Saturated Absorption Spectroscopy using an ECDL

Introduction

Doppler-free saturation spectroscopy was a groundbreaking advance in optics made in 1981 by Bloembergen and Schawlow [1]. The development of this technique actually earned them the 1981 Nobel Prize for Physics. Saturated absorption spectroscopy is a technique of non-linear optics that makes use of counter-propagating beams to measure the rest-frame electronic energy states of complex atoms at room temperature. The success of saturated absorption spectroscopy is the elimination of the Doppler-broadening of the energy spectrum when the molecules of interest are at a non-zero temperature. It turns a multi-atom experiment into a single atom one by ignoring atoms with lab-frame velocities significantly greater than zero.

In the time of its discovery saturated absorption spectroscopy (SAS) was a very important improvement to spectroscopic technique and continues to be important and widely used today. Used in tandem with broadly tunable lasers, SAS was used to accurately measure the Lamb shift in the Hydrogen Balmer series [1]. This was a major achievement because the smallest Lamb shift measured at the time was sodium's, which was four times greater. After its invention, SAS was implemented in many laboratories to make more accurate measurements of atomic spectra. Today SAS is a common tool used to ensure the frequency of a laser. It is this property that makes SAS so useful in high precision experiments.

The focus of this experiment is to build and subsequently use an extended cavity diode laser to measure hyperfine splitting of the 5P_3/2 state of Rubidium 85 and 87. The first sections are devoted to building the extended cavity diode laser (ECDL) and then setting up the piezo electric drive to add tunability to the laser. Hyperfine splitting is a result of coupling between the electron and nuclear magnetic moments and each level is characterized by their total angular momentum quantum number F­. Skipping over the math of determining the levels, the splitting of Rubidium 85 and 87 are depicted in Figure 1 below.

Figure 1: The hyperfine splitting of ­⁸⁵Rb (left) and ⁸⁷Rb (right). The experiment is focused at the 5P_3/2 lines or the 780.0 nm D₂ line. F is the total angular momentum quantum number and Δν is the displacement from the unsplit line. Figure taken from [3].

As shown above in Figure 1, the hyperfine splitting is on the order of 100MHz or less and given that the Doppler broadening present in normal absorption spectroscopy is on the order of 500MHz at room temperature (REFERENCE), regular absorption spectroscopy will be unable to resolve the hyperfine splitting. This is where Doppler-free saturated absorption spectroscopy (SAS) comes into play.

Theory

Simple setup for a saturated absorption spectroscopy experiment. Original Figure.

We begin with a simple setup for a SAS experiment shown in the figure above. Two beams are derived from the same laser; One travels through the cell to be registered by a photo-diode (the "probe beam"), the other (the "pump beam") crosses through the cell in the opposite direction. This setup accomplishes two important tasks: the pump beam saturates, or bleaches, the gas inside the cell and the cross-propagation pin-points the molecules in the gas that have zero velocity with respect to the two beams.

The pump beam is on the order of ten times more intense than the probe beam and as a result, makes the gas in the cell essentially transparent to the probe beam. The pump beam accomplishes this through the promotion of most of the electrons to excited states in the gas and as a result, the less intense probe beam doesn't have enough photons to promote a significant proportion of electrons. To get an idea of why this works, let us examine a simplified fictitious atom with only two state, a ground and an excited state. To understand the population of each state we use the rate equations

where N_{g} and N_{e} are the populations of electrons in the ground and excited states respectively, Γ is the natural linewidth discussed above in Laser Physics, σ is the absorption coefficient, and Φ is the incident photon flux [4]. Notice that the first term is the spontaneous emission and the second term is due to stimulated emission. If we use the fact that N_{g} + N_{e} = N, where N is the total number of electrons, the above equations simplify to

The solution to the differential equation is

and gives the population of the excited state at a given time t. With this equation, two important observations can be made. In the case of a strong beam (i.e. pump beam), we have σΦ >> Γ and the equation simplifies to

which clearly approaches N/2 as time increases. Therefore, when the pump beam is passing through the gas cell, we can can assume that half of the electrons are out of the ground state. A more important observation is when we have a weaker beam (i.e. probe beam) passing through the cell. For this case, σΦ << Γ so the equation instead simplifies to

This equation is a pure exponential decay and will approach zero. If we combine the two cases, the pump and probe passing through at the same time, we get that half of the electrons are excited due to the pump while very little are being promoted by the probe. Thus the gas is essentially transparent to the probe beam.

