Optical Pumping

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All pages in this lab. Note To print Full Lab Write-up click on each link below and print separately


I. Optical Pumping

II. OPT Pre Lab Questions and Staff Sign Off Sheets.....PRINT, FILL THIS OUT, Turn it in

III. Error Analysis Notes

IV. Data Analysis (OPT)

V. Optical Signal vs Temperature

VI. Photodiode Data Sheet

VII. [DS345 Manual]


Reprints and other information can be found on the Physics 111 Library Site



Contents

Optical Pumping

Discuss the Physics about this experiment with the faculty or the GSI's in the 111-Lab before starting.

You should keep a laboratory notebook. The notebook should contain a detailed record of everything that was done and how/why it was done, as well as all of the data and analysis, also with plenty of how/why entries. This will aid you when you write your report.


Introduction

Measuring the energy levels of atomic, molecular, nuclear, and particle systems is a large part of experimental physics. The technique of optical pumping is used to measure atomic energy level differences with great precision. This experiment uses optical pumping to measure the splitting of rubidium atomic energy levels when Rb atoms are placed in a magnetic field. It is so easy to make these measurements that you can use the opportunity to consolidate what you know and understand about atomic physics and quantum mechanics. You can get a solid appreciation of physics and how elegant it is from this simple experiment. It also gives you an idea of how grubby an actual laboratory set up is compared to how slick the physics looks in a textbook.

Your goal in this lab is to find the resonance frequencies, and thereby measure the Zeeman splitting, of Rb85 and Rb87 for various magnetic field strengths. From this, you will then determine the nuclear spins of the isotopes and the strength of the Earth’s magnetic field.

Prerequisite Reading Materials

References 1 and 2 are the most informative. Note, however, that Bloom does not discuss pumping of Rubidium. For simplicity, he instead describes pumping of a hypothetical atom.

  1. †R.L. De Zafra, “Optical Pumping”, American J. of Physics. 28, 646 (1960). #QC1.A4
  2. †A.L. Bloom, “Optical Pumping”, Scientific American, October 1960, p.72. #T1.S5
  3. †N.F. Ramsey, Nuclear Moments, Wiley, 1953. #QC174.1.R31
  4. C.M. Sitterly, Atomic Energy Levels Vol. II, National Bureau of Standards, 1952. #QC453.M6
  5. J.R. Taylor, [Taylor Book 2ed "An Introduction to Error Analysis"], Oxford,
  6. L. Lyons, ["A Practical Guide to Data Analysis for Physical Science Students"], Cambridge, 1991. #QC33.L9
  7. James Camparo, [“The Rubidium Atomic Clock and Basic Research”], Physics Today -- November 2007
  8. Carver, Thomas R. "Optical Pumping"; Science: vol. 141, Aug 16, 1963, pp. 599-608.
  9. Electron Spin Resonance by Optical Pumping Experiment 7
  10. Corney, Alan, "The Hanle Effect and The Theory of Resonance Fluorescence Experiments"; Atomic and Laser Spectroscopy, (1977). Pp. 473-533.
  11. Check out all the [Reprints ]for this experiment;

† Contained in the Optical Pumping Reprints, located in the Physics Library, or available here.

Before The Lab

Starting with the articles by Bloom and de Zafra, read through the Optical Pumping Reprints. The reprints for this lab are all theoretical, and should be understood before coming to lab. Note, however, that not all of the diagrams or discussions are correct for our experiment: some of the articles discuss only transitions between hyperfine levels, while we have Zeeman splittings as well. Try to keep clear which splittings are which, and which are important for our transitions. See, for example, de Zafra (p.647). (You will also find that there is some variance in notation between the various reprint articles; parsing these differences can be challenging, but it is an important skill to have. Let the consistency of the base physics guide you.) As you study, here are some terms to understand:

absorption electron configuration linear and circular polarizers radiative lifetime
atomic energy levels equilibrium distribution LS coupling relaxation
atomic orientation fine structure magnetic dipole moment resonance
buffer gas Helmholtz coil Maxwell-Boltzmann distribution selection rules
Breit-Rabi equation hyperfine structure modulation spontaneous emission
degeneracy interference filter nuclear spin stimulated emission
discharge lamp Larmor frequency Paschen Bach effect spectroscopic notation
electric dipole transition line width quantum numbers Zeeman effect


