Table of Contents
Optical Pumping (PHYS 334)
Optical pumping is an experimental technique by which specially prepared photons are used to repeatedly excite an ensemble of Rb atoms in a way which drives the atoms into a specific atomic energy state from which the atom can no longer be excited by the photons. Once you learn how the technique works and how to apply it to Rb atoms in a vapor cell you will use it as a tool to make measurements of the energy of the Zeeman splitting as a function of magnetic field. You will be able to test the predictions of the quantum mechanical model for Zeeman splitting for a range of magnetic fields which covers both the small field approximation and larger fields at which larger order terms become important.
Modern research
Since the zero-field crossing resonances where pumping occurs in Rb are very sensitive to local magnetic fields, such setups can be used to measure minute magnetic fields. Previously SQUID (Superconducting QUantum Interference Device) magnetometers were best for such measurements, but they tend to be bulkier or require extensive cooling (see Moving magnetoencephalography towards real-world applications with a wearable system.)
Optically pumped Rubidium is also of interest in the field of quantum optics. The German group Laboratoire Kastler Brossel have published papers on storing and retrieving images in Rb85, with a long-term goal of creating a memory for a quantum communications network (see Spatially addressable readout and erasure of an image in a gradient echo memory).
More broadly, the dependency of the polarization of atomic emission spectra on local magnetic field is being used by astronomers to gather information about the conditions on the surface of stars (see Discovery of Ground-state Absorption Line Polarization and Sub-Gauss Magnetic Field in the Post-AGB Binary System 89 Her.
Before you get started...
Before your first day in lab, you and your lab partner should do some background research. The purpose of this is so that you can go into your first day with a picture of what you need to measure, how those measurements will be made, what complications you are likely to encounter, and how you might deal with them.
Questions that your group should answer are the following:
What is Optical Pumping?
- How is Optical Pumping achieved for the D1 transition of Rb?
- For the D1 transition in Rb, which energy state does the electron occupy when the atom has been pumped? Why can the electron not absorb another photon?
- What does “depumping” mean?
- What happens to the intensity of the light passing through the vapor cell as the atoms are being pumped?
- Would optical pumping work if we used left-circularly polarized photons instead of right-circularly polarized?
- Would optical pumping work for the D1 line of Rb in the absence of an external magnetic field?
- What would happen to an optically pumped ensemble of Rb atoms if the external magnetic field was reduced to zero?
What is Zeeman Splitting?
- What is the Zeeman Effect and why is Zeeman splitting necessary to optically pump Rb?
- What does the atomic energy level structure look like for the D1 line of Rb, both with and without Zeeman splitting?
Physics
This lab will help you explore your understanding of electricity and magnetism, as well as the basic quantum mechanics of single electron atomic transitions.
Atoms may occupy only discrete energy states, and if the atoms are in thermal equilibrium, the relative numbers of atoms occupying each state is given by the Boltzmann distribution. If we shine light of the appropriate energy and polarization on those atoms, some atoms will be excited to a higher energy state. If the atoms have no easy escape path from this excited state, then the population of atoms will no longer be Boltzmann-distributed. Such an inverted population is described as optically pumped.
In this experiment we will look at the behavior of rubidium-87 (Rb-87) atoms in a vapor cell, illuminated by light from a rubidium lamp. The rubidium atoms have an intrinsic net magnetic dipole moment and therefore will react to an applied magnetic field and exhibit energy level splitting due to the Zeeman effect. These atoms also posses angular momentum and can transition from energy level to energy level only through interactions with light that conserve the total angular momentum of the atom and absorbed/emitted photon system.
Optical pumping
Overview
This link takes you to a short video description of optical pumping. The following text covers everything in the video more thoroughly, and the video is intended to supplement the information in the rest of this section.
In this section, we present a qualitative description of the phenomena of optical pumping. (If you are interested in a more complete description check out the Theory of Optical Pumping page [LINK?]).
Simply stated, optical pumping is a process by which an atom is caused to repeatedly absorb and emit photons so that the atom eventually ends up in an energy state which does not allow it to continue absorbing photons.
In this lab you will optically pump an ensemble of Rb atoms by placing them in a precisely controlled magnetic field and illuminating them with 794.8 nm photons which have been right circularly-polarized. Absorption of the right circularly-polarized photons drives the Rb atoms into a pumped state which cannot then absorb a right circularly-polarized photon. A photodetector is used to record the intensity of the light which passes through the Rb vapor. As more of the atoms are driven into the pumped state, fewer photons are absorbed by the gas and thus more light reaches the photodetector. Changes in the opacity of the vapor are correlated with the degree of pumping which has occurred.
