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MOT - Atom Trapping
Physics 111B: Advanced Experimentation Laboratory University of California, Berkeley
- 1 Atom Trapping (MOT) Description Contents
- 2 Introduction
- 3 Atom Trapping Experiment Photos
- 4 Before the 1st Day of Lab
- 5 Objectives
- 6 Background
- 6.1 Physics Background
- 6.1.1 Scattering Rate
- 6.1.2 Radiation Pressure
- 6.1.3 Doppler Shift
- 6.1.4 Doppler Cooling
- 6.1.5 Capture Velocity
- 6.1.6 Doppler Temperature Limit and Doppler Molasses
- 6.1.7 Rubidium Spectrum
- 6.1.8 Effects of the Zeeman shift on light scattering: How a MOT traps
- 6.1.9 Sub-Doppler Cooling
- 6.2 Using atoms as a frequency reference
- 6.2.1 Doppler broadened absorption in a vapor cell
- 6.2.2 DAVLL method
- 6.3 Feedback control
- 7 Safety
- 8 Equipment used in this experiment
- 9 Experimental Setup
- 9.1 Standard Operating Procedures (SOP)
- 9.2 Optical setup
- 9.2.1 Laser and isolator
- 9.2.2 MOT optics
- 9.2.3 Rubidium Spectroscopy Setup
- 9.3 Vacuum System
- 9.4 Electronics for Laser Stabilization
- 9.5 Rubidium Getters
- 10 Procedure
- 10.1 Overview and time-line
- 10.2 Task 1: Understanding Your Laser and Vacuum System
- 10.2.1 MOT Optics To do:
- 10.2.2 Vacuum Chamber To Do
10.2.3 Rb Spectroscopy To Do................................... 18 10.3 Task 2: Generating and Calibrating an Error Signal....................... 18 10.3.1 Inputs............................................. 18 10.3.2 Front panel controls..................................... 18 10.3.3 Outputs............................................ 19 10.3.4 Generating the error signal................................. 19 10.4 Task 3: Locking the Laser...................................... 21 10.4.1 Measuring the system transfer functions.......................... 21 10.4.2 Tuning the lock box..................................... 22 10.4.3 Measuring the closed loop response............................. 23 10.5 Task 4: Magneto-Optical Trapping................................. 23 10.5.1 Qualitative characterization of the MOT.......................... 24 10.5.2 Using the MOT Software.................................. 25 10.5.3 Quantifying the number of trapped atoms......................... 26 10.5.4 Measuring the MOT loading rate.............................. 27 10.5.5 Measuring the MOT temperature.............................. 28 10.5.6 Observing optical molasses................................. 31
References 31
A Polarizaiton gradient cooling 32
B Control theory 32 B.1 Control and Feedback........................................ 33 B.1.1 Basics............................................. 34 B.1.2 Conditions for stable feedback............................... 34 B.1.3 Laser Stabilization System................................. 35
C Your Feedback 36
1 Atom Trapping (MOT) Description
- Note that there is NO eating or drinking in the 111-Lab anywhere, except in rooms 282 & 286 LeConte on the bench with the BLUE stripe around it. Thank You the Staff.
2 Introduction
In this experiment we make use of laser spectroscopy and electronic feedback to stabilize the frequency of a coherent optical field to roughly one part in 10^8 , allowing us to examine precisely the interactions between atoms and light. We exert control over both the internal dynamics and also the center-of-mass motion of atoms, the building blocks of matter, reaching the lower reaches of the temperature scale and establishing conditions for the study and application of quantum coherence.
Our focus is on the technique of laser cooling, wherein the mechanical impacts of atom-light interactions are employed to extinguish the motion of atoms in a dilute gas. While discussions of such mechanical effects trace far back in the history of physics, laser cooling was developed most intensely in the 1980s by a broad community of atomic and laser physicists, including three scientists, Steven Chu, Claude Cohen-Tannoudji, and William Phillips, who shared the 1997 Nobel Prize in Physics for its invention. The history of these developments, and much of the theory underpinning laser cooling, is chronicled in their Nobel lectures [1, 2, 3].