The spectrum as a result of only feeding the pump beam into the Rb cell is shown in the upper figure. The spectrum with both beams is shown in the lower figure. Image taken from [4]

Now we turn our attention to the counter-propagation of the two beams through the gas cell. At any temperature above absolute zero, the molecules in the gas cell will have velocities according to a Maxwellian distribution. This means the gas molecules will see the light red/blue shifted by the Doppler effect. If the pump beam is blocked, the upper image in figure shown above is seen. This is the characteristic Doppler profile of absorption.

The counter-propagation works because the molecules will see the two beams with a different shift. For example, molecules moving to the right will see the probe beam bluer and the pump beam redder. Now, only the molecules with zero velocity with respect to the beams will see the beams at the same frequency\cite{doppler}. Combining this with the saturation discussed above, a peak in the middle of the absorption profile appears (Figure above (lower)) known as the Lamb-Dip [4].

Tunable ECDL Setup

DO NOT connect the wrong leads! This will lead to irreparable damage to the diode.

DO NOT exceed 80mA of current

Above is a picture of the current and temperature controllers. When operating this it is important to follow a specific order: First, ensure the knob on the controller is turned all the way counter-clockwise. Next, press the 'enable' button in the top left corner of the interface. Finally adjust the knob to the desired current/temp.

Beam setup:

Once the diode is in place and the laser is operating, we turn our focus to the beam. The first step is to collimate the beam. Pictured below is the tool to adjust the lens, and the lens. Place the tool in the small divots and turn either clockwise or anti-clockwise. Check the beam using the infrared card. Continue the process until the beam is roughly the same diameter at ~1cm from the diode to ~2m.

Next is assuring the free-running mode of the laser is sufficiently far from Rb resonance. To do this simply point the beam into a spectrometer. If the spectrometer is overloaded (which most likely it is), do not point the beam directly in, instead direct a fraction of the beam in. Depending of the temperature setting of the diode, the spectrometer should read ~780nm. If it reads ~778nm or ~782nm, you’re done and can move on. If not, look to the temperature regulator for the diode. Move the DISPLAY light to ‘Tset’ and adjust the knob. Wait until the spectrometer is reasonably stable to decide if the laser is ~ 2nm from 780nm, repeat steps until satisfactory.

Diffraction Grating & PZT setup

Once the laser’s free-running mode is far from resonance, the next step is incorporating the diffraction grating. Locate the diffraction grating and the PZT. Using your best judgement, place the diffraction grating a concentric square inside the PZT mount (See picture). Keep in mind the orientation of the laser with respect to the table. Fix the diffraction grating in the mirror mount such that the beam will reflect onto the mirror and (!!)the knobs are easily accessible(!!). Mount to the face of the diode using four 3” posts (See picture).

If you haven’t already, find a place to dog down the ECDL. You will need a space about 2m long and 1m wide but more is always nice. Here comes the challenging part. Once the ECDL is constructed and dogged down, the diffraction grating must be aimed just right to tune the laser to 780.4nm. The best process to do this is laid out below.

Step 1: Eyeball it. Turn the H and V knobs to locate the part of the beam reflected back to the diode. Then adjust so it roughly points into the diode.

Step 2: Ignore the V knob for now and scan through the H knob. Turn the knob until the beam is not pointed into the diode anymore or until you see two peaks in the spectrometer reading. If you move the beam too far, go the other way until one of the conditions is met. If two peaks never happen, move roughly back to center, slightly change the V knob and repeat.