Understanding the details of how optical pumping works in this case is analogous to the quantum description of the hydrogen atom and requires a conceptual understanding of the following:
- Quantum numbers associated with atomic energy states such as $n$, $l$, $s$ and $m_{s}$; and
- Electromagnetic transitions between atomic energy states and their associated selection rules; and
- Behavior of magnetic dipoles in an external magnetic field; and
- Hyperfine and Zeeman effects.
In the next section we provide a qualitative description of the physical processes involved in optical pumping.
Descriptive theory
Details
Rubidium is a hydrogen-like atom in the sense that its ground state has just a single electron in the outermost shell. Thus. the structure of the energy states (outside the full inner shell) is very similar to that of hydrogen which also has only one electron in its outermost shell. Figure 1 below shows the energy level structure for the ground and first two excited states of Rb.
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| Figure 1: The electron energy states of rubidium |
This diagram uses spectroscopic notation to denote the values of the quantum numbers of the various energy states. As a refresher, the relevant quantum numbers are:
- $n$ - The principle quantum number denoting which orbital the electron is in.
- $L$ - The orbital angular momentum of the electron.
- $S$ - The spin angular momentum of the electron.
- $J$ - The sum of the orbital and spin angular momenta of the electron: J = L + S.
- $F$ - The hyperfine quantum number which is the sum of the electron momentum $J$ and the nuclear angular momentum $I$: F = J + I.
- $m_{F}$ - The magnetic quantum number which denotes the orientation of $F$ with respect to the quantization axis defined by an external magnetic field $B$.
As indicated on this diagram, transitions between the first excited state $^{2}P_{1/2}$ and the ground state $^{2}S_{1/2}$ absorb (in the case of excitation) or emit (in the case of de-excitation) a photon with a wavelength $\lambda$ = 794.8 nm. Likewise transitions between the ground and second excited states involve photon wavelengths of wavelength 780.0 nm.
For an ensemble of Rb atoms at 50 $^{\circ}$C, the number of atoms in the ground and first excited states at any given moment is determined by the Boltzmann distribution, such that there will be more atoms in the ground state than are in the first excited state; this is the equilibrium state of the ensemble. This equilibrium state is the result of a balance between physical processes which drive atoms from the ground state into an excited state (such as the thermal motion of the atoms in the gas) and processes which cause excited atoms to de-excite (such as the natural lifetime of the excited state and thermal interactions).
We can produce a non-equilibrium distribution of energy states by shining 780.0 nm light into the vapor. Some of the 780.0 nm photons will be absorbed by Rb atoms in the ground state, thus putting them into the first excited state. These same 780 nm photons will also stimulate atoms in the first excited state to de-excite back to the ground state, and thus simply shining 780 nm light on the ensemble of atoms alone will not significantly alter the state of the ensemble.
There are, however. additional contributions to the various energy states of Rb. Referring back to Fig 1, we see that both the ground and first excited states split into additional energy sub-states. Rubidium nuclei have an intrinsic spin (and corresponding magnetic moment) which interacts with the electron's magnetic moment resulting in two hyperfine states. If the atom is in an external magnetic field, (such as the Earth's magnetic field, for example), there will be additional splitting of the hyperfine states due to the interaction of the electron magnetic moment with the external field. This is known as the Zeeman effect.
Thus, in the presence of an external magnetic field, electronic transitions between the ground and first excited states are in fact transitions from the different Zeeman levels of the excited and ground states. Although there are a lot of possible combinations of transitions between ground and first excited state Zeeman levels, many of these combinations are “forbidden”. In this context, saying that a particular transition is “forbidden” simply means that the probability of that transition occurring is 0 or very near 0. You have probably encountered these quantum selection rules for electromagnetic transitions, summarized below:
| $\Delta L = 0, \pm 1$ (but not $0\rightarrow 0$) |
| $\Delta S = 0$ |
| $\Delta F = 0, \pm 1$ |
| $m_{F} = 0, \pm 1$ |
As an example, let's walk through one possible sequence of transitions for the case where the light being absorbed is right circularly-polarized. In Fig. 2 above, we show a sequence of five hypothetical electronic transitions events – (a), (b), (c), (d), and (f) – and discuss each in detail below.