A. Starting with the Hamiltonian

H = - \overrightarrow {\mu_I} \cdot \left ( \overrightarrow {B_J} + \overrightarrow {B_{ext}} \right ) - \overrightarrow {\mu_J} \cdot \overrightarrow {B_{ext}} (eq. 1)

where \overrightarrow {\mu_I} is the nuclear magnetic moment, \overrightarrow {\mu_J} is the electronic magnetic moment, \overrightarrow {B_J} is the magnetic field at the nucleus arising from the rest of the atom, and \overrightarrow {B_{ext}} is an externally applied field, derive the Breit-Rabi law in the low-field case:

\frac {\nu} {B_{ext}} = \left ( \frac {2.799} {2I + 1} \right ) \quad MHz / gauss (eq. 2)

(See Ramsey, for example. [Again, look for any notational differences that may exist; Ramsey lays out his conventions in the text, but some analysis may be required nonetheless.])

Also work out the numerical values of the g-factor associated with the split hyperfine states for Ru85 and Ru87.

B. Derive the expression for the magnetic field at the rubidium bulb due to the Helmholtz coils:

0.9 \times 10^{-6} \left ( \frac {tesla \cdot meter} {ampere} \right ) \frac {Ni} {a} (eq. 3)

where N is the number of turns of the coils, i is the current, and a is the radius of the coils. (Recall that there are 104 Gauss in a Tesla.) Discuss the Helmholtz coil. Why is the field so uniform at the center, both laterally and longitudinally? How inhomogeneous is the magnetic field at the bulb? What are the qualitative and quantitative effects of this inhomogeneity? Are they important in this experiment?


C. What are the effects of the earth’s magnetic field? What would happen if the Helmholtz coils where not perfectly aligned with the earth’s field?

Then view the Optical Pumping video, discuss the pre-lab questions with an instructor, and get the OPT Pre Lab Questions and Staff Sign Off Sheets signed.....PRINT, FILL THIS OUT, Turn it in.

Experimental Procedure

Taking data for this experiment is more straightforward than for any other lab in this course. But the experiment deserves more time and thought than most because it illustrates fundamental ideas about quantum mechanics which you probably have only vague notions. Take the time to think about what’s going on, and answer any questions that occur to you.


