The Saturated Absorption Spectroscopy Lab 1 Purpose Joshua Symonds, Ian Kleckner, Brian Anderson Advanced Lab, Fall 2005 Atoms can only absorb and emit photons of very specific, quantized energies, which translate to a specific photon frequencies given by hc E = h ν = (1) λ The process of identifying these energy levels available to the electrons in the atom is known as spectroscopy. To accomplish this in our experiment, we take laser light of a known frequency and see if the atoms absorb the light, indicating we have found the energy level of one of the electron transitions available in our atom. Investigating certain energy levels tends to be more difficult than investigating others because of the immense precision needed to stimulate the electron transitions to and from some of the finely spaced energy levels. In this lab we are investigating a group of energy levels called the hyperfine energy levels. As their name implies, they are so close in energy that their separation is rarely observed. A common spectroscopy technique is using a laser to stimulate the atom until it absorbs the beam. One reason for the complexity in this method of finding finely spaced energy levels is the random motion of particles due to their thermal energy. As the atoms move about, the incoming laser light is Doppler shifted in frequency, making it impossible for all the atoms to absorb light with the same frequency simultaneously. This has the effect of taking the specific amount of energy that would be absorbed by a stationary atom and spreading it out, since the atoms in motion will absorb photons with small range of different energies due to this Doppler shifting. As mentioned before, these transition levels are very small and require careful precision to accurately find the proper transition, and the Doppler shifting completely obscures these subtle transitions. To find the needle in the haystack, one needs to employ saturated absorption spectroscopy.
2 Theory Saturated Absorption Spectroscopy This experiment focuses on the hyperfine transition levels of the alkali element, Rubidium 87 ( Rb). We want to stimulate a transition from the level 5 2 S 1/2 to 5 2 P 3/2 which is a transition that requires the absorption or emission of a photon with frequency ~384230 GHz. By using a laser with a very narrow emission spectrum (fixed frequency), we can probe Rubidium and pick out its natural absorption frequencies even after Doppler shifting. This is done by a process which highlights atoms that happen to be stationary in the lab frame, and consequently are absorbing the light that was not Doppler shifted, and was at the natural absorption frequency of Rb. One critical part of this process is to have a laser with a very narrow, but tunable spectrum, the construction of which will be described in later sections. By scanning the frequency of the laser over a small range, Rb atoms with different velocities can be pumped up to their excited state. There is a finite range to the velocities of the atoms and therefore a finite range of frequencies (due to Doppler shifting) that stimulate a transition. If we scan the laser across this range of frequencies we can stimulate a transition in every atom. After passing the laser beam through a gas of Rb, some atoms will have absorbed photons, and just before they emit them again, they are in a brief transitional state of elevated energy. If we pass our beam back through the cloud of atoms in the opposite direction and hit that same atoms again, the second beam of light will be Doppler shifted in the opposite direction with respect to the atoms, and other atoms that were moving in the wrong direction to absorb the first beam will pick up the second one. This would result in a beam with some range of frequencies absorbed going in, and an identical absorption spectrum for the beam coming back the other way, except for one special case: the atoms that were not moving with respect to either beam. These atoms will have been pumped up by the first beam, but since some of them are lingering in their excited states, they will be unable to absorb the second beam so it passes right through to the detector. Since we have a laser with a very specific frequency, as we scan the laser s frequency across the Doppler shifted frequency spectrum of Rb, we see reduced
absorption spikes in our detector. This happens because as we pass through the frequency where only the atoms stationary in the lab frame are absorbing, we encounter the effect that excited atoms cannot absorb another photon. At other frequencies, as described above, there will be roughly the same amount of atoms with the velocity required to shift the light from the first beam into an absorbable wavelength as there are with a velocity to shift and absorb the second beam, just by virtue of the random nature of thermodynamics. This is what causes continuous, uninterrupted absorption at the frequencies we want to filter out in the Dopplershifted absorption profile. Consider a long jar of rubidium atoms situated on the x axis. Now consider two laser beams at a certain frequency, ν laser, coming into the jar, with one going in the + ˆx direction and another going in the ˆx direction. The frequency of light observed by the Rubidium atom is given by the Doppler formula: vx atom 1+ c 1+ β ν observed = νlaser = νlaser vx 1 β atom 1 c where vatom is the velocity of a Rubidium atom in the laboratory reference frame due to thermal excitation. From (2) it should be clear that if a certain Rb transition level occurs when a photon with frequency ν 0 is absorbed, a laser photon will be absorbed whenν = ν0. This happens in two different situations. The first is observed when vatom is some nonzero value, and v laser is greater than or less than v 0 by just the right amount to have the photon Doppler shifted to the correct frequency. The root mean square velocity of Rb atoms in the saturation cell can be found by using the kinetic energy of the atoms 1 2 3 KE = mv = kbt (3) 2 2 (2) v rms 23 2 3kT 3 1.38 10 J B K 295K = v = = kg 1 m.08547 mol 23 6.022 10 293 m s (4)