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| Figure 2: A sequence of four hypothetical transitions |
(a): For purposes of this example, we pick an arbitrary starting point where the atom is in the $^{2}S_{1/2}(f = 1, m_{f}=0)$ ground state. This atom absorbs a right circularly-polarized photon. (Right circularly-polarized is another way of saying the photon carries +1 unit of angular momentum, so upon absorption the $m_{f}$ quantum number must increase by +1.) In this example then, the $F$ quantum number increases by 1, and since $m_{f}$ must increase by 1, this puts the atom in the $^{2}P_{1/2}(f = 2, m_{f}=0)$ state.
(b): When the atom de-excites, it is not required to lose +1 unit of angular momentum; that requirement only exists for absorption because of the circular polarization of the incident light. Instead, the atom can lose 0, +1 or -1 unit of angular momentum (which corresponds to the possible amounts of angular momentum that a photon can carry with it.) Therefore, the atom could potentially decay to any one of three possible states: $^{2}S_{1/2}(f = 2, m_{f}=0, 1, \textrm{ or } 2)$. As an example, let's suppose the atom decays to the $m_{f} = 1$ state.
(c): If the atom now absorbs another right circularly-polarized photon, it would only be able to be excited to the $^{2}P_{1/2}(f = 2, m_{f}=2)$ state because of the requirement that $\Delta m_{f} = +1$.
(d): At this point the atom can de-excite to more than one possible ground state. One possibility is that it ends up in the $^{2}S_{1/2}(f = 2, m_{f} = 2)$ state.
(f): The atom is now pumped because it cannot absorb another right circularly-polarized photon since that would require it to go to a $m_{f} = 3$ state (of which there are none). Therefore, unless some other process drives the atom into some other ground state (such as thermal agitation or stimulated emission by an RF frequency photon), the atom is stuck in the pumped state.
The sequence of excitations and de-excitations described above is just one of many possible permutations of allowed transitions. Not all atoms in the ensemble will end up in the pumped state, but some will end up there. The rate at which atoms are driven into the pump state is in part determined by the intensity of the light source. At the same time energy exchanges due to random thermal collisions between atoms will tend to depump atoms out of the pumped state. Equilibrium is reached when the rate of pumping equals the rate of depumping.
Zeeman splitting as a function of magnetic field
For Rb-87, the relation between the applied magnetic field and energy splitting is
| $E = -\vec{\mu}\cdot\vec{B} = g_f \left(\frac{e}{2m_e}\right)\vec{F}\cdot\vec{B} = g_f \left(\frac{e\hbar}{2m_e}\right)Bm_F$, |
where $\mu_B = e\hbar/2m_e \approx 5.7883 \times 10^{-9}$ eV/G is the Bohr magneton. The Landé g-factor, $g_f$, relates the atom's magnetic dipole moment to its quantum numbers, and is given by
| $g_f = g_j\frac{f(f+1) + j(j+1) - i(i+1)}{2f(f+1)}$. |
Here, $g_j$ relates the electron's contribution to the total magnetic moment and is given by
| $g_j = 1+\frac{j(j+1) + s(s+1) - \ell(\ell+1)}{2j(j+1)}$. |
The energy level shifts are therefore given by
| $\Delta E = \mu_B g_f \Delta m_f B \approx (5.7883 \times 10^{-9} \textrm{ eV/G })g_f \Delta m_f B$. |
Note that this energy difference represents the shift up or down from the un-split (hyperfine) level characterized by quantum number $g_f$.
Apparatus
In this section, we describe the apparatus and help you obtain an initial signal. In the image above, you see (from left to right) the main apparatus, the control console and digital scope, a function generator, a DC power supply, a couple digital multimeters, some compasses, and a computer.
Main apparatus
This section shows a short video description of the TeachSpin Optical Pumping apparatus. The following text covers everything in the video more thoroughly and the video is intended to supplement the information in the rest of this section.
The main apparatus consists of a Rb vapor cell in a temperature-controlled oven situated in the center of a pair of Helmholtz coils, all sitting atop an optical rail. Mounted to the optical rail, we have the following (from left to right):
- An amplified photodiode detector;
- a focusing lens;
- the vapor cell inside the Helmholtz coil assembly;
- a quarter-waveplate;
- a linear polarizer;
- a D1 transition filter;
- a collimating lens; and
- a rubidium lamp light source.
The light source uses a radio frequency (RF) oscillator to excite Rb atoms, thereby producing light at wavelengths needed to pump the Rb atoms in our vapor cell. Light from the source is collimated before passing through the filter which is tuned to only pass light from the D1 transition.