Of the many variants of laser cooling, the magneto-optical trap (MOT) is undeniably the workhorse. Invented at MIT and first demonstrated at Bell Labs [4], it combines the abilities of both cooling and also trapping
MUST be submitted as the first page of your lab report. Quick links to the checkpoint questions are found here: 1 2 3 4 5 6
- Note: In order to view the private Youtube videos hosted by the university, you must be signed into your berkeley.edu Google account. View the Atom Trapping Video
- Before using the apparatus in this experiment, you must complete training in the safe use of lasers detailed on the Laser Safety Training page. This includes readings, watching a video, taking a quiz, and filling out a form
- View the fundamentals of optics tutorial, a review of the principles of optics, Fundamentals of Optics Tutorialand the Optical Tutorial Video, Energy Levels (part 1) Video and Energy Levels (part 2) Video.
- View the Laser Guide.pdf and the Gaussian-Beam-Optics.pdf
- Last day of the experiment please fill out the Experiment Evaluation
Suggested Reading:
- C. Wieman, G. Flowers and S. Gilbert. “Inexpensive laser cooling and trapping apparatus for undergraduate laboratories,” American Journal of Physics 63 , 317 (1995). Many of the specifics on their experimental setup are different, but they cover the physical and technical concepts of vapor cell MOT’s very well.
- C. Monroe, W. Swann, H. Robinson, and C. Wieman. “Very Cold Trapped Atoms in a Vapor Cell.” Physical Review Letters 65 , 1571 (1990).
- H.J. Metcalf and P. van der Straten. Laser Cooling and Trapping (Springer, 1999). Most directly relevant are Ch. 3 (“Force on two-level atoms”), 7 (“Optical Molasses”), and 11.4 (“Magneto- optical traps”). Searchable PDFs Metcalf Chapters
- J.J. DiStefano, A.R. Stubberud, and I.J. Williams. Schaums outline of theory and problems of feedback and control systems online book
- (McGraw-Hill; New York; 1990). See chapters relevant to frequency-domain analysis of feedback systems.Chapter PDFs Searchable chapters 1, 10, 15 16
Reprints and other materials can be found on the Physics 111 Library Site
Other References
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.
5 Objectives
- Learn what real experimental physics is about
- Learn the synergy between experimental and theoretical work
- Learn to use pieces of equipment that are commonly used in research
- Learn how measurements are performed, analyzed, and interpreted.
- Learn how to present your work and results
- Learn problem solving strategies
- Learn how to manage and organize your time
6 Background
6.1 Physics Background
The operation of a MOT can be understood starting with a few basic principles of atom-light interaction. Here we provide just a sketch of the physics principles involved. A more quantitative treatment, to which you will want to compare your measurements, is found in Ref. [5] H.J. Metcalf and P. van der Straten. Laser Cooling and Trapping full book or Searchable PDFs Metcalf Chapters
This description of the operation of a MOT starts with some basic ideas about light-atom interactions and their mechanical effects. We exhibit these basic effects by considering a simple, fictional, “two-level” atom. We then consider implications of the specific atomic structure of a real atom, rubidium. Namely, we show how that specific structure allows a MOT not only to cool atoms down to fairly low temperatures (via Doppler cooling), but also to trap them (via Zeeman shifts of optical transitions) while also cooling them to much lower temperatures (via polarization-gradient cooling).
6.1.1 Scattering Rate
Consider the absorption and spontaneous emission, or scattering, of light. We focus on a single optical transition between a particular ground state |g〉 and excited state |e〉 of the atom, neglecting the complexities of real atomic structure. Such a two-level atom, assumed to have zero velocity, and exposed to monochromatic light with frequency ωL, will scatter photons at a rate Γscat given as
Γscat =
×
s 1 + s + (2δ/Γ)^2
with the following definitions:
- Γ = the natural linewidth of the transition, given as an angular frequency (units s−^1 ) so that Γ−^1 is the lifetime of the excited atomic state.
- s = 2Ω^2 /Γ^2 = the saturation parameter (unitless). We may also express s = I/Isat where I is the laser intensity and Isat is the saturation intensity.
- Ω = the Rabi frequency (same units as Γ). This quantity relates to the strength and polarization of the electric field of the laser, and to quantum-mechanical matrix elements that tell us how strongly the ground and excited states of the atom are coupled by laser light. Formally, ¯hΩ = 〈e|d · E|g〉 where d is the electric dipole operator and E is the laser’s electric field in the co-rotating frame. Clearly, Ω^2 ∝ I.