  1. Look over the block diagram (Figure 1) and check the connections of the equipment carefully (you need not hook up the oscilloscope or the [DS345] yet). Make sure you understand what each unit does and that you know the equipment limitations (e.g. don’t run the coil current higher than 3 amps; don’t drive the RF at more than 5 volts, don’t heat the bulb over 50o C, etc.) Inspect and open carefully the Rb light box to see its construction. Can you explain how the Rb lamp works? Be particularly careful of the D1 pass filter. It is expensive to replace! All pieces in this unit are already in their proper places. The large bulb filled with Rb85 and Rb87 should be in the light box. You should use many different type of bulbs may need to check the other Optical pumping experiment. The ratio of Rb in the bulb mirrors the natural ratio.
    Figure 1: Equipment Block Diagram
  2. Warning: Never turn off the plug strip power if any of the equipment is powered up. Turn on all of the equipment, starting with the System switch (lower right hand corner of the Coil Driver Panel). Set the Rubidium Supply Output Current for the Rb lamp to approximately 25 milliamperes using the Adjust Knob. (Like much of the experimental apparatus, the Rb lamps at the two Optical Pumping stations are not identical; one may require a higher current to light the lamp at station 2 [perhaps 30 milliamps].)
    Figure 2: SR560 Amplifier
  3. When you turn on the [SR560 Voltage PRE-AMP] make sure that the INPUT ‘A’ is selected, the DC/GND/AC button is set to the AC position. To start, set the Gain to 500, LF Roll-off to 0.1 Hz, and the HF Roll-off to 10 KHz. You may have to change some settings to make your signal clear. Also note that if you suddenly lose your signal, i.e. if your scope trace goes to a flat-line, you should press the OL REC (OverLoad RECovery) button. The SR560 requires you to adjust the dynamic reserve and the filter roll-off; set the gain mode to low noise and the roll off to 6 dB per octave for both the high and low pass filters.
  4. We will be using a DS 345 synthesized function generator to drive the RF coils in this experiment (see Figure 1). Before you begin taking data, it would be wise to familiarize yourself with its capabilities, its limitations, and its interface (see Figure 3 and the [DS345 Manual]).
    • You should start by looking at the DS 345’s output on an oscilloscope. Try running the 345’s “Function” output to Ch. 2 and driving it with a 5 V p-p, 5 kHz sine wave. (You can adjust the frequency by hitting the “Freq” button and then using the entry keypad [followed by V p-p] or the “Modify” arrows in conjunction with the step button to adjust the magnitude of the steps. Similarly, the amplitude can be set with the Ampl button.) Measure the amplitude of the signal on the scope; is it what the DS 345 claims to be outputting? You can use a BNC splitter and a 50 Ohm terminator to terminate the 345’s output and bring it closer to what is desired. Considering how we will be using the 345 in this experiment, will it be important to have it produce a precise amplitude? Throughout this experiment, in order to avoid damaging the RF coils, you shouldn’t drive signals of much more than 5 V p-p, and you should terminate the frequency output to keep the DS345 honest.
    • Try experimenting with the DS345’s signal modulation capabilities as we will use the 5V p-p sine wave which we already set up as a “carrier” signal for frequency modulation (FM). Start by running a BNC cable from the modulation output of the DS345 (on the back panel, see figure 3) to the Ch. 1 (X) input of the oscilloscope hook up the scope’s Ch 2 (Y) input to the terminated function output of the DS345. Set the scope to trigger off of channel 1 in the “Norm” mode. Set the scope to “Alt” rather than “Chop”. First, try amplitude modulating the 5V p-p, at 5 kHz sine wave (the carrier signal) with a 500 Hz square wave. The frequency of modulation is set using the “Rate” button, the modulation can be turned on and off using the “Sweep” button, and the shape of the modulation function [square, sine, etc.] is set using the second set of arrows in the Sweep/Modulate panel. The depth of modulation can be adjusted with the “Span” button; for AM modulations, the span is a percentage (0-100) of the carrier (unmodulated function) amplitude. Start by setting the span to 100. Looking at the output with a dual linear sweep, what do you see? What is the maximum amplitude of the Function output? How does it compare with the unmodulated amplitude? Experiment with different modulation waveforms, span, and rate settings. You might also try using the scope’s X-Y mode to observe the DS345’s output (Function output against Modulation output) but don’t let it confuse you. It is important to have a clear understanding of what the X-Y mode represents and when to use it. In the X-Y mode, the scope no longer displays a time axis. The Voltage amplitude for an input is displayed on the respective axis. (See the XYZ’s of scopes at the BSC stations)
    • Note that the modulation output is just a 0-5 volts representation of the modulation function (as described in DS345 Manual). If “sweep” is on, the modulation output will always vary between zero and 5 volts, regardless of the size of the actual span. In other words, it is a relative indicator. (With AM modulations, the modulation output will always be zero when the function amplitude is at a minimum and 5 V when the function amplitude is at a maximum [2.5V would then correspond to the amplitude of the unmodulated carrier].)
    • Now try frequency modulation. Give the 5 kHz, 5V p-p sine wave, carrier signal a 500 Hz square wave FM modulation. As with AM mode, the rate of the modulation (the frequency of the modulation signal) is set with the “rate” button. In FM mode, the span button sets the peak to peak frequency shift that occurs in a modulation cycle. Set the span to 8 kHz; the frequency of the function output should shift between 1 kHz and 9 kHz. Note that you can’t set the span to twice the carrier frequency or more (the DS345 has trouble making oscillations with zero or negative frequencies). Try different modulation waveforms; look at sine, triangle and ramp modulations. Again, start by using the oscilloscope’s linear, time sweep mode. X-Y mode can also be revealing if you keep in mind what the modulation output represents. (As with AM, in FM the modulation output gives a 0-5 Volt representation of the modulation function. Again, zero volts corresponds to the minimum frequency [the carrier frequency minus half the span] and 5 volts corresponds to the maximum frequency [the carrier frequency plus half the span], and so forth.) You should now have the familiarity with the DS345 required for this experiment.