The filtered photons then pass through a linear polarizer and a quarter-waveplate whose optical axes are oriented such that light which emerges is right circularly-polarized. A quarter-waveplate will convert linearly polarized light into circularly polarized light. (If you send unpolarized light through a quarter-waveplate, you will get a mixture of left and right circularly-polarized light out. By placing a linear polarizer in front of the quarter waveplate, and setting the correct angle between the optical axes of the two, you can produce an output beam ranging from pure right circular polarization to pure left circular polarization (or anything in-between).) To produce a beam of right circularly-polarized photons, the linear polarizer should be set to an angle of 45° and the quarter waveplate should be set to 0° in their holders. If you do not remember how polarizers and quarter waveplates work, Google them to refresh your memory.
Vertical and horizontal Helmholtz coils
The vapor cell sits in the middle of a pair of orthogonal Helmholtz coils; one produces a vertical magnetic field when current is passed through it and the other produces a horizontal magnetic field when energized. These coils are used to produce the horizontal and vertical magnetic fields that define the net magnetic field in which the Rb atoms reside. If you do not recall how Helmholtz coils work, Wikipedia has a nice description.
Vertical coil
The vertical coil frame contain $N = 20$ turns on each of the two coils. (Recall that a Helmholtz coil is actually a pair of coils, so the use of the word “coil” can get confusing.) The wire has been wound 5 across and 4 layers deep. According to the manufacturer, the coil radius is about $4.61 \pm 0.01$ inches. The spacing of the coils should match their radius.
With this information, you can calculate the magnitude of the magnetic field created by this coil if you know the current which is flowing through the wires. One of the functions of the TeachSpin control console is to control this current.
Horizontal coils
The horizontal coil frame actually contains two separate pairs of coils; the wire of the second coil is wound directly atop the first coil. This arrangement allows us to create two independently-controllable magnetic fields along the horizontal axis. We call one set of these coils the “Horizontal Sweep Coil” and the other the “Horizontal Field Coil.”
Horizontal field coil
The power supply for these coils has stopped functioning properly and so they will not be used this quarter.
These coils contain $N = 154$ turns on each of the two coils of the pair. The wire has been wound 11 across and 14 layers deep. According to the manufacturer, the coil radius is about $6.22 \pm 0.01$ inches. The spacing of the coils should match their radius.
These coils will be used to create a steady magnetic field along the horizontal axis, similar to how the vertical Helmholtz coil is used. The TeachSpin control console can be used to set the current in this coil.
Horizontal sweep coil
The top layer of wires which you can see make up the “Horizontal Sweep Coil”. This coil contains $N = 11$ turns on each of two coils of the pair. The wire has been wound 11 across in a single layer. According to the manufacturer the coil radius is about $6.46 \pm 0.01$ inches.
This Helmholtz coil is used to create a magnetic field which sweeps periodically over a range in a sawtooth pattern. This small time varying magnetic field component is central to how the TeachSpin apparatus achieves depumping (as you will soon see).
Note that there is a control labeled Recorder Offset directly beneath the Range and Sweep controls. The recorder offset should be turned all the way down (fully clockwise). This control adds a DC offset to the voltage being sent to the oscilloscope. The offset voltage does not have anything to do with the currents flowing through the coils; it only moves the field sweep signal up or down on the scope.
Calculating the coil currents
The TeachSpin control console is set up to allow you to measure the voltages and currents to the different coils so that you can then calculate the magnetic fields being generated.
For the Vertical Coil, there is a pair of test points across a 1$\Omega$ monitor resistor which is in series with the coil wire. Thus, by measuring the voltage drop across the 1$\Omega$ resistor, you can get the current flowing through the coil using Ohm's law.
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For the Horizontal Sweep Coil, getting the current is a bit trickier. Since this voltage (and therefore the current) changes in time, we view it on the scope. However, the actual value of the voltage which is sent to the scope via the Recorder Output is amplified for viewing on a scope. Thus, the voltage you read on the scope is not the same as the voltage going to the sweep coils.
You can determine the conversion factor to go from scope voltage to coil current by either using the test points across the 1$\Omega$ monitor resistor on the front panel next to the sweep coil output jacks, or by reconnecting the coil wires at the output jacks to run through an ammeter to directly measure the current. In either case, you want to set the Sweep Range to zero, then set the Start voltage to several different values from its minimum to maximum. For each Start voltage setting, you can measure both the voltage of the signal at the scope and the actual current in the coils. This will give you all the information you need to determine the linear relationship between scope voltage and coil current.