- δ = ωL − ω 0 = the detuning of the laser frequency from the atomic resonance frequency ω 0.
6.1.2 Radiation Pressure
In a single scattering event, the atom absorbs a photon with momentum ¯h~kL from the laser beam, and emits a photon with momentum ¯h~ks with the wavevector ~ks randomly oriented according to the dipole emission pattern. Over many scattering events, the average momentum of the emitted photons is zero, giving an average radiation pressure force on the atom:
F^ ~ = ¯h~kLΓscat (2)
6.1.3 Doppler Shift
In the frame of a moving atom with velocity ~v, the frequency of laser light will be different than that observed in the stationary lab frame. The detuning of this light from the atomic resonance frequency will then be given to first order as δ′^ = δ − ~kL · ~v (3)
Figure 5: Hyperfine levels for the 5S 1 / 2 ground state (hyperfine spin quantum number F ) and 5P 3 / 2 excited state (hyperfine spin quantum number F ′) are shown (not to scale). Rb-85 is on the left, and Rb-87 is on the right. Energy differences shown in frequency units. The transitions used for cooling and rempump light are indicated.
6.1.7 Rubidium Spectrum
Rubidium is composed naturally of two stable isotopes, 85 Rb and 87 Rb. In this experiment, we create a MOT for 85 Rb atoms (though both isotopes are present in the chamber). A pertinent level diagram for (^85) Rb is shown in Figure 5 (left). Further detail on both isotopes of rubidium is available in Ref. [6]. The
transition used for laser cooling drives atoms from the F = 3 ground state to the F ′^ = 4 excited state of the D2 line. This transition is nominally closed, meaning that atoms will continue to scatter light through many absorption/emission cycles. However, rare off-resonant excitation to the F ′^ = { 2 , 3 } excited states does allow the atom to decay to the F = 2 ground state, where it is far-detuned from the cooling light and thus lost to the laser cooling process. To mend this problem, we introduce also light resonant with the F = 2 → F ′^ = 3 transition, which pumps atoms back to the laser cooled states.
The F = 3 and F ′^ = 4 levels each contain a number of magnetic sublevels. The strengths of transitions between them are related according to the Clebsch-Gordan coefficients (tabulated in Refs. [5, 6]). The strongest transition (lowest saturation intensity) occurs using circular polarized light driving the |F = 3 , mF = 3〉 → |F ′^ = 4, mF = 4〉 transition, with Isat = 1.7 mW/cm^2 [6]. In estimating the fluorescence rate of atoms in a MOT, for the purpose of determining the number of trapped atoms, it is suggested that you account for the simultaneous excitation by the many laser beams of the MOT by averaging over all possible atomic ground states and laser polarizations.
6.1.8 Effects of the Zeeman shift on light scattering: How a MOT traps
In the presence of a magnetic field, the energies of the ground and excited state sublevels are shifted by the linear Zeeman shift as ∆E = gF μB mF B, where the Lande g-factors are gF = 1/3 in the ground state and gF = 1/2 in the excited state, μB = h × 1 .4 MHz/G is the Bohr magneton, B is the magnetic field strength and the magnetic quantum number mF is defined with the quantization axis along the magnetic field direction. These Zeeman shifts vary the atomic resonance frequencies, allowing the radiation pressure force in a MOT to be not only velocity dependent (giving cooling) but also position dependent (giving trapping).
More explicitly, we see that σ+^ transitions (that increase mF ) have higher resonance frequencies than σ− transitions. Given that cooling light in a MOT is red-detuned from the atomic transition (δ < 0), we see that a magnetic field will bring the σ−^ transitions closer to resonance, increasing the radiation pressure force
from such light. Now we return to the one-dimensional laser cooling used to explain Doppler cooling and molasses. We consider that both light beams have left-handed circular polarization; such polarization drives a σ+^ transition when the laser wavevector points along the magnetic-field axis. Now we consider laser cooling atoms in presence of a linear gradient of the magnetic field, i.e. B~ = B′z ˆz. This configuration ensures that stationary atoms are always forced back to the zero-field position.
In our three-dimensional MOT, we apply gradient fields along all spatial dimensions by creating a spherical quadrupole field:
B^ ~ = B′z zˆ − B
′ 2
(xˆx + y ˆy) (10)
The change of sign of the gradient requires that we reverse the laser polarizations of the beams along the ˆx and ˆy directions.