Plugging this into the Doppler formula we find the observed frequency: ν observed 293 m 1+ s 8 310 m = (384230 GHz) s = 384230.3407 GHz 293 1 310 m s 8 m s (5) Corresponding to a Doppler shift in frequency of ν broader than the 10MHz lines we are hunting for. observed ν 341 MHz, much The second instance, when v atom = 0, occurs in the case whenν laser = ν 0. If the frequency of the laser is less than v 0 by some amount, such that ν laser = ν1 < ν0, the beam entering the saturation cell in the + ˆx direction will be absorbed by the atoms moving towards the beam with just the right velocity, so the frequency observed by the Rb atoms is shifted up to ν 0. As the beam with frequency ν 1 passes through traveling in the ˆx direction now, the atoms moving with the opposite velocity will absorb the photons and get bumped up to the excited state. Since thermal excitation is a completely statistical process, there will be the same amount of Rb atoms with +v velocity as there will be with v in the saturation cell, and the amount of light absorbed will be equal for both beams. If we pass a beam with frequency v 0 through the cell in the laser + ˆx direction, only the atoms that are not moving in the ˆx direction will be able to absorb the light, since the observed photons will not be Doppler shifted. Now when we pass the beam back in the ˆx direction, we expect to excite the same atoms, but since they have already been excited by the first beam they cannot absorb any more light. Thus we have absorption from the first beam, but not from the second! If all of the atoms are saturated in this way by the first beam and remain in the excited state for the second beam pass, the total amount of absorbed light will be less than or equal to half that observed for a slightly different frequency of laser light. On our oscilloscope, as we scan across frequencies, this effect is seen:
Where we observe the sudden reductions in absorption we know we have isolated the atoms that are not moving in the ˆx direction, and so those frequencies correspond to photons associated with transitions in Rb, without any Doppler shift. With this technique we can identify many different transitions that were blurred out by thermal motion before, namely the hyperfine structure of the Rb atom. As noted above, a finely tuned laser is necessary for performing spectroscopy. One may wonder how it is possible to stimulate a single transition given that the atom will accept only photons are certain energy. Given the narrow frequency of a laser, it would be difficult to find the single exact frequency needed. Luckily, however, transition levels have a natural line width which is a small, but finite range of frequencies which can stimulate a transition. This phenomenon arises from, not surprisingly, Heisenberg s Uncertainty Principle. In alkali elements, like Rb, the natural line width is about 10MHz. This frequency is quite small however compared to the transition frequency of 384THz. To be in this range is finding the needle in the haystack mentioned before. As described in the next section, the laser frequency is controlled primarily by the length of the resonant cavity. We can calculate how well we will need to control the cavity length to keep the laser within the natural line width. To set up a standing wave in the cavity we have: nλ = L, (6) 2 where n is an integer, λ is the laser wavelength, and L is the cavity length. We know that:
c λ =. (7) ν Inserting this equation into (6) yields mc L 2ν =. (8) Taking the differential with respect to ν yields mc ν = L (9) 2 2ν Using a wavelength of 780nm we can estimate the number of wavelengths that fit 6 inside a cavity of length L = 0.2m to be 10. For a frequency change of 10 MHz we have: 6 10 c (10 MHz) 20 nm (10) 2 2 384 THz ( ) From this we can see that very fine control over the length of the cavity is needed. Frequency Stabilized Diode Laser A laser, such as the familiar tube of Helium and Neon gas, emits a frequency dependent on a few different factors, including the emission frequencies available to the atoms, the molecular structure of the lasing material, and the length of the laser cavity. In most stabilization experiments the cavity length is the variable one tries to control, because often the other factors are constant in the experiment, inaccessible to the experimenter, or both. In the stabilization of a HeNe laser, the cavity length is controlled by controlling the temperature of the tube of gas. We employ this technique to stabilize the semiconductor lasing medium as well through the use of a temperature controller device that does most of the work for us. The current in a diode laser is also a factor that helps determine its frequency, and this value is similarly controlled by another system. A diode laser by itself, unlike its gaseous counterparts, produces a fairly wide band of frequencies. To control this, we employ a diffraction grating to set up what is known as an external cavity on the laser. By bouncing a small part of the beam back into the diode, the distance from the back of the laser diode to the diffraction grating becomes our new cavity length, and by changing this distance we can control the frequency of our laser. Longer cavity lengths have the favorable quality of being quite selective in the lasing frequencies they promote in the laser, so by adding the
