A22. Optical Pumping
This is an experiment in atomic physics and magnetic resonance. Circularly polarised light has the ability to polarise (or optically pump) atoms in a vapour by selectively populating one of the Zeeman levels in a magnetic field. This changes the amount of light absorbed by the vapour. You will observe this effect with Rb atoms, and you will then observe changes in transmission of the Rb vapour due to the redistribution of atoms among the ground state Zeeman levels arising from resonant radiofrequency radiation incident on the vapour. This will be used to measure various properties of the atoms and their interaction with radiation.
1 Introduction and Background Theory
The rules governing transitions between atomic levels can be exploited to populate selected levels preferentially. Induced transitions from such overpopulated levels can then be used either as a diagnostic, as in the rubidium magnetometer, or to provide a source of coherent electromagnetic emission, as in a laser.
As a simple model, consider the atomic level system shown in figure 1. This hypothetical atom has a single electron outside closed shells. The ground state and first excited state are shown, each with spin (S) equal to 1/2 and orbital angular momentum (L) equal to zero. In zero external magnetic field there will therefore be (2S+1)=2 degenerate levels in each state, with MJ= ±1/2. These levels are separated by an energy 2BB when a magnetic induction B is applied to the system, B being the Bohr magneton.
Initially the levels in the ground state will be equally populated. If the system is irradiated with circularly polarised photons along the direction of the applied magnetic field with each photon having an energy corresponding to the energy difference between the two states, then this must result in both an excitation of some of the atoms into the upper state and, because circularly polarised photons carry angular momentum, a change in the angular momentum of the atom. Hence, if circularly polarised light is used, the population in the ground state level with MJ = 1/2 can be lifted into the excited state level with MJ = +1/2. The population in the MJ = +1/2 ground state level cannot however be excited because angular momentum has to be conserved and no suitable excited state is available. As the excited state +1/2 level can decay spontaneously to the ground state +1/2 level as well as to the 1/2 level, the net effect is that the +1/2 ground state level becomes more fully populated while the 1/2 ground state level becomes nearly completely depopulated. Only some process which produces a transition between the two closely spaced ground state levels can restore the equilibrium.
To see how this model applies to a real atomic system, consider the level structure of Rb-85 shown in figure 2. Rubidium is in the same group of the periodic table as sodium and potassium and has the same atomic structure, one electron outside a closed shell with zero orbital angular momentum (5s state). Rb-85 has nuclear spin (I) of 5/2, which couples to the electronic spin (S) of 1/2 to give possible values of the total angular momentum quantum number, F, of 3 or 2 for the ground state. The energies of the states with these two values of F are slightly different due to the fact that in one of them the nuclear magnetic moment is aligned parallel to the magnetic field arising from the magnetic moment of the electron, while in the other it is antiparallel. This 'hyperfine' splitting is small compared with typical atomic line separations because the nuclear magneton is about 1800 times smaller than the Bohr magneton.
The first excited, L=l, p state of rubidium has a total electronic angular momentum, J, of 1/2 or 3/2, which adds to the nuclear spin to produce the effect shown in figure 2. In figure 2, the 5p 2P1/2 F=3 state corresponds to the +1/2 excited state in figure 1. Hence this state can be populated by irradiating the atoms with circularly polarised photons with a wavelength of 795 nm. Note that this wavelength is characteristic of the separation of the principal electronic energy levels and therefore has the same value for both Rb-85 and Rb-87.
If the total angular momentum quantum number F is a good quantum number with which to describe the system then the electronic and spin magnetic moments, rigidly coupled together, can take up 2F+l possible orientations with respect to an external magnetic field. Hence there are 2F+1 values of the magnetic quantum number MF associated with each F. Normally these MF levels are degenerate, but they separate in an applied magnetic field as shown in figure 2. The energy shift in each magnetic sublevel is linear with B until the applied field is high enough for the nuclear and electronic spins to begin to decouple (c.f. break-down of LS coupling).
According to the classical theory of the Zeeman effect, the electromagnetic radiation emitted by an atom in a magnetic field is linearly polarised when viewed perpendicular to the field and circularly polarised when viewed along the field. Hence if transitions between the states are to be induced by the circularly polarised pumping light in this experiment, which is necessary because the transitions have to involve a change in angular momentum, the magnetic field applied to split the magnetic levels must be in the same direction as that in which the light is propagating.
The transitions which take place when the circularly polarised light is applied are determined by the selection rules for MF which state that MF = 1 This means that, for the D1 line at 795 nm, upward transitions can take place from the ground state from all levels except F=3, MF =+3. Hence this is the level that becomes overpopulated.
In the experiment all transitions to the 5p 2P3/2 excited state are suppressed, in order to exclude unwanted transitions, by inserting a D2 line blocking filter at 780 nm into the light path. This is in fact accomplished by using a narrow band pass filter at 795 nm.
