Optic Rotation Project OneDoppler-Free Saturated Absorption Spectroscopy of Rubidium

Lei HuangSUNY at Stony Brook

Index1. Introduction 2. Background knowledge

2.1. Doppler Effect in Absorption Spectroscopy 2.2. Doppler-Free Absorption Spectroscopy 2.3. External-Cavity Diode Laser 2.4. Rubidium Energy Levels

3. Experiment 3.1. Optical Circuitry Design 3.2. Tuning Parameters 3.3. Coarse Tuning 3.4. Fine Structure Revealing 3.5. Some Quantitative Analysis

4. Conclusion 5. References

1. Introduction

Based on a smart design, Doppler-free absorption spectroscopy circumvents the problem of Doppler-broadening effect of main peaks in common absorption spectroscopy, and dramatically improves the resolution and probing potential of this widely-adopted technique. As my first optic rotation project, I set up an optical circuitry in Laser Teaching Center to test the availability and effect of such a technique, using the 4 main transition of naturally mixed Rubidium (72% 85Rb and 28% 87Rb) as target absorption peaks.

2. Background knowledge

2.1. Doppler Effect in Absorption Spectroscopy

It’s not hard to imagine that when a mixture of atoms are in a thermal equilibrium state, the value and direction of the velocity of each individual particle can have full of possibility. To put this into a quantitative manner, it has been proved by Maxwell,

where P(VZ) is the probability of finding V=VZ along Z direction, M is the mass of single atom, kB is Boltzman constant, and T is environmental temperature.

This universal property of matter, however, brings some negative effect for conventional absorption spectroscopy techniques. Let us assume ∆E equals to the energy required to excite an atom from its ground state to a certain excited state in its rest frame. If this atom itself is moving in the lab frame of reference, with a velocity component VZ along the direction of exciting photons, ∆E will change. To be more specific, if the atom is moving face-to-face with the photon, ∆E will increase (so-called blue-shift), while on the other hand, if the atom is moving in the same direction with the photon, ∆E will decrease (so-called red-shift).

This Doppler Effect has a direct consequence on our experiment—it will add a width to each originally sharp absorption peak with zero-width. Center frequency of each absorption peak corresponds to the energy required to excite atom with zero velocity component along photon beam direction, while other frequencies correspond to the cases when the atom has a velocity component on the photon beam direction. The absorption intensity for each frequency is directly proportional to the percentile of each group of atoms with different velocity. After integrating Maxwell velocity distribution along beam direction, we can predict that the resulting absorption peak should have a Gaussian shape profile, as shown in Fig 1.

Fig. 1 Doppler-broadened absorption peak

Technically speaking, this Doppler-broadening effect is really a bad thing. Because when individual broadened peak width is comparable, or larger than the separation of neighboring peaks, the spectrum will end in a blur and fail to reveal fine structure details.

2.2. Doppler-Free Absorption Spectroscopy

Absorption spectrum is always acquired by recording the residue laser beam intensity by photo diode when varying the frequency continuously within a certain range. Thus the problem of Doppler-broadening can be successfully circumvented by introducing a new experimental design—let another beam (saturated beam), at same frequency, yet opposite direction than original probe beam, overlaps the probe beam in sample region, as shown in Fig 2.

Fig. 2 optical circuitry to create Doppler-free absorption spectrum

During the experiment for absorption spectroscopy, laser frequency is swept as usual. When frequency is deviated from central position, for example a little smaller, (vice versa for opposite case) then the atoms excited by probe beam should have certain velocity to the left. While for saturated beam, the same group of atoms corresponds to red-shifted case, thus cannot be excited. As a result, the residue probe beam intensity recorded does not change compared with Doppler-broadened case. But if laser frequency is tuned to be exactly at central position, qualified atoms has no VZ component, thus can be excited by both probe and saturated beams. This interference will reduce the energy absorbed from probe beam, and results in a increase in residue intensity recorded, as shown in Fig. 3. Practically, the intensity of saturated beam is always set to be much larger than probe beam, so that the residue intensity recorded will increase more dramatically. Finally, if this whole absorption spectrum is subtracted from Doppler-broadened one, fine structure will emerge and Doppler Effect can be circumvented.