diffraction grating we go from a very short cavity which allows a broad range of frequencies to a longer one with a much tighter spectrum. By mounting the diffraction grating on a piezoelectric transducer and applying a voltage across it, we can control its position on the order of hundreds of nanometers, and thus tune our laser cavity, and laser frequency, very carefully. 3 Experiment Stability of the Experiment There are a few tricky parts to getting this experiment to actually work. The first one we tackled was vibration isolation. Since we are trying to adjust the distance between the diffraction grating and the laser diode very precisely, any vibration will really make our lives difficult. To combat this issue, we have our entire experiment on a floating table, which consists of a very heavy piece of steel atop four pressurized legs that significantly damp vibrations. The diode and diffraction grating are housed in a sturdy aluminum box that keeps out air currents, some sound vibration, and provides some temperature isolation as well. Inside the box, the diode mount and diffraction grating are bolted onto a separate daughter plate, and a bar connects the tops of the diode mount and the diffraction grating assembly to prevent the formation of any moment arms in the system. The daughter plate is seated on the base plate of the box on top of four Zorbothane pads which keep the diode and diffraction grating very isolated from vibrations outside the box, or traveling along the surface of the box (note later photos for our setup). The Diffraction Grating We use a grating centered around ~250nm, far from the ~785nm light the diode emits, so we only get a small fraction (~10%) of the light reflected back into the diode. This is important because of the delicate nature of diode lasers, and too much light going back into the diode can destroy or damage the semiconductor device. When this happens, the spatial mode (beam intensity distribution) can be distorted, and often there is an associated loss of laser output power for the original current input.
The diffraction grating reflects the beam at an angle equal to the incident angle, and this beam is directed out of the box to be used in the experiment. One should be careful to never pass the beam through any perpendicular surfaces, as back reflection is always a matter of concern for the aforementioned reasons, and we don t want any of the stray light finding its way back into the diode. Along with the reflected beam, there is a first order diffracted beam that appears as a dimmer beam with approximately 40 degrees separation from the reflected beam. This diffracted beam is what we want to feed back into the laser diode, acting like the mostly silvered front mirror on a HeNe laser. Refer to the Alignment Cookbook in this manual for the process of feeding the diffracted beam back into the diode properly. Equipment Box: ½ 6061 aluminum plate, inner dimensions: 10 x7 x6 (LxWxH) Thorlabs Model TCLDM9-TE-cooled laser diode mount with collimating lens Thorlabs TEC2000 Temperature controller Thorlabs LDC2000 Current controller Rubidium saturation cell (4 )
Diffraction grating Thorlabs Model AE0203D04 Piezoelectric transducer (100V, only ~10V used) Optics: mirrors, posts, post holders, bases, clamps, blank plate for piezo Electronics: connectors for box (DB-9, BNC), wire (2) Photo diode assembly: diodes, batteries, resistors, small box on post IR card for viewing beam Laser goggles Zorbothane foam CCD camera and TV monitor (or IR viewer, in a pinch) Oscilloscope Frequency generator 4 Setup Construction Build the box and construct any necessary braces required to stabilize the laser mount and diffraction grating assembly, if this is not already done. This is a longer step than this manual would indicate! Make the necessary connections inside the box (again, if not complete) to allow all cables to be plugged into ports on the surface of the box. Two DB-9 connectors will be needed to connect the current and temperature controls, and one BNC connection should be used to connect the piezo. Settings Current controller: First, read the manuals. These are the settings we used: Current limit: 50mA Threshold for diode was typically ~33mA Temperature controller: Current limit: 1.8A (though 2A should be fine) Temp setting: 10 15kΩ
