggested that you get some advice and pointers from an instructor before starting to build the interferometer.

Once you have aligned the interferometer and obtained a clean interference pattern on the scope, use the cursor feature of the scope to measure the locations of the interference maxima (including an estimate on the uncertainty of these measured values) and record them in your lab notebook. You should also transfer a screenshot and the digitized data to the lab computer for inclusion in your out of lab assignment.

Do not for get to measure and record the dimensions of the interferometer.

If you have time, we strongly recommend that you calculate the time difference to frequency difference conversion factor in the lab, and check with an instructor that the value you get is reasonable.

On Day 1 of this lab you setup the optics necessary to observe absorption of the IR laser light passing through the vaporcell, and to perform a calibration of the IR laser frequency sweep using an interferometer.

Begin by placing your small optics table on the main table, and attach it in the same location you used in Day 1. If the fixed beams from the lasers still pass through the two irises, all of your alignment from Day 1 will be good. You might have to do some very minor tweaking of some mirrors on your optics table, but at the 99% level everything should still be well aligned.

Since the same photodetectors and the wedge beam splitter are used by all groups, you will have to reposition them for your setup. Regardless, you should be able to get the whole apparatus set back up to where it was at the end of Day 1 in under 30 minutes, including turning the IR laser on and tuning it to resonance.

Today you will perform a more in depth investigation of the temperature dependence of the thermal doppler broadening effect.

On day one you measured the FWHM of the doppler broadened absorption peak for one of the Rb D1 emission lines as part of the initial setup and optical alignment. Now you will measure the FWHM of the same doppler broadened peak as a function of temperature, up to 50ºC.

Instead of using the stand alone vaporcell you will use the vaporcell and Helmholtz coil apparatus which includes a built in temperature controller. Once you have reinstalled your small optical bench on the main bench, carefully place the larger vaporcell assembly on the table so that both beams from the wedge beam splitter pass through and into the photodetectors. You will notice that for this instrument the vaporcell is imbedded deep within the heater and coil assemblies making it more difficult to observe directly where the guide laser beams are striking it. It is not however too difficult to tell when both beams are passing cleanly through the vasporcell by looking for the to spots at the photodetectors. A piece of foam core board can help with locating them.

Once you have the vaporcell in place, switch to the IR laser and tune it onto resonance as you did on Day 1. On the scope obtain a stable trace that passes cleanly through all of the absorption features.

Connect the thermocouple and heater wires to the laser electronics rack as shown. You should now be able to read the temperature of the vaporcell from the LED display on the temperature controller module. There are instructions in the lab for how to adjust the temperature of the vaporcell, which can be set to temperatures up to 50ºC.

On the scope zoom in on the same doppler broadened peak you used on Day 1. The procedure now is very straight forward. Starting with the vaporcell at room temperature, approximately 20ºC, use the scope to measure the FWHM of the doppler broadened peak for ~10 temperatures up to 50ºC. For each measurement you will need to;

• Adjust the temperature setpoint on the controller,
• wait for the temperature of the vaporcell to come to equilibrium,
• capture the absorption profile of the peak on the scope,
• transfer the digitized waveform to the lab computer,
• and measure the FWHM using the scope cursors.

Do not forget to estimate the uncertainties in your measured quantities.

This procedure should not take more than a couple hours. Once you are finished, return the vaporcell to its default temperature of 50ºC.

You are now ready to move on to building the full Doppler Free Saturated Absorption Spectroscopy setup.

Before doing so however you need to familiarize yourself with the physics involved in both the phenomena you are studying, and the technique of DFSAS. While none of the physics involved is more advanced than PHYS235 level quantum mechanics, there are a number of processes at work which can take some thought to sort out to the point where you truly understand what you are trying to accomplish with the optics and laser beam.

We highly recommend that you review the material in these two links PRIOR to coming to lab on day 2 of the experiment. By the end of day 2 you are likely to be ready to begin on this check point exercise. Regardless of whether or not you have read the material, you should go over it with an instructor before proceeding.

Rb Hyperfine

Doppler Free Saturated Absorption Spectroscopy

Your goal is to setup the optics to perform DFSAS measurements of the hyperfine splitting in ${}^{87}$Rb(F=2) and ${}^{85}$Rb(F=3).

Over the first two days of this lab you will have built and aligned virtually all of the optical setup needed for the DFSAS measurement. If this work is still intact on your personal optical table, you can proceed straight to the next section on creating and aligning a pump beam. If this is not the case you first need to reestablish the optical setup from day 2 before continuing.

Once you have the optical setup from day 2 fully functional, meaning you see interference fringes from the interferometer and the two beams from the wedge beam splitter pass cleanly through the vaporcell plus Helmholtz apparatus, all that is needed is to add a 50/50 beam splitter as shown in Figure X. Before you begin this process however it is important that you first collect a spectrum of the output of the interferometer for calibration. Once you put the 50/50 beam splitter into the beam path, the beam entering the interferometer will be displaced enough to require realignment. So it is easier to take the calibration data now.

• Tune the laser onto resonance.
• If necessary, tweak the alignment of the two mirrors in the interferometer to get a good interference signal.
• Record the interference spectrum on the scope and save both the screenshot and the digitized waveform to the lab computer for later use.

The final optical component which needs to be positioned and aligned is the 50/50 beam splitter as shown in Figure X. This beam splitter must be positioned so that the beam labeled “Probe” from the wedge beam splitter passes through it and into photodetector #1, while not obstructing the other beam from the wedge beamsplitter which needs to still reach photodetector #2. At the same time the 50/50 beam splitter mush be positioned such that the beam traveling right to left in the figure is reflected into the vaporcell overlapping the Probe Beam. This new beam will function as the Pump beam.

Getting this last optical component in the proper location and aligned is a little tricky. Before you begin you should consult with an instructor who will give you some tips on how to proceed.

Once you have the pump beam in place and aligned with the probe beam, connect the outputs of photodetectors #1 and #2 directly into channels 1 and 2 on the scope. The output of photodetector #2, should show the same doppler broadened spectra as days 1 and 2. The output of photodetector #1, which sees the probe beam, should now show the doppler broadened spectra but with dips now superimposed on each transition peak. These dips are the doppler free features associated with the individual hyperfine states and their cross overs. Each of the four transitions, two for each isotope, should in principle show 6 of these doppler free dips. However it is likely that you will need to spend a bit of time fine tuning the alignment and intensities of the probe and pump beams to see all of them.

From this point forward you will want to focus on the first two doppler broadened features, the 87Rb(F=2) and 85Rb(F=3) transitions. For each of these two peaks you need to record and save a scope trace which has been zoomed in enough to see all 6 doppler free dips clearly. You should also use the cursor feature to carefully measure the locations of these dips, with estimated uncertainties.

You will need to spend some time adjusting the overlap and power of the probe and pump beam in order to see all 6 of the expected doppler free features on each of the doppler broadened peaks. The optimal beam powers for the 87Rb(F=2) and 85Rb(F=3) transitions are different enough that you will need to optimize and record them separately.

For each isotope present your DFSAS spectrum. (10 points)

Describe how you performed your energy difference measurement. (10 points)

For each isotope present your full data set. (10 points)

Compare your experimental result with the literature values. (10 points)

Present your measurement of the natural line width for one Hyperfine transition. (5 points)

Compare your measured natural linewidth with the theoretical line width. (5 points)

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.

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

R. C. Pooser1, et. al., "Quantum correlated light beams from nondegenerate four-wave mixing in an atomic vapor: the D1 and D2 lines of 85Rb and 87Rb ", Optics Express, Vol 17, No. 19, Sept 2009