Step 3: When you do see two peaks (See picture) on the spectrometer reading gently rock the H knob back and forth to test if you have control over the expression of the modes (i.e. there is direct correlation between movement of the knob and where is the spectrometer peaks). If you do not have control over the modes, slightly adjust the V knob and check again.

Step 4: When the diffraction grating is correctly aimed, you should have total control over the output of the laser. Gently rotate the H knob until the spectrometer is peaked at 780.4nm. Now find the PZT cord corresponding to changing the diffraction grating’s H direction. The cords should be labeled by which knob does the same job. Dog down the cords, keeping the important cord separate, to minimize vibrations and keep a clean work station

Beam Alignment

Next in the setup is alignment of the beams. The main objective of this part is to get two beams crossing inside the cell and two beams registered by photodiodes.

Step 1: Direct the beam with two mirrors away from diode and point it along the long axis of your setup. Make the beam parallel to the table. To do this you will need two irises and two mirrors. Place one iris close to the last mirror (the last one before the RB cell) and one far away. Adjust the back mirror until the beam passes through the close iris. Now adjust the front mirror until the beam passes through the far iris (or gets blocked by the close iris). Iterate though until the beam passes perfectly through both irises. For a more in depth explanation click this link How To Optics.

Step 2: Split the beam into three using two neutral density filters. Two less intense beams (probe and reference) will be traveling in the same direction, while the third (pump) is the remainder. Adjust the neutral density filters so the probe and reference beams are equal in intensity and about an order of magnitude less intense than the pump beam.

Step 3: Send the pump beam as far away as the table allows and use a mirror to reverse its direction. Bounce the reference and probe beams once more to be pointing in the opposite direction as the pump beam. Keep the beams about 1cm apart. This will be a cramped mirror setup.(??? Provide some diagrams to make this more clear. Be sure to label each beam???)

Step 4: Raise or lower the reference beam out of the plane of the other two beams. This is done best by very slightly adjusting the V knob on the neutral density filter so by the time the reference beam hits the Rb cell it is out of the plane.

Step 5: Cross the probe and pump beams about a third of the way in between their mirrors by moving the pump beam. You want to keep the reference and probe traveling in about the same direction. Be careful where the pump beam ends up; You don't want it hitting a mirror again. Place the Rb cell where the two beams cross. Be sure there is a viewing window for an old camera(??? Give model name ???) or an IR viewer to clearly see the cell.

Step 6: Set up camera about 2ft away from the Rb cell and connect it to a cathode ray TV.

Step 7: Get two glass slides mounted and pick off some of the pump beam for use by a Fabry-Perot and the spectrometer. Be sure not to obstruct the view of the camera.

Step 8: Set up a photodiode subtraction circuit* and have the A diode catch the probe beam. Finagle the reference beam to pass through the cell(??? How?), not cross the pump or probe, and aim it into the B photodiode.

When finished the setup should look some like this.

*Notes on the subtraction circuit:

To power the circuit, plug +9V into the red terminal, GND into the green, and -9V into black and turn the power switch to on. The box is constructed counter-intuitively so you need to check to see if it works before incorporating it. After powering the box, test each of the three outputs (A, -B, A-B) with an oscilloscope. If the outputs do not work, open the box up and check three things.

First, see if there are any unwanted shorts in the system. If so, bend wires around to fix the issue.

Second, check the connections in the board. If there any loose connection you may need to solder them.

Third, determine if the op-amps are opperational.

Next up is equalizing the reference and probe beams to see the small Lamb dips that are drowned out by the Doppler noise. Outlined below are the steps to take to equalize the two beams.

Step 1: Block the pump beam. With the pump beam the probe and reference beams might not be equal(???Clarify this???). You may use a beam stopper, another mirror, or a regular opaque object.

Step 2: Connect all three outputs to an oscilloscope (A, -B, A-B) and adjust the scaling so you can see all three. You should see a high line, a low line, and a line somewhere in between.

Step 3: Adjust the neutral density filters until A-B is zero and the other two have the same magnitude. You want to be very careful about the adjustments because they might mess with the alignment. You also want to be careful not to completely ignore the 10:1 intensity ratio between the pump and these two beams.

