OPTICAL PUMPING

Optical pumping is a technique for producing spin alignment in a gas of suitable atoms. Circularly polarized light is applied at the frequency of an electronic transition from the ground state, causing transitions to an excited state. Each photon absorbed adds one quantum of angular momentum in the direction of the axis of the light beam to the system of atoms. However, atoms in the single Zeeman sublevel of the ground state with highest angular momentum projection cannot be excited because there is no excited level of higher angular momentum. Thus a surplus of atoms (if there were no relaxation process, all atoms) accumulates in this sublevel, producing a net macroscopic magnetic moment. This condition can be detected by the resulting increased transmission of the pumping light.

The technique is comparatively simple, but is of great utility. It can be used to measure hyperfine splitting and nuclear magnetic moments in suitable atoms, and is the basis for an atomic clock and a low-field magnetometer.

What one normally does is a "double" resonance experiment, applying an r.f. field at the frequency corresponding to the Zeeman splitting interval. This tends to depolarize the polarized ground state and results in increased optical absorption, which is monitored by a photodiode.

The sensitivity of the technique results in part because absorption of one r.f. photon at Zeeman-splitting resonance leads to the absorption of one optical photon, and this amounts to an enormous power gain.

You should be familiar with the principles of optical pumping before you begin the experiment. For general background, see Bloom (1) and Carver (2). Later you may consult Benumof (3) for more detailed theory. We use a rubidium-85 sample, in an experimental arrangement essentially the same as those described in the references. The apparatus was built by Physics 43 students several years ago.

The light source, filters, ⁸⁵Rb absorption cell, and photodiode are all mounted in a bakelite cylinder. A calibrated solenoid provides a magnetic field to produce the Zeeman-splitting, while a µ-metal shield excludes the Earth's field. Before starting, heat the cell (center of the bakelite cylinder) to approximately 40 degrees C.

Among the measurements you can make are the following: (You will not have to do all of (3), (4), and (5).)
 

1. Zero field dip: Look for a dip in light transmission when the axial magnetic field is swept through H=O. Understand why this happens, on the basis of the semi-classical vector model. (Note that the transverse field is small but not exactly zero -- µ-metal is not perfect.) What determines the width of the dip?
2. Apply a transverse r.f. field and again sweep H, to look for resonances. Make a careful study of the effect of r.f. frequency and also r.f. power level.
3. Quadratic Zeeman effect: At higher frequencies (greater than 10 MHz) the resonance splits into multiple dips due to higher-order terms (in H) in the Zeeman effect. From a measurement of this splitting you can determine the hyperfine splitting of the electronic ground state of ⁸⁵Rb (see Benumof). Use the "red" solenoid to apply a DC bias field slightly smaller than required for resonance, then sweep with the "black" solenoid as before.
4. Spin relaxation time: The question is how fast (and why) does the polarization decay if pumping is stopped (see Benumof).
5. Measurement of the Earth's field: Remove the apparatus from the µ-metal shield and align the axis approximately with the Earth's field. Does the resonance measure the component of field along the light beam, or total field? (Think about how spins precess in a misaligned field.)

Useful information

• For ⁸⁵Rb: I = 5/2
• In the ground state, g_F = ± 1/3 (Derived in Benumof)
• For ground state Zeeman transitions in low field,
• v = g_F (e/4pm) B
• B/v @ 2.14 gauss/MHz (See Benumof).
• Solenoid Calibration:
• Black leads (1 layer): 8.99 gauss/amp -> +.20 MHz/a
• Red leads (5 layers): 44.8 gauss/amp -> 20.9 MHz/a

References

1. A.L. Bloom, "Optical Pumping," Scientific American, October 1960, p. 72 and
2. T.R. Carver, "Optical Pumping," Science, August 1963, 144, p. 599.
3. R. Benumof, "Optical Pumping Theory and Experiments," Am.J.Phys., 1965, 33, p. 151. (Note that Benumof treats explicitly ⁸⁷Rb, so you need to revise the last step.)

4. C.P. Slichter, Principles of Magnetic Resonance (Harper & Row, New York, 1963), pp. 1-22.
5. R.M. Eisberg, Fundamentals of Modern Physics (John Wiley and Sons, Inc., New York, 1961), parts of Chapter II.
6. K. Ziock, Basic Quantum Mechanics (Wiley, New York, 1969), Chap. 7, and 12.4-12.5.

Warmup Procedure

1. Connect heater for the Rb⁸⁵ absorption cell (about 400 mA into heater). Start this at the beginning of the lab period, then adjust the power to stabilize at the desired thermistor reading.
2. Connect the power supply to the Rb lamp:
1. 6.3V, 3A AC to heat filaments. Let the filaments warm up 1 minute before turning on DC voltage (B+).
2. After 1 min. turn on DC voltage (B+) between the filaments(-) and the plates (+). Do not exceed 180 V (about 17.5 mA). {Varying this will control drift; it can be very touchy.}
3. Connect the HP 8601A signal generator "r.f. output" to the transverse R.F. coil and the "aux. Output" to the frequency counter. Set the signal generator to CW, 100 KHz to start.
4. Connect the output of the Photodiode Signal to a DC voltmeter and oscilloscope (and later, XY plotter).
5.  Connect the photodetector power as follows:
1. red = +15V DC
2. blue = -15V DC
3. black = ground
6. Connect black leads of the solenoid (one wire, one plug) to the DC power supply/amplifier (HP 467A), in power supply mode. The red leads are not needed until Part (3) of the experiment.
7. For automatic sweep of the magnetic field, use the HP 467A in amplifier mode, and use the ramp generator as its input. For preliminary observations at low field on the oscilloscope, use a function generator instead of the ramp generator.
8.  If the XY recorder does not have enough zero offset to expand the scale of the photodiode signal, construct a 1-op.-amp. DC offset circuit.