      Figure 3a: DS 345 Synthesized Function Generator (Front)
      Figure 3b: DS 345 Synthesized Function Generator (Back)
  5. Heat the sample to 48 C, then turn the heater off to reduce noise, (noise due to what?) but remember that you want the temperature between 38 and 45 degrees for good data. (Why? See Optical Signal vs Temperature) Make sure the temperature does not go above 50 C, if you start to approach this temperature, turn down the thermostat. The heater has an overtemperture shutoff switch in the heater box. If you overtemperture the box it will need time to rest and you should call one of the staff. A reading from the temperature sensor is output to an LED display labelled 'Oven Temperature'.
  6. We will now attempt to roughly observe the variations in the opacity of Rubidium gas that occur when it is optically pumped and then hit by resonance frequency RF by applying a variable frequency signal. We will look at a wide range of frequencies so that we will be sure to see resonance effects for both isotopes.
    • Connect the function output of the DS345 to the RF coils. Set the DS345 to output a 3 MHz sine wave with a 10 Hz, ramp function FM modulation. (Use the “Freq” button to set the carrier frequency to 3 MHz; use the “Rate” button to set the modulation frequency to 10 Hz.) Set the span of the modulation to a little less than twice the carrier frequency (5.9999 MHz). Try setting the DS 345 Span to 6 Mhz. Why does it give an error? See DS345 Manual: FM Modulation section. Run the output of the PRE-AMP (the amplified photodiode output, see [Photodiode Data Sheet] for photodectector operation) to Ch.2 (Y) of the oscilloscope and keep Ch.1 (X) connected to the DS 345’s modulation output. Set the oscilloscope to X-Y mode. (See the Photodiode Data Sheet for details on the photodetector’s operation)
    • Turn on the DC power supply. (We want a DC field at this point; check that the field switch on the coil driver is off.) Set the coil current to one amp (1.0A). Use the Current knob on the Power Supply to adjust the current and the shunt to measure it. The shunt is a calibrated resistor and is temperature compensated. The voltage that develops across the shunt is 10mV per Amp of current through the coils. The Digital Volt meter reads the milivolt reading. (Note that there is a button on the front of the Digital Volt meter that changes the connections from front to rear of the unit.) This button should be in the front position. On the oscilloscope, you should see something like what is shown in figure 4. (You may see some 60 Hz noise in your signal; adjusting the connections may help minimize the problem.) Explain what you see. Make sure you understand what the scope, in X-Y mode, is showing. What do the axes represent? Make an approximate measurement of the two resonant frequencies. Again, keep in mind that the span gives the peak-peak frequency variation, so the modulation output should be varying from ~0 to ~6 MHz. If you set the Ch1 [X] scale to .5 V/div, then the signal sweeps out exactly ten divisions. Each division would then correspond to a change in frequency of 0.6 MHz, with the far left end of the range [corresponding to 0V] being at roughly 0 MHz. To get a more accurate measurement of the resonance peaks, adjust the carrier frequency of the FM and narrow the span. This can be done successively to yield a reasonably accurate result. Which resonance is stronger? Which isotope does this resonance correspond to (the natural abundances of the two isotopes might provide a clue)? This information can be found on the nucleotide chart. What happens to the signal as the temperature is varied? Do the relative strengths of each resonance change? Now try varying the current; go from zero to two amps in both the forward and reverse directions. What happens to the resonance frequencies and the size of the corresponding voltage changes? Are there any values of the coil current for which there is no resonance? What happens at zero current? Try adjusting the span, rate, and carrier frequency, and using a triangle rather than a ramp modulation.
      Figure 4: Amplified photodiode signal with large span frequency modulation.
  7. In order to measure the resonance frequency more precisely, we will look at how the amplified light from the photodetector varies with a 60 Hz modulation in the magnetic field. That is, we will modulate the coil current and not the RF. Turn off the modulation on the DS345. Turn on field modulation by flipping the “Field” switch on the Coil Driver panel , and turn on the “Phase Out” output with the “Phase Switch.” Why do you think we use a 60 Hz modulation?
    • Familiarize yourself with the Coil Driver panel. The PHASE ADJUST control on Coil Driver panel changes the phase of the modulation signal seen by the scope (the Phase Out signal) relative to the modulation signal seen by the rubidium sample (that is, the actual modulation in the coil current on whose phase the photo-detected signal should depend). To examine how it works, feed the Phase Out (field modulation) signal through the divide-by-ten attenuator to Ch 1 (X) of the oscilloscope and feed the amplified photodetector signal (the PRE-AMP output) to Ch 2 (Y). With the scope in Dual Trace Mode (Both Channels), trigger on Line Source (60 Hz PG&E power line) and set the time scale to around 2 msec/DIV. You may have to adjust the trigger Level knob to get a stable trace. Now change the phase with the Adjust knob: the modulation signal (Ch. 1) moves because we are changing its phase relative to the 60 Hz line signal that we are triggering on. The detected signal does not, though, because the Adjust knob does not change the phase of the signal that the sample sees.
  8. Put the scope in X-Y mode. You should now see the detected signal (Ch. 2) displayed on the y-axis versus the field modulation signal (Ch. 1) on the x-axis. How you can tell when you have found the resonance condition in this mode? Should there be any symmetry? If so, how should it be symmetrical? Along what axis should the symmetry be found? Consult the reprints. They have many useful figures to help you understand the relationship between the displayed signal and the conditions of resonance. It is up to you to determine which of the modes (Time Trace or X-Y) gives a more precise determination of the resonance condition–you might consider using both. Try them for repeatability. Estimate your errors using each method.