Fig. 3 Doppler-free absorption Spectrum

Another effect to be noticed is crossover transition peaks. This will occur when the laser frequency is halfway between two nearby transitions that share a common ground state. Consider the case when there are one ground state and two excited states with energies E1

and E2, assuming E1 is larger. When the laser energy is at midpoint (E1+E2)/2, groups of

atoms capable of being excited by probe beam should either have a blue-shift of (E1-E2)/2 to E1 transition, or red-shift of (E1-E2)/2 to E2 transition. While for saturated beam, both groups correspond to red-shift and blue-shift case with same amount. Thus interference also exists in such a situation. Note that the crossover transition always has larger intensity increase than original transitions.

2.3. External-Cavity Diode Laser

The laser used in our experiment is an external-cavity diode laser, of which the output frequency is tunable and has a much smaller FWHM. An external cavity is installed on a conventional laser, with optical feedback from a diffraction grating. The grating equation is

where m is diffraction order, d is grating constant, is wavelength, i is incident angle, d

is diffraction angle. With Littrow configuration (Fig. 4), i is set to be equal to d for first order, , and equal to -d for zeroth order. Zeroth order diffraction will be reflected off for output, while the first order component will be diffracted back for resonance. So that once the incident angle is fixed, the output wavelength is also determined. By adding external cavity, the grating essentially filters the gain curve of the free running diode laser, thus decrease the output line width to an proper range (~ 1MHz) for our experiment.

Fig. 4 External cavity diode laser with grating in Littrow configuration

The diffraction grating is installed in such a way that it is attached to flexible mount by the extension and contraction of a piezoelectric transducer (PZT). By doing this, the external cavity length can be changed. PZT’s crystal size has a linear response with the voltage bias. During practical experiment, we can tune the size of PZT by varying the voltage bias applied on it, and the details will be mentioned later.

2.4. Rubidium Energy Levels

Rubidium has two isotopes, 85Rb and 87Rb, each with natural abundance 72% and 28%,

nuclear spin quantum number I=5/2 and 3/2.

Let us first concentrate our discussions on 87Rb, and 85Rb has a similar result. Rubidium atom has 37 electrons, with ground state configuration of [1s2, 2s2, 2p6, 3s2, 3p6, 3d10, 4s2, 4p6], 5s1. The [] part is fully occupied and constitutes a ‘hard core’, while the 5s1 is an outermost valence electron. This valence electron can be excited easily to different higher energy level, each corresponds to different excited state of the entire atom.

We can write down the total Hamiltonian of Rb atom as

where the first term is the kinetic energy K of single electron, second term is Coulomb interaction V of this single electron with the rest of the atom, third term is spin-orbital coupling of single electron, and last term is coupling between total angular momentum and nuclear spin.

Effect from each term of total Hamiltonian can be viewed in Fig. 5. Different orbital quantum number L will result in different effective charge Zeff, thus K+V introduces splitting of S and P state, shown in the left part. Each orbital quantum number L will also couple with intrinsic electron spin S to form different total angular momentum J. This spin-orbital coupling will then create fine structure coupling for each L, as shown in the middle part. If we furthermore consider the spin of the nuclei I, and it will couple to J, and introduce the effect of hyper fine structure splitting, with a new quantum number F. The energy modification resulted from the effects mentioned above can be calculated theoretically, and the result is indicated in Fig. 5. Notice that there are still many terms included in total Hamiltonian, but we sill ignore their effects at present, considering their orders of magnitude.