6.1.9 Sub-Doppler Cooling
When researchers carefully measured the temperature of atoms emerging from MOTs or from optical mo- lasses, they found the atoms were cooled substantially below the temperature limits described by for Doppler cooling alone. If your experiment is successful, you will confirm this finding. Soon, it was determined that another cooling mechanism, polarization-gradient (PG) cooling, was also at work. PG cooling involves an interplay between optical pumping and light-induced energy shifts of the atomic ground state. You can learn more about PG cooling in Appendix A.
6.2 Using atoms as a frequency reference
If you’ve been following the discussion above, you will realize that the operation of a MOT requires light whose frequency is within just 10’s of MHz from the atomic transition frequency. Producing light whose frequency is defined within 10’s of MHz is not difficult: we use a commercial external-cavity diode laser, which produces light with a linewidth of around 1 MHz or less. But how do we fix the central frequency of that laser light to be precisely some 10 MHz below the resonance frequency of 85 Rb on its F = 3 → F ′^ = 4 optical transition? The answer is to use 85 Rb atoms themselves as a frequency reference. That is, we use a rubidium vapor cell to generate an electronic signal that tells us what is the instantaneous frequency of our laser light, and then we use electronic feedback based on that signal to keep the laser’s optical frequency fixed.
In this experiment, the optical frequency measurement is made using a method called “Dichroic Atomic Vapor Laser Lock” (DAVLL) [16]. To explain how this method works, let us start by describing the absorption of light by a room-temperature rubidium vapor cell. As you read this section, you will find it helpful to refer to the actual experimental setup in the MOT experiment, both as sketched in Fig. 6, and also as actually laid out on the optical table.
6.2.1 Doppler broadened absorption in a vapor cell
As shown in Fig. 6, the “spectroscopy setup” includes two rubidium cells, which are both held at temperature a bit above room temperature. One of them is held within a housing that includes also several permanent magnets – that one is used to generate the DAVLL signal. Two light beams pass through this DAVLL cell, after which they are detected on separate photodetectors. A second cell is used to measure the rubidium spectrum at near-zero magnetic field. One light beam passes through this cell and is detected. Let us begin by explaining the signal that is detected in this second cell.
If one slowly scans the frequency of the laser light over a broad range – say 15 GHz or so – and measures the intensity of light that is transmitted through the vapor cell, one obtains (that is, you will; see Sec. 10.3.4) a signal such as shown in Fig. 10. We see that the light arriving at the detector is attenuated around four characteristic frequencies. These correspond to the frequencies for optical transitions from the following ground hyperfine levels: the F = 2 state of 87 Rb, the F = 3 state of 85 Rb, the F = 2 state of 85 Rb, and the
control. You might turn to Sec. B to learn more, or look up some helpful references [9, 10, 11].
Briefly, in this experiment, the optical frequency emitted by the laser is controlled by three properties of the laser: its temperature, the current supplied to the laser diode, and the voltage provided to a piezoelectric transducer (PZT) that moves an optical element with the laser cavity. All three quantities can be set manually using the New Focus laser controller. In addition, two quantities – the laser current and the PZT voltage – can be varied by applying external voltages to the laser controller. Small voltages applied at those external outputs each change the laser frequency by an amount linearly proportional to the applied voltage.
The DAVLL method is used to generate a voltage that effectively measures the frequency of the laser light. Near the settings at which we want to stabilize this frequency, the DAVLL signal can be used as an error signal to be used as part of a negative-gain, closed-loop feedback circuit.
The concept of negative-gain feedback stabilization is fairly intuitive. Consider the example of driving and keeping your car on the road. Your eyes and brain produce an error signal, telling you whether the car is veering to the right or the left. You respond to this veering through negative feedback: if the car drifts right, you steer so as to turn the car to the left, and visa versa. In contrast, if you feed back with positive gain, steering to the right when you veer to the right, you’ll only make things worse.