The arrangement of the apparatus is shown in figure 3. The main elements are a rubidium discharge lamp producing strong emission at 795 nm, a quarter wave plate and polariser producing left-handed circularly polarised light, an absorption cell containing rubidium vapour, and finally a diode light detector and amplifier. A long solenoid, whose axis is directed along the optical axis in the direction of propagation of the light, can be used to apply a static longitudinal uniform field, B0, to the absorption cell. The whole system is surrounded by a set of cylindrical mumetal shields. These not only cut out all external magnetic fields but also have the effect of making the internal solenoid producing B0 appear infinitely long.
When the absorption cell is put into the light beam the signal falls as the resonance radiation is absorbed. However, as atoms in the absorption cell are transferred into the F=3, MF=+3 level in the ground state by the action of the polarised light then the signal from the diode will begin to rise again because there are fewer atoms in absorbing ground state levels. In effect the pumping process 'polarises' the atoms in the absorption cell. However, if the atoms are now transferred from the overpopulated level ground state back to other levels by some mechanism then the light will once again be absorbed and the signal will fall. Hence an increase in the absorption of the light by the cell is a measure of the relaxation processes taking place within it.
In practice there will always be some relaxation processes counteracting the pumping procedure. Whether or not these have a significant effect on the signal depends on the time constants associated with them. A rapid redistribution between adjacent levels can be achieved by applying a radiofrequency signal at the resonance frequency for transitions of the type 5s 2S1/2 F=3 (MF = +3 MF = +2), which immediately allows pumping to resume. Such a transition takes place at a frequency of E/h, where h is Planck's constant and E is the energy level separation due to the applied magnetic field. The value of E can be derived from IJ coupling theory, according to which the magnetic moment associated with a nuclear spin angular momentum I coupled to an electron with a magnetic moment of one Bohr magneton B and spin 1/2, the combined system being in state F,MF, is
(MF)= MFB[F(F + 1) + (1/2)(1/2 + 1) - I(I + 1)] / [(1/2)2F(F+ 1)]
MFI [F(F + 1) + I(I + 1) - (1/2)(1/2 + 1)] / 2IF(F + 1) (1)
For Rb-85, which has a nuclear moment of 1.3482±0.0005 nuclear magnetons, E=[(MF)(MF1)]B0, and the corresponding transition frequency is 4.6619 MHz/mT.
It has already been stated that the applied static magnetic field must be perpendicular to the plane of polarisation of the circularly polarised light. The radio frequency (RF) field used to induce transitions between the magnetic sublevels must also be circularly polarised if it is to induce transitions which involve a change in angular momentum. This circular polarisation can be achieved by simply applying a sinusoidally varying RF magnetic field perpendicular to the beam direction using a pair of small Helmholtz coils. This produces a linearly polarised oscillating field which is equivalent to the sum of two circularly polarised fields rotating in opposite senses.
The action of the RF field can also be understood from a classical point of view. The angle which the total magnetic moment (F) and individual angular momentum vectors make with the static applied field is determined by the magnetic quantum number MF which describes the state. The interaction between the tilted magnetic moment of the atom and the applied field produces a torque on the atomic angular momentum which results in a gyroscopic precession around the magnetic field direction. It is easy to show that the angular frequency of this precession, the Larmor frequency, (torque)/(angular momentum), divided by 2, is equal to the E/h calculated above. At resonance therefore the vector representing the RF field is rotating at the same frequency as that at which the angular momentum vector is processing. In the frame in which these two vectors are stationary the magnetic moment experiences a torque exerted by the RF field which induces precession around the RF field direction, causing the direction of the magnetic moment with respect to the applied static field to change cyclically. In other words, the time averaged populations of the MF = +3 and MF = +2 states are equalised but the ensemble of atoms all precess in phase.
In practice the fact that other depolarisation effects are present means that the angular momentum vectors of different atoms which were previously aligned become 'dephased' with respect to each other on a timescale comparable with the relaxation time constants. The width of the resonance should be inversely related to the lifetime defined by these time constants, which can be measured by applying the RF field in bursts. At the onset of the burst a coherent precession of the magnetic moments of many atoms will be set up around the direction of the RF field vector. This will result in periodic reversal of the angular momentum vectors with respect to the direction of the static B field, that is to say, periodic occupation of all the F=3 levels, which results in periodic availability of atoms for optical pumping and therefore a periodic variation in the signal from the detector. The period of this variation will be related to the strength of the RF field in the same way that the RF frequency is related to the static B field. Thus, if the RF field amplitude is 2 T, the period should be given by 1/T = 4.6619 kHz. The factor 2 difference arises because only half the oscillating field amplitude contributes to each sense of circular polarisation.