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Control console
The TeachSpin optical pumping control console is pictured above. Controls on the console are grouped based on function and consist of the following (from left to right):
- RF Amplifier - Not used (and therefore not highlighted in the photo).
- Cell Heater/Controller - Controls and indicates the temperature of the vapor cell. It automatically starts when the power switch is turned on and requires no user input. The temperature display will stabilize at 50°C in about 10 minutes.
- Magnetic Field Modulation - Not used (and therefore not highlighted in the photo.)
- Horizontal Magnetic Field Sweep - These controls are used to set up a time-varying current to the horizontal Helmholtz coils. Note that the BNC output labeled Recorder Output on the lower panel is connected to channel 1 of the scope and is used to monitor the current going to the coils.
- The Range control allows you to set the range over which the current to these coils will sweep.
- The Start control sets the starting current of the sweep. In other words, the Start control can be used to move the whole sweep Range up and down.
- Vertical Magnetic Field - This 10-turn potentiometer is used to set the current going to the vertical Helmholtz coils.
- Horizontal Magnetic Field - This 10-turn potentiometer sets a constant current to the horizontal Helmholtz coil. This current is in addition to any current being provided by the Horizontal Magnetic Field Sweep controls.
- Detector Amplifier - The output from the photodetector on the optical rail comes here. The user can amplify and add an offset voltage to the detector signal, and filter out high frequency noise. The final signal is then sent to channel 2 on the scope.
Part I: Observing optical pumping and depumping
Zero field depumping
Start by turning on the control console; the power switch is located on the upper left (as viewed from the front of the apparatus) corner on the back of the unit.
Conceptually, you are using the controls on the console to do the following two things:
- Create magnetic fields along the horizontal axis of the optical rail and along the vertical axis by sending current to the Helmholtz coils.
- Amplify and filter the signal from the photodetector so that you can view it conveniently on the scope.
(That's pretty much it. It looks more complicated, but at the basic level those are the only two things.)
Our initial goal is to use magnetic fields generated by the the Helmholtz coils to cancel out the ambient magnetic field present in the lab where the Rb vapor cell is located. We then want to use those same coils to create an additional magnetic field (whose properties we know and can manipulate) and watch how the intensity of the light passing through the vapor cell changes as we change that known field.
Set all the coil currents to zero
There are four 10-turn potentiometers which control the currents to the horizontal and vertical coils. Turn all of them fully counter-clockwise to zero. In the Horizontal Magnetic Field Sweep control section, there are two toggle switches. Flip both down so that they are in the Reset and Continuous settings. There should now be no external magnetic fields being generated by the coils and the Rb atoms are now sitting in the ambient magnetic field of the basement lab.
Optical pumping is very sensitive to the presence of external magnetic fields. You want to make sure that there are no magnets near the apparatus. You might be surprised by how many common items contain magnets. (For example, your cell phone likely has some strong magnets in it.) There should be a compass on the table. Take it and move it around the apparatus, looking for any unexpected deflections of the needle which would indicate the presence of something magnetic. Don't forget to take your cell phone out of your pocket.
We can only control the field along two axes – vertical and horizontal along the axis of the optical rail – using the Helmholtz coils. To completely zero the magnetic field in the vapor cell, you will also want to rotate the whole apparatus so that the optical rail is aligned with the horizontal component of the ambient field in the room. Do a rough alignment using the compass; there is no need to be super-precise as we will fine tune this alignment in a moment.
Now that you have roughly aligned the optical axis of the apparatus with the horizontal field in the room, use the Vertical Magnetic Field control on the console to cancel out the vertical component of the ambient field. There is a magnet mounted in a gimbal which you can use as a 3-D compass. Hold it near the vapor cell, inside the volume enclosed by the vertical coils. Now turn up the current to the vertical coils and watch how the magnet behaves. You can easily turn up the vertical field enough to reverse it. Play with the current to the vertical coils while observing the effect on the 3-D magnet and convince yourself that you understand what is happening. Then, set the current to create roughly zero field along the vertical axis. You will fine tune this cancellation in a later step.
View the zero field crossing on the scope
This link takes you to a video which gives an overview on how to use the digital scope to see the depumping signal.
Measure the Earth's magnetic field
Once you have fine tuned the vertical and horizontal fields to make the zero crossing signal on the scope as narrow as possible you have all the information you need to calculate the ambient horizontal and vertical magnetic fields in the lab at the point where the Rb vapor cell sits. The main ambient field in the lab is the Earth's magnetic field. There are likely to be other sources of magnetic fields in the lab (such as the magnetic blackboard and AC electrical lines in the room with the apparatus). You should, however, be able to confirm that the dominant field is the Earth's (to within about a factor of 50%). Doing this calculation at this point will help to ensure that you fully understand what all of the currents, coils and fields are doing.