  9. Refine the resonance frequency measurements that you made previously. Set the DC coil current to 1 Amp, as before, and, with no modulation (sweep off) vary the RF frequency about the stronger of the two resonances you found in part F. (Start by setting “freq” to the resonance frequency estimate you got in part F, then adjust it by relatively large increments [step size = 10 kHz], until you see a shift in the signal, then hone in on resonance with ever decreasing step sizes until you have it precisely.) Set the Field Modulation Powerstat knob to around 10 (relative scale). Take care not to set the modulation amplitude so large that you see resonances of both isotopes simultaneously (if this is possible). Make sketches of what the resonance signal looks like with proper and improper adjustments of modulation amplitude and phase; to get a sense of what setting for the phase is appropriate, you might check the appearance of the signal with a dual linear sweep. If you can’t find a resonance, get help. (You could search for resonance by setting the frequency to some fixed value and then varying the coil current. The oscilloscope pattern would look exactly the same.)
  10. Once you have found the resonance condition; vary all of the parameters – current, voltage, temperature, phase, and whatever variables are under your control to get an idea of what the signal looks like under various conditions. How sensitive are your resonance measurements to changing variables? Record the qualitative behavior, and explain it. You should also get a quantitative estimate of the statistical error in you measurement technique; try making several independent measurements of the resonance frequency and see how they vary (See the Error Analysis Notes for further discussion of errors). Are there any possible sources of systematic error? You may want to check that the field is properly aligned; find the field direction meter (vertical compass) and place it close to the center of the Helmholtz coils. See what happens to the magnetized “needle” when you reverse the current or turn off the power supply. You should also get a sense of what effects 60 cycle pick up might have on your measurements.
  11. You can measure the pumping time at resonance with a square wave amplitude modulation. Turn off the field modulation (field switch) but keep the coil current set to 1 Amp and the function (carrier) frequency set to the frequency of the stronger resonance that you measured. Keep Ch.2 of the scope connected to the PRE-AMP, and run the modulation output of the DS345 into channel 1. Again, make sure that you keep the temperature in the right range, but take data with the heater off. Set the DS345 to amplitude modulate the resonance frequency signal with a depth of 100%. With the scope in linear mode, adjust the modulation rate so that the gas reaches equilibrium before each shift in RF amplitude. Measure the rate of change in the signal height when the RF is gated on or off (that is, when the modulation signal goes from low to high or from high to low). (The time for the signal to change by 1/e is a good number to get.) Which corresponds to the pumping time and which to the relaxation time? To get a good measurement of the pumping and relaxation times, try using “Norm” triggering on Ch.1. You should also take advantage of the scope’s magnification capabilities. (The horizontal mode can be set to Mag, with magnifications of x5, x10, and x50.) You may see a lot of 60 cycle pick up in you photodiode signal; you might try adjusting the co-ax line from the photodiode to the PRE-AMP to minimize this. You should also be mindful of the effects the PRE-AMP’s filters and source coupling can have on your signal; adjust them to make sure that your values are real. Try looking at the resonance for the other isotope. Are the time constants the same?
    • If you observe the relaxation process with a high enough magnification (say x50 at 20 sec/div) you will see small oscillations in the signal even after you eliminate 60 cycle noise. These are real, physical effects in the relaxation process known as Rabi oscillations. (You should be able to distinguish them from noise by modulating the frequency by small increments, [less than 1 Hz, say]; if they continue to track with the modulation, they’re probably real.)
  12. We will now use coil current modulation (as in part I) to measure the resonance frequencies for both isotopes over a range of currents. Keep Ch.2 of the oscilloscope attached to the PRE-AMP output and run the Phase Out (field modulation) output to Ch.1, and use X-Y mode. Starting at zero current, the two curves can be found near 200Khz and 300Khz. Starting at 2 amps, the resonance points can be found near 4.31 Mhz and 6.48 Mhz. The best way to take this data is to find a resonance point at either zero or 2 amps and follow it up or down the frequency spectrum by making small adjustments to both the current and the frequency. Again, steps of 10Khz works well. The goal is to keep the resonance pattern on the scope as to not lose it or worse jump to the other isotope’s resonance curve. Take at least 10 data points in increments of approximately 0.2 amps over the range of 0-2 amps for both isotopes in both normal and reverse current directions. That means four sets of data. You can take both current directions simply by revering the polarity at each step of current and refine the tuning of resonance. You should have an estimate of the error for the frequency and current measurements. Derive a method for determining this error with your lab partner utilizing the Error Analysis Notes. Discuss this method with a GSI Before Taking Data. You need not repeat Section J for every measurement, but you should get a representative sample that at least includes both isotopes (the isotopes have different intensities, so one might expect different error values). It should be possible to get fairly accurate and precise resonance measurements using small span RF frequency modulation (as in part L); if you have time, you might try retaking your points with this alternate methodology.
  13. Turn off the RF generator, and vary the current while looking for a resonance. The field should be on with reverse polarity. Set the field modulation to 10. Set the oscilloscope for a linear internal sweep in the x-direction. The zero resonance should be found around 0.08 amps.( This is know as the Zero field)