Alignment Cookbook I. Collimating: 1. Place a mirror in the box in the laser path, directing the beam out of the window and across the room somewhere. 2. Using a spanner wrench, adjust the small lens in the laser diode mount until the beam is collimated. It is important to note that this does not mean focused, but rather a uniform dot size along the entire beam path, even far (~ 8-10 m) away (on the other side of the room). Care should be taken never to bounce the beam off the edge of any mirrors or partially through any windows or beam splitters, make sure the dot is always safely centered in the optics to avoid any cutting of the beam. A collimated, uncut beam should look very similar to the beam coming out of the box at any distance. These diodes aren t perfect and exact collimation isn t always possible, but it should be fairly close. Good collimation is important for the feedback step. 3. If the small lens in the laser mount goes through its range of motion without attaining collimation of the beam, it will be necessary to use an adjustable spanner wrench or two thin objects to rotate the 1 disc the collimating lens is seated in. This will move the collimating lens closer to or further away from the diode, increasing the range of available lens positions. II. Installation of the diffraction grating: 1. Using epoxy, glue the piezoelectric transducer to a blank plate. This is just a surface that is finely adjustable with knobs on the back, we use a simple mirror mount from New Focus. We choose this company specifically for the high quality controls which ensure stability over time on the order of weeks. Careful measurements must be made to ensure the beam will be centered on the diffraction grating when installed, since these heights are not easily adjustable later. 2. After the epoxy on the piezo is cured, epoxy a diffraction grating onto the opposite end, so the diffraction grating surface is parallel to the surface of the blank plate. There is usually an arrow drawn on the grating,
III. and this should point in the direction of the incident beam from the laser mount. It is drawn on a side perpendicular to the grooves etched into the grating, which should be oriented in the vertical plane. In our experiment, this led to the arrow side of the grating facing the floor of the box. Obviously, check the instructions before gluing, just to be safe! Feedback: This is one of the tricky parts. The beam leaving the diode must hit the diffraction grating, bounce out of the box, and simultaneously the first order diffracted beam must be pointed back into the diode. There is what appears to be a fixed angle between the reflected and 1 st order diffracted beams of about 40 degrees, so the box must be built with this constraint in mind. Now, to get your laser fed back: 1. Turn the current down to just above threshold (~33 ma), and set the temperature to about 12.5kΩ to leave room for adjustment 2. Center the knobs on the blank plate. Ours had 3 knobs total: the top acts as y axis control (translating the beam in the y axis), the knob on the opposite side acts as x axis control, and the knob in between the outer two should not be used while aligning. 3. The blank plate should be mounted on a wide pedestal post, which is to be clamped to the daughter plate. With the laser on, carefully position the assembly on the daughter plate so the dimmer diffracted beam is close to hitting the collimation lens, taking care not to reflect the main beam back into the diode. When a suitable position is found, clamp down the post tightly. 4. Turn the current down to just below threshold (< ~32 ma) (you should notice a quick drop in intensity of the beam for just a small change in current) 5. Using an IR card with a pinhole in it, place the card facing the grating with the beam from the diode passing through the pinhole. You should then see the diffracted beam bouncing back onto the card. Using the x and y knobs on the blank plate, direct the 1 st order diffracted beam back through the pinhole. When you have done this correctly, you should notice the intensity of the beam increase again, and the card will glow
more brightly. If you are having trouble getting this, turn the current up very slightly and try again. This step is best done in the dark. 6. Once you are centered enough to find the intensity peak, take the IR card out of the box and place it in the beam path somewhere outside. A CCD camera is really useful for this step, but either way it is best done with the lights kept off. Turn the current down to just below threshold again, which should now correspond to a slightly lower current, and using only the y axis knob repeat the process of finding the brightness peak. The beam should remain centered in the x axis. Repeat the process of lowering current to below the new threshold and finely tuning the y axis knob to find the peak until it can not get any better. It is important that you do this step well, because it will cause poor mode stability later on if not fed back correctly. 7. Introduce a wavemeter into the beam path somewhere outside the box. You may have to turn the current up a small amount (3 or 4 ma) to get a reading. The light frequency will probably be much different than the 384230.4 GHz we are looking for. Move the temperature knob in one direction a small amount and wait for it to stabilize. Using this temperature change as a test, keep changing the temperature to get as close to the correct value as possible, staying approximately between 11 14kΩ. It might be a good way off still, but that should be expected. 8. Using the x axis knob now, rotate the diffraction grating until the frequency is as close as you can get it to the desired value, typically within about 40GHz. It may be necessary to adjust an intermediate mirror to keep the beam going into the wavemeter during this step. 9. When the frequency is close, use the current control as a fine adjustment to reach the desired value. If the saturation cell is in the beam path, you should observe IR glowing of the atoms in the cell where the beam passes through. If not found immediately, refer to the resonance section before rearranging everything!