RF depumping and measurement of Zeeman splitting vs $B_{net}$
At this point, you should be familiar with the concept of optical pumping and comfortable setting up and using the apparatus to observe the depumping signal while sweeping $B_{net}$ through the zero field condition.
Now we want you to extend your knowledge of the apparatus and the technique to include RF depumping which can be used to directly measure the energy of the Zeeman splitting for a given $B_{net}$. Recall that there is one more set of coils on the apparatus which we have not yet used. These are the RF coils which are connected to the output of a function generator. By sending an oscillating current to these coils, we produce an oscillating magnetic field which is orthogonal to the sweep field generated in the horizontal coils. When the energy of the RF photons, $E=\hbar \nu$, matches the energy difference between Zeeman energy levels, they will drive electronic transitions between the Zeeman states. If the gas is in the pumped state when we turn on this RF field, electrons which are in the pumped state will be driven into a different state and gas will be depumped.
To begin, set up the apparatus so that it is sweeping through the zero field condition and so that the zero field depumping signal occurs at approximately the mid-point of the horizontal field sweep. Set the Horizontal Sweep Range to its maximum value so that the Rb atoms are seeing the largest range of $B_{net}$ possible.
Now turn on the function generator and set it to produce a 40 kHz sine wave with an amplitude of ~0.5 V peak-to-peak. Turn on the output to channel 1 which should already be connected to the RF coils on the apparatus. The signal from the detector should now show additional depumping dips on both sides of the zero field point.
Spend a bit of time making sense of what you are seeing on the scope. Keeping in mind that the vapor cell we are using contains natural Rb which is a mixture of Rb-85 and R-87b, see if you can understand the following:
- Can you explain why you see the number of RF depumping dips which appear when the RF coils are energized?
- What is the significance of where along the horizontal sweep these RF depumping signals appear?
- Increase and decrease the RF frequency and see if you can explain how the RF depumping signals change in response.
- Increase and decrease the amplitude of the RF. Do you understand how the signals respond?
Once you understand how the system responds to the RF depumping, it is time to measure the magnitude of the energy splitting of the Zeeman levels as a function of $B_{net}$ over the widest possible range of $B_{net}$ values. The goal is to test the low energy approximation for Zeeman splitting. This approximation predicts a linear relationship between the energy of the Zeeman splitting and the net magnetic field which is related to the Lande g factor.
Part II: Extending your measurements
Part II of the experiment is intentionally left open-ended. You may need to consult outside resources for more theory information or equipment manuals for details about the apparatus. Given your experience collecting data in Part I, use your judgement to determine effective collection and analysis strategies, and budget your remaining time in lab appropriately.
The information given below is only a suggestion for how to proceed. Based on your interests and the quality of your work after Part I, you and the faculty instructor may discuss alternate goals. You are encouraged to bring ideas and propose ideas at your meeting, but you should also be prepared to defend approaches which stray far from the outline below.
Rabi oscillations
As seen in Part I, a pumped system can be actively depumped by the application of an RF magnetic field perpendicular to the light axis. In the multi-level electron system we have here, many competing effects are at play:
- The RF field stimulates both emission (from higher energy to lower energy state) and absorption (from lower to higher energy state).
- Pumping continues to push electrons preferentially to one state over the others.
- Spontaneous emission continually removes electrons from the higher energy states.
As a result, these effects will eventually balance out to an equilibrium steady state where the electron population is spread over many electron states.
On short time scales, however, the RF stimulated transmissions are the dominant effect and one should be able to observe so-called Rabi oscillations which drive electrons sinusoidally from the pumped state to a (relatively) unpopulated state and back.
Develop a strategy and consult with staff to discuss your plan and to get access to equipment as necessary.
Investigation of the Zeeman splitting in the strong field regime
NOTE: The internal power supply required for this part is currently broken. This investigation can be done by attaching an external power supply (of sufficient current output), but it will take some consultation with the lab staff to get working.
The energy level shift due to Zeeman splitting is approximately linear for weak magnetic fields, but becomes very non-linear at stronger fields. Use the techniques already developed in Part I to push your depumping investigation into this non-linear regime. In particular, you should…
- look at the dependence on depumping frequency as a function of magnetic field, and
- look for evidence of multiple depumping resonances (and their relative intensities as a function of applied RF field strength).