Fig. 5 Effect of each term in total Hamiltonian on energy levels of 87Rb

Because the laser output can be tuned conveniently around 780nm, we will choose the transition from ground state to 52P3/2 as our target transition. We zoom in the related energy levels in Fig. 6. The selection rules for electric dipole transitions are given by

It is then not difficult to figure out all the possible transitions, and also the crossover transitions, as shown in Fig. 6. Considering together with the energy separates, we can conclude that the absorption spectrum for these transitions will be consist of two groups, each correspond to F=1, and F=2. Different F’ destination, as well as different resonance transitions, will be revealed as fine peaks within individual group.

Fig. 6 Target transition of 87Rb

Finally, combining the energy levels of 85Rb and 87Rb, we shall expect 4 main groups of peaks around 780 nm wavelength ranges, with different strength resulted from value of transition operator and isotope abundance, as shown in Fig. 7.

Fig. 7 Four main peaks due to hyperfine splitting of ground state

Zooming in at each of these four main peaks, even finer structures are shown separately in Fig 8. So during our actual experimental process, we will use conventional Doppler-broadened absorption spectroscopy to reveal Fig. 7, and then using Doppler-free saturated absorption spectroscopy to reveal Fig. 8.

Fig. 8 Fine structure due to splitting of (5p)2P3/2 excited state

3. Experiment3.1. Optical Circuitry Design

The whole experimental circuitry layout is shown in Fig 9. Polarized laser beam will first pass though an optic isolator, which will rotate the polarizing plane of laser light, and create a one-way passing path. This will prevent reflected laser light from going back into the laser apparatus, because otherwise, the resonance condition and mode competition can be seriously disturbed. Then, the beam will meet a beam splitter. Two beams with approximately equal intensity are reflected and directed through Rubidium cell for probing use, while one beam will pass through the splitter, be reflected sequentially by M1, M2, M3 and then directed through Rubidium cell for pumping use. Note that the intensity of pump beam should be higher than probe beam, so that the fine structure will have high peak intensity. Also note that the angle between pump beam and probe beam should be as small as possible so that the pump beam can has larger overlap with one probe beam, while at the same time having less with the other. Two photodiodes are installed properly and connected to different channels of an oscilloscope to record intensity signals from two probe beams, and the subtraction of their outputs will reveal

Doppler-free fine structure.

Fig. 9 Optical circuitry design

3.2. Tuning Parameters

To obtain the spectrum, laser output frequency must be scanned within a certain range continuously. As mentioned previously, this can be realized by varying the temperature and injection current. But there are some drawbacks: although temperature tuning has the largest frequency-varying range, about 4GHz/0C, the heating and cooling process is too time-consuming, and is very hard to stabilize (usually will spend up to half an hour); injection current has somewhat smaller frequency-varying range, about 40MHz/mA, but it’s still too coarse for our intended range. So what we actually do is leaving these two parameters fixed to optimized values, and then seeking for other tuning options.

So first, tune the temperature to a specific position and stabilizes it, then tune the injection current from zero to allowed maximum value. If the temperature is chosen well, we should be able to eyeball at most 4 times (Or less, depending on the frequency varying range created by current tuning ) of flashing of Rubidium through CCD and TV monitor for different injection current values. If no single flashing does happen, then temperature value should be relocated to another position and then repeat. The tuning separations are best set to about 10C each step. Note that you will observe some hops in flashing intensity at one flashing position, and this is due to the specialty of grating-feedback laser output profile.

Now temperature and injection current are fixed to a position where most flashings are achieved. The task of frequency scan will then be accomplished by another combination

of devices. We have installed a PZT to one end of the diffraction grating, and now we use a pulse/function generator to generate a cyclic triangle-shaped voltage and apply it on PZT. The PZT crystal will then accordingly contract or extend depending on the strength and polarity of the voltage bias, and in this way, the output frequency can be changed by grating formula. A wave/pulse generator, two DC power supplies will connected together with an amplifying circuitry, so that the small amplitude of triangle wave produced by generator can be increased to hundred of volts.

One DC supply (+/-12V) powers the amplifying circuitry, while the other (1.5kV) is used to add power to the wave. So that by setting the power out put from the 1.5kV DC power supply, we can set a limit to the peak strength of triangle wave.