The 'periodic availability for pumping' mentioned in the previous paragraph means that the pumping light is periodically absorbed, leading to an oscillating signal. It also means that some rof the processing atoms are removed. Not all of these return in phase to the F = 3, MF= +3 level, so the pumping process contributes to the decay of the oscillations.
Other relaxation processes that lead to a decay of the oscillating signal arise through a loss of coherence between the phase of the precession of the magnetic moments. Relaxation processes which contribute to this loss of coherence include collisions between Rb atoms, collisions between Rb atoms and gas molecules in the cell, collisions with the wall of the cell, loss of atoms into the stem of the cell, and the effect of inhomogeneities in the magnetic field across the cell.
2 Apparatus
A schematic of the apparatus is shown in Fig. 1.
Fig.1. Schematic of the apparatus for studying Optical Pumping. You should check this carefully yourself.
a)Rubidium Lamp. This is in the box covered in black cloth on the wooden optical table. Inside is a bulb filled with rubidium vapour, a heater to heat the stem of the bulb, silicone oil, two high power heaters to heat the oil and a tuned circuit to excite the rubidium.
The bulb needs to be kept under oil to maintain a constant temperature, it is very unstable when the temperature varies. The oil is heated to around 115 C by the two large heaters and the smaller stem heater. This means the outside of the box gets to around 100 C, so be careful. The temperature of the outside of the box is monitored using a thermocouple.
b)RF Power Supply. This is a big metal box with a fan on the top. It supplies around 15W of RF at about 67MHz to excite the rubidium vapour.
c)Photodiode Detector. This is at the back of the optical table (inside the mu-metal shields) and has a switch on top for changing between AC and DC coupling.
d)RF Helmholtz Coils. A pair of Helmholtz coils in the middle of the optical table connected in series. Diameter 10cm; Separation 5cm; 9 turns each; Combined resistance 47.2 ohms.
e)Absorption Cell. This is a glass bulb in a protective black foam case with rubidium vapour inside. It sits in the centre of the optical table inside the RF Helmholtz coils.
f)Circular Polariser. This comes immediately after the lens in front of the bulb and consists of a quarter wave plate and a linear polariser. Do not adjust it as it takes quite a long time to align the two plates.
g) Filter. This is an interference filter which transmits light at just the right wavelength (795 nm) to excite the correct rubidium transition in the absorption cell.
h) Long Solenoid. This is a solenoid inside a mu-metal magnetic shield. The mu-metal makes the solenoid appear to be infinitely long. Length of coil 1.07m; Radius 0.19m; 830 turns; Resistance 15.3 ohms.
i)Signal Generator. For supplying the RF coils. It is capable of generating pulses of RF and modulating the frequency automatically. Make sure you learn how to operate this early on as it is a complicated piece of equipment which is capable of giving different types of signal.
j)Dual Power Supply. Capable of two independent outputs. One used as a constant current source for supplying the solenoid. The other can be used as a constant voltage source for backing off the DC output firom the photodiode (so that small changes on a large constant background signal can be seen). Again, make sure that you learn early on how to operate this supply properly.
k)Oscilloscope. Digital storage scope with cursor control.
l)Power Supplies. Photodiode power supply with ±12V outputs. Low power lamp stem heater supply, capable of delivering a maximum of around 10W. Higher power supply capable of delivering about 40W for powering high power heaters (called 50W heaters because this is the maximum they can be run at).
The wooden optical bench can be slid in and out of the magnetic shield for easy access to the absorption cell and photodiode switch. Be careful when removing though as the oil in the bulb box can be spilled out of a vent hole in the top, i.e. keep it horizontal and move it carefully.
Always use the setup with the bulb box nearest the open end of the solenoid as excess fields from the power supply cables can affect the solenoid field. There are sockets mounted on the front of the optical table for easy connection to the equipment mounted on it. The socket for the RF coils is underneath the table in the middle.
The set up is microphonic, i.e. it is very sensitive to vibrations, so when experiments are being carried out try not to knock it about. The oil in the bulb moves about and takes a little time to settle down. Also if the optical table is pulled out when the bulb is on, the oil needs time to settle down again.
3 Experiment
- Familiarise yourself with the apparatus. If necessary, consult a demonstrator or technician.
- The temperature and colour of the discharge lamp are important. Learn how to control these.
3.1 Starting The Bulb
See appendix for extra instructions on this (especially on avoiding instabilities).
Turn on the stem heater to 20V (constant current) and the 50W heater to 2.5A (constant voltage). Heat up the bulb for about 20 minutes or until the box reaches about 55C (The value will depend on the ambient temperature). Switch on the RF. If the bulb does not start, switch off and try again when the box gets hotter. The bulb is on when there is a purple glow from the back of the box. When the RF lamp power is switched on the power increases slowly (over a few seconds) so the bulb will not strike immediately, even if the box is hot enough. The power can be seen increasing on the power meter.