Finding Resonance With the frequency of the laser at or very close to 384230.4 GHz, it is time to start looking at the saturation cell. It should be installed in the beam path in such a way that the faces of the cell are not perpendicular to any of the beams entering it. You want to be able to have the beam go through the cell in one direction, hit a mirror close to the opposite face, and bounce back along almost the same path so the two beams intersect somewhat in the cell, but making sure that they do not hit the same mirror and accidentally reflect back into the diode. This usually requires one mirror far away down the table that directs the beam into the cell at a slight angle, a mirror near the face which may be close to parallel with the face of the cell which bounces it back out, and another mirror just behind the first and slightly off to the side to catch the exiting beam and send it to the detectors. That alignment does not need to be done for this step, but it doesn t hurt. With the beam passing through the sat cell you should be able to see if your laser is emitting at a frequency that the Rb can absorb. If this is the case, you will see (in the IR viewer or CCD camera) the gas glowing where the beam travels through the cell. If this is not the case immediately, scanning the piezo and diffraction grating may do the trick. Connect the piezoelectric transducer to the frequency generator, and simultaneously (in parallel, with a T junction) connect it to the x axis input of the oscilloscope. A photodiode output can be connected to the y axis of the oscilloscope. Set the frequency on the frequency generator to about 5Hz, and set the
amplitude (output range) to about 5V, or halfway on the generator we used. Now using the DC offset, scan around while watching the saturation cell through the IR viewer or on the television screen, and look for a blinking beam in the cell with a frequency of 5Hz, or whatever you set it to. It should be possible then to decrease the output amplitude on the frequency generator to a minimum and use the DC offset to keep the cell glowing almost all the time. When you have the laser at resonance frequency, set the frequency generator to about 300Hz and turn on the photo diode. Adjust the oscilloscope to plot x vs. y, and you should see a curve with a fixed width on the screen (this should look like a U or possible an upside-down U on the screen, if the photo diode is sending an inverted signal). By placing a neutral density filter (a piece of dark glass) in the beam path before the saturation cell, the intensity of the light going to the detectors can be reduced and more sensitive settings on the oscilloscope can be used, yielding a more dramatic absorption spectrum. If the beams are overlapping properly and your scan goes through one of the absorption frequencies of Rubidium, at this point you should see the hyperfine structure.
5 Potential Problems Mode Hopping This is an issue you are likely to encounter. Mode hopping occurs when the laser is trying to select a frequency to resonate at, and two or possibly more frequencies are coexisting as the most probable ones, and the laser flips back and forth between the different frequencies. On the oscilloscope this will look like a step function in the absorption curve, with one or more hops to a different level. Sometimes tweaking your temperature and current slightly can alleviate these problems, but if a stable mode cannot be found it might be necessary to redo the feedback alignment. Perfect alignment of the feedback beam in the y axis is important to good, single-mode behavior, so be careful with that step. Breaking the Diode Needless to say, you should avoid doing this. Back reflection will probably be your primary concern, and the main threat to the diode. Even with careful work, however, diodes can just go bad after a certain time, so be sure to plot the voltage output of the photo diode when using a known working laser diode, since when the laser goes bad it will usually decrease its optical power output.
Instability Over Time When you come back to the lab and find your laser off resonance, do not start playing with the current and temperature control. Rather you should make a note of which temp and current settings were working before, and when the laser gets out of alignment go into the box and move the x axis knob until it is back where it should be. If this doesn t work, it may be necessary to repeat the alignment process (starting after collimation).