There are several variables for the triangle wave signal that you could set or change in pulse/function generator: frequency, amplitude and offset. The frequency is not important for our experiment and it can be simply set to a few hundreds Hz. The amplitude will determine the size of frequency sweeping range. The offset will determine the central frequency value of sweeping range. In another word, the amplitude is in charge of zoom-in and zoom-out, while offset is in charge of relocation of the spectrum window in oscilloscope. The amplifying circuit is so designed that no negative voltage can be produced. As a result, to produce maximum triangle wave from this circuit, amplitude should match the limit of 1.5kV DC power supply, and offset should be set to half peak-to-peak amplitude.

The most accurate way to determine the amplitude is by reading and calculating from the wave curve displayed in oscilloscope. Notice that the oscilloscope has a maximal voltage input limit of 25V, and we designed a 100:1 voltage divider circuit to reduce the actual PZT voltage bias to be the monitor signal for oscilloscope. Similarly, special circuit is designed to couple the voltage output of photo diode with voltage range of oscilloscope input.

The oscilloscope we used in this experiment has two input channels and one auxiliary input. The two input channels can be displayed simultaneously for comparison or simple math operation, and the auxiliary input will not be displayed, but can sometimes employed for trigger signal.

The main apparatus we used in this experiment is: HP 8116A pulse/function generator, HP 6515A dc power supply (1.5kV), Tektronix TDS 2012 oscilloscope.

3.3. Coarse Tuning

First, we find 4 peaks in Fig. 7 using Doppler-broadened absorption spectroscopy. We tune the temperature and injection current until observing flashings via CCD, as shown in Fig 10. Temperature is changed from 180C to 240C, and it is observed that best value should be 22.70C, where we can observe 2 flashings with best position. We did not observe all 4 peaks because the frequency varying range created by injection current tuning is about 120mA times 40MHz/mA, i.e., about 4.8 GHz. Referring to Fig 7, this is

not capable of covering the whole range of 4 peaks. What’s more, at small injection current, the power of laser light is too small, and the flashing at that position is too faint to observe. Connecting the recorded current values at flashing position for different temperatures, we can estimate the separation between each peak, and then compare with Fig 7. Finally, it is concluded that the two flashings should correspond to 87Rb F=2→F’ and 85Rb F=3→F’.

Fig.10. “flashing”

Then we connect one PD signal (blocking the pumping beam) and reduced PZT voltage bias signal together into oscilloscope, and can reveal the Doppler-broadened peaks as shown in Fig 11. Note that this time, it is measured by setting the triangle wave to be maximum amplitude, with temperature and injection current fixed. The scanning range is determined by the triangle wave amplitude. It is noticed that some periodic pattern is recorded, because of the laser output hopping phenomenon as mentioned above. For each repeating unit, we can see just one and a half broadened peaks are revealed. But if at this time, injection current is tuned slightly, we can concentrate on either peaks.

Fig. 11, maximum frequency scanning

Then we zoom in at one unit of this periodic repeating pattern, and reduce the triangle wave parameters to fit it. The result is shown in Fig. 12. Channel one is displayed in yellow curve, and channel two is displayed in blue curve, from which we can see the shape is part of a triangle wave. Parameters are set to be: Temperature=22.70C, amplitude=2.12V, offset=1.84V, current=78.5A, 78.8A. Injection current should be tuned slightly to reveal the whole shape of each peak.

Fig. 12, Doppler-broadened peaks for 87Rb F=2→F’ and 85Rb F=3→F’

For the next step, we can start zooming in the 87Rb F=2→F’ transition to reveal fine structures. Parameters are now set to be: Temperature=22.70C, amplitude=1.09V, offset=1.77V, current=79.0A. We use reduced PZT voltage signal as trigger signal (channel 3), and connect PD1 and PD2 as channel 1 and channel 2. Originally, you will find that the two curves are of same shape, but different amplitude. But they ought to be calibrated into exactly same shape for future use. Calibrated curves are shown in Fig. 13. This can be realized by carefully moving the position or direction of one photo diode, so that to change its effective probing aperture. In the meantime, you can display the curve for CH1-CH2 (as shown in the picture of the red curve). When your job is done successfully, this curve should be a constant and stable horizontal line.