The feedback circuitry used in this lab has very many knobs and switches. This setup is holdover from a previous version of this lab where we asked students to adjust many things and characterize the feedback circuit very thoroughly. At present, however, you should only need to adjust a few things to stabilize the laser at the right frequency, observe a MOT, and get going on making various measurements on the MOT. Essentially, you just have to get all the signs right: (1) Produce an error signal with a linear slope at the frequency where you want to lock the laser. (2) Apply current feedback, with fixed feedback sign, and see whether that results in negative or positive feedback. If the feedback is positive, then you have to change the DAVLL signal so that the signal vs. frequency varies with a slope of opposite sign. (3) Apply PZT feedback and see whether this results in positive or negative feedback. If the feedback is positive, you can reverse the polarity of the PZT feedback by flipping a switch on the control box. (4) Adjust the magnitude of the gains. If the gain is too low, the laser frequency will vary a lot and your MOT will be unstable and hard to observe. If the gain is too high, the feedback will become unstable and/or the system will “fall out of lock.” Fortunately, the feedback circuitry is sufficiently stable over a very broad range of gain settings (simply because we have built such an awesome experimental setup!).
7 Safety
In working with this experiment, you must be mindful of a few hazards.
- Laser light: This experiment uses a ∼50 mW beam of laser light at a wavelength of 780 nm. This light is infrared, beyond the range of human vision except for very bright illumination. Such a Class IIIb laser may damage your eye both from direct viewing and from diffuse scattering. Thus, you must wear laser safety goggles (provided in the laboratory) once the curtain around the table is drawn open. To align optics or search for stray laser light, you should use a fluorescent laser viewing card or an IR scope. Be particularly careful working near the vacuum chamber, where there are vertically oriented beams and also horizontal beams at several elevations.
- High voltage: Both the ion pump and the ion gauge are supplied with high voltage for their operation. You should not touch or modify the ion-pump and ion-gauge setups. Rather, ask a professor or teaching assistant for help.
- Ultra-high vacuum: You must be careful not to drop anything on the glass viewports of the vacuum chamber. If they break, not only will your experiment be ruined, but also the imploding glass can be hazardous. If you must use a metal tool near those viewports, block the glass windows in case the tool slips from your hands.
8 Equipment used in this experiment
- Vacuum setup (a) ion pump and controller (do not adjust) (b) ion gauge and controller (do not adjust) (c) turbo and roughing pump station: Used only to fix major vacuum problems and with staff super- vision. (d) rubidium getter and current source (labeled “Power 1, Getter 1” and located below optical table). (e) rubidium metal sample, not used since the rubidium getters were installed.
- Optical setup (a) New Focus external cavity diode laser, 50 mW output, 780 nm wavelength (b) optical setup consisting of many mirrors, lenses, polarization optics, beam splitters, electro-optical modulator, optical isolator, and photodetectors (c) video camera with adjustable lens to view atoms in vacuum chamber (d) photodiode with focusing lenses to collect fluorescent light from the MOT (e) triggered CCD camera (Allied “Guppy” camera) controlled by LabView program and used to measure atom number and distribution (f) hand-held IR viewer, used for alignment and checking for stray beams of light (g) IR viewing cards, which fluoresce visibly when exposed to IR light, used for aligning optics (h) two heated rubidium vapor cells (i) laser saftey goggles, to be worn when the curtain around the table is open
- Instrumentation setup at the work station (a) Digital oscilloscope (b) SRS DS345 Function Generator Click here to watch an instructional video (c) “DAVLL Error box” which houses a subtraction op-amp circuit (d) “MOT Laser Feedback Signal Processor” which is the two-branch electronic feedback circuit for stablizing the laser frequency (e) Computer with LabView VIs and a National Instruments I/O block
- Other equipment near optical setup (a) 50 A current supply for MOT coils (b) Uniblitz optical shutter controller (c) Power supply to heat single-pass Rb vapor cell (always on) (d) Heater and temperature sensor for DAVLL cell (e) Voltage Controlled Oscillator for generating microwave signal (f) GHz-range frequency counter
9 Experimental Setup
9.1 Standard Operating Procedures (SOP)
- Note you need 80 PSI water pressure. Look at the pressure meter on the south wall behind the computer and see that is at 80 PSI. If it is not, see the staff immediately.
into the laser, in which case the staff may want to adjust the optical isolator. A λ/2 waveplate before the isolator rotates the optical polarization so as to match the input polarizer of the isolator.
- A pickoff beam-splitter sends some of the light toward the rubidium spectroscopy system.