Step 4: If the 10:1 ratio was severely skewed, place another neutral density filter after the splits to adjust the pump's intensity and adjust to get the desired ratio.

Oscilloscope, PZT Scan, and Data (Hopefully)

In this section the PZT will be connected to a function generator and the intensity subtraction of the probe and reference will be related to the PZT length.

To begin, find the small circuit box (see picture). It will have two inputs and one output. Connect the PZT wire you found earlier into the output of this box. Gather a function generator (Aglient NUMBER HERE) and power supply (HP NUMBER HERE will usually work). KEEP THEM POWERED DOWN FOR NOW. Next, connect the function generator to the 'in' input and a power supply to the floating input. What you have done is float the power supply on top of the function generator. Turn on the power supply and feed ~5V into the system. Next turn on the function generator and get a 1Hz, 3Vpp triangle wave on the output. Turn off any DC offset the function generator has. IMPORTANT: Never let the PZT get a negative voltage! This will damage the material. It was for this reason the power supply was turned on before the function generator. Finally, use a BNC Tee to split the function generator output and send it to an oscilloscope Ch 1.

Find the subtraction output (A-B) and connect it to the same oscilloscope Ch 2. Adjust the scaling so small bumps on the second channel are seen. The screen should look something like the picture below.

PICTURE

If the output is moving discontinuously, check to see if the scope is triggering on Ch 1. Do this by pressing the 'Trigger Menu' button and looking at the source category on the screen. If the screen is still jumping, try sending the SYNC from the function generator into the AUX Trigger port on the scope. Switch the scope into XY mode by pressing the 'ACQUIRE' button and pressing the 'XY Mode' button next to the screen.

Now we need to find Rb resonance with the laser. This part is more of an art than a science, so do not get frustrated if it takes a while to get. Outlined below are steps used to find resonance.

Step 1: Turn on the camera and TV set up earlier and make sure it is pointed at the Rb cell. Also re-check the spectrometer to make sure the laser is operating at 780nm and turn off the function generator.

Step 2: Adjust the voltage given by the power supply while looking at the Rb cell on the TV screen. BE SURE NOT TO DROP BELOW ZERO! Adjust until you see a faint pencil of light inside the cell. If no pencil appears, reduce the voltage, VERY slightly adjust the V knob on the diffraction grating and sweep the voltage again. If still no pencil is seen after a couple of V knob adjustments, increase the current sent to the diode very slowly and see if you can get a pencil that way. BE SURE NOT TO GO ABOVE 85mA!

Step 3: Once the pencil of light is seen, increase the current by 0.1mA. This is an EXTREMELY small turn of the knob. Basically breathing on the knob results in a 0.1mA change. Bump up the current and then slightly adjust the V knob. You are looking for the pencil to get brighter.

Step 4: Once the pencils are brighter, adjust the voltage until the cell is glowing. You won't see it with your eyes but the camera should pick it up. Turn the function generator back on and increase/decrease the peak-to-peak voltage until the laser is not mode hoping. Meaning the Fabry-Perot reading should be moving back and forth continuously.

Step 5: You may have a bunch of noise on your signal. If so, place a neutral density filter before the beams are split to reduce the intensity of the entire system. You can also run your composite signal through a current pre-amp.

Converting Voltage to Frequency:

References

[1] Schawlow A., "Spectroscopy in a New Light", Nobel Lecture, Dec. 8. 1981.

[2] Azmoun B., Metz S., “Recipe for Locking an Extended Cavity Diode Laser from the Ground Up”, Stony Brook University, 2013, http://laser.physics.sunysb.edu/~bazmoun/RbSpectroscopy/

[3] Daryl W. Preston Doppler-free saturated absorption: Laser spectroscopy, Amer. J. of Phys. 64, 1432-1436 (1996).

[4] Rieger T, Voltz T., "Doppler-free Saturation Spectroscopy", Max-Plank-Institut fuer Quantenoptik, Garching