Fig. 13 Aperture tuning of two photo diodes

3.4. Fine Structure Revealing

What will happen if we use the Doppler-free design and let in the saturation beam? Fig 14 shows the result of making the very bright saturation beam intersect with one probe beams. Red curve is the subtracted part, or the Doppler-free fine structure. Compared with Fig. 7, we can mark individual transitions on the peaks revealed. Because not all the peaks are revealed clearly enough, there are some tricks used. First, mark the most strong peaks, usually the crossover peak, as marked in yellow, then once you locate one non-crossover peak, you can using the symmetric property to reveal all the rest.

Similar phenomena also were observed for the peak 87Rb F=2→F’, as shown in Fig 15. The parameters are set to be: Temperature=22.70C, amplitude=1.31V, offset=2.24V, current=78.6A.

Fig. 14 fine structures for 87Rb F=2→F’ revealed

Fig. 14 fine structures for 85Rb F=3→F’

3.5. Some Quantitative Analysis

Finally, we can do some quantitative analysis based on the data we have achieved. To be more specific, we can calculate the effect output frequency vs. PZT tuning with a unit of MHz/V. First use the data of 87Rb F=2→F’. At the time of zoom in at broadened peak 87Rb F=2→F’, the slope of the triangle wave is 218V/8.5div=25.7V/div (div stand for division in horizontal direction). When we proceed to the right picture of Fig. 14, the horizontal scale has been zoomed in for 3 times, thus the slope should be 8.57V/div. Also we can see from Fig 8 that 2nd and 3rd strongest fine peaks have a separation of 128.6MHz, while they occupy a separation of 3.5 div in the oscilloscope. This creates a dependence of 128.6MHz/3.5div=36.7MHz/div. In this way, we can calculate the response of output frequency vs. PZT voltage change, and the result is 36.7MHz/8.57V=4.28MHz/V.

Similarly, we can do the same analysis for 85Rb F=3→F’, and the result is 6.1MHz/V. And finally, the response for output frequency to PZT Voltage is calculated to be about

5.2+/-0.9 MHz/V. Back to our coarse position tuning step, 424V of scanning voltage amplitude corresponds to 2.205GHz of frequency sweeping range, thus can only reveal two neighboring Doppler-broadened absorption peaks. This is in good accordance with our previous observation in Fig. 11.

4. Conclusion

In this experiment, I successfully established a optical circuitry and revealed the Doppler-Free absorption spectrum for two peaks 85Rb F=3→F’ and 87Rb F=2→F’ of Rubidium. I really faced a lot of problems during the initial time, especially for those complicated and unknown structure of ECDL, temperature controlling circuit or amplifying circuit created by former students. But then I patiently treated them as black-boxes, and compared the input-output relationship, and at the same time, browsing relevant literatures. I feel a really learned a lot during the process, especially those optical experimental skills, which I think are very precious for my future use.

Thanks a lot for Dr. John Noe for his warm-hearted help on photo camera, my webpage and all the advices.

5. References

Daryl W. Preston, “Doppler-Free Saturated Absorption”, ELECTRO-OPTIC EXPERIMENTS FOR THE ADVANCED LABORATORY, 2000

Bob Azmoun and Susan Metz, “RECIPE FOR LOCKING AN EXTENDED CAVITY DIODE LASER FROM THE GROUND UP”, http://laser.physics.sunysb.edu/~bazmoun/RbSpectroscopy/

Jan Max and Walter Kruger, “A NOVEL TECHNIQUE FOR FREQUENCY STABILISING LASER DIODES”, http://hubble.physik.uni- konstanz.de/jkrueger/thesis/thesis.html/

Rita Kalra, experiment log book in Laser Teaching Center