Analysis

(See Error Analysis Notes for further discussion.)

  1. Make plots of frequency vs. current to help you analyze your data. You should have four sets of data and four lines when you plot them. The individual points, the slopes of the curves, and their axial intercepts have an interrelated significance.
  2. You have two equations to work with; one is the Breit-Rabi equation (eq. 2), and the other is the field of Helmholtz coils as a function of current (eq. 3). Write down the equations, rearrange them, see how the two isotopes fit in, see how additions or subtractions can help, use both + and – currents. Keep in mind that the B-field in the B-R equation is the sum or difference of the Helmholtz field and the earth’s field. From equation (2) we have a relation between ν1 and I1, and ν2 and I2 where the subscripts refer to the Rb85 and Rb87 isotopes. From your data determine the best ratio \frac {\nu_1}{\nu_2} and from this deduce the values of I1 and I2. Their true values are exactly half-integral. (Are the ratio, and this half-integral expectation, sufficient to determine both nuclear moments?)
  3. Having now determined the values of I1 and I2, use equation (2) to determine the value of B at the bulb for one positive and one negative value of the current in the coil. Compare these values with those calculated from the coil dimensions and current. Which values are more accurate? Why? Once you have determined the nuclear spins, the Breit-Rabi equation is as accurate as the numerical constant 2.799, since the nuclear spins must be odd half-integers exactly. The Helmholtz coil field is not as accurate as the numerical constant 0.9x10-6 since the radii of the copper wire turns are not all exactly the same, and the separation of the coils is not exact. By using the Breit-Rabi equation, you can determine this constant more accurately. Try drawing a line parallel to the frequency axis at a particular current, both plus and minus. What can you learn from the intersections with the curves? Do the same with a line parallel to the current or B axis.
  4. Perform a line fit on each of your four data sets. For each, find the slope and intercept and there respective errors using the theory and techniques of error analysis as illustrated in Lyons, Data Analysis for Physical Science Students, Section 2.9, page 63ff. (Also see Error Analysis Notes). Show clearly how you do this, with a sample calculation. If you use Excel you must show that you know what the program is doing. What is R? What influences its value? Don’t just use a data reduction code blindly – you don’t learn anything that way. You might also try a Chi-Squared analysis to check whether your data and error estimates are consistent (again, see Lyons). Also, check to see that their slopes are consistent with the values of nuclear spins that you found.
  5. From the intercepts calculate the earth’s field, and its errors. Ultimately you can have four values for the earth’s field for each isotope. Check to see that all eight values fall within the range of your statistical errors. If they don’t, what might be wrong? Say something about which values you think are the most accurate, and why.
  6. Explain why there is a resonance at zero frequency.
  7. What do you need to know and to take account of, in order to make a rough estimate or calculation of the pumping time to compare with your experimentally measured value?
  8. Go to the page on data analysis and complete the steps.

Notes and advice from Prof. Budker

  • Nov. 19, 2007. The Physics-111 Optical Pumping experiment utilizes radio-frequency transitions between Zeeman sublevels split in energy in an external magnetic field (for example, the field of the Earth). The experiment illustrates how an optical-pumping device can be used as a magnetometer. Another interesting and very important application of optical pumping is atomic clocks. The clocks are based on microwave (rather than rf) transitions which are between the two ground-state hyperfine-structure levels (i.e., the levels with different total angular momentum F). A nice discussion appropriate for the Physics-111 students (particularly those who have mastered the Optical Pumping experiment) is given in an article by James Camparo, "The Rubidium Atomic Clock and Basic Research," Physics Today -- November 2007.
  • Here, I plan to list some common misconceptions about OP.
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