9.2.2 MOT optics
- Continuing on the main optical path, the electro-optical modulator (EOM) is a non-linear optical crystal placed within a tuned microwave resonator. A resonant microwave signal creates a strong time-varying electric field that distorts the crystal and varies its index of refraction. The laser beam, passing through that varying index material, becomes phase modulated at the frequency of the microwave input. In this manner, we add frequency sidebands to the laser, shifting some of the laser power (a few percent) to a frequency that will repump atoms on the repumping transition. The EOM crystal is birefringent, and its refractive index varies only for one linear polarization. The waveplate after the isolator rotates the polarization appropriately. Further details on this EOM are available in the EOM 4431 Data Sheet. You shouldn’t need to adjust the EOM, but you may need to check the optical alignment through the EOM (see below).
- Several lenses act as a telescope to expand and circularize the beam. The beam should be aligned through the center of and parallel to all these lenses. It may be that the lenses themselves are misplaced. In this case, one may have to remove the lenses, direct the laser beam along the desired beam path, and then replace the lenses so that they are centered with and with surfaces normal to the laser beam.
- A variable iris sets the diameter of the laser beams. Using the IR viewer and viewing the input face of the iris, you should see that the laser beam is reasonably well centered on the iris.
- We use half-wave plates and polarizing beam cubes to split the optical power between the different MOT beams. The H/V splitter divides between the horizontal and vertical beams, while the X/Y splitter divides between the two horizontal beams.
- On each of the three MOT beams, light passes first through a quarter-wave plate. When rotated to the correct position, this waveplate converts the incoming linear polarized light to circular polarization of the correct helicity for the operation of the MOT. After passing through the vacuum chamber, the beams pass another quarter-wave plate and are retro-reflected.
- The many mirrors in the optical path are placed there intentionally so that the optical system can be adjusted to match its many constraints. For example, we highlight two mirrors (M1 and M2) before the EOM. These two mirrors are used to align light through the EOM. This alignment must satisfy four constraints: we require that the beam enter the EOM near the center of the input facet (a specific location in 2D, giving two constraints) and exit near the center of the output facet (two more constraints). The two mirrors before the EOM have four degrees of freedom - the horizontal and vertical tilts - matching the number of constraints. These mirrors should be aligned iteratively to satisfy the alignment constraints, a procedure known as “walking the beam.” [15]. This mirror arrangement is known as a “dog-leg,” and is repeated throughout the optical setup.
9.2.3 Rubidium Spectroscopy Setup
Now we return to the optical setup where a rubidium vapor is probed in order to determine the frequency of the laser with respect to the rubidium resonance lines.
- Following the beam pickoff, light is divided again into two beams.
- The first beam passes through a glass cell containing a dilute Rb vapor before being sent to photode- tector PD2. In this arrangement we obtain Doppler-broadened features that mark frequencies within the rubidium D2 optical spectrum. We use these features as frequency markers by which to interpret the error signal obtained from PD1a and PD1b.
- The second beam is used for the Dichroic Atomic Vapor Laser Lock (DAVLL) setup [16]. A λ/ 2 waveplate and a polarizing beam splitter cube are used to divide the beam along two separate paths, steered by several independent mirrors. The beams propagate side-by-side, parallel to one another, through the heated Rb vapor cell. The cell is placed within a couple of strong permanent magnets, which apply a field along the optical axis. Before entering the cell, the beams both pass through a λ/4 waveplate, which endows the two beams with opposite ellipticity. The magnitude and sign (σ+^ vs. σ−) of the ellipticity is determined by the angle of the rotatable waveplate. The beams are directed onto two separate photodetectors, PD1a and PD1b. The photodetector output is sent to the instrumentation rack where each can be viewed separately on the oscilloscope. The DAVLL error box takes the difference between these signals and inputs it into the feedback circuit.
9.3 Vacuum System
Figure 7: Vacuum chamber details.
The MOT is created at the center of an evacuated, octagonal vacuum chamber graced with many glass viewports to allow laser light to be directed at the atoms, and surrounded with electromagnets to create the requisite magnetic field. Follow along as we describe the elements of the vacuum apparatus, illustrated in Figure 7.
- You will be using a getter to supply the MOT cell with rubidium. Within this getter there is a chemical compound that contains rubidium. Current run through the getter causes the getter to heat up owing to resistive heating. At a high temperature, the compound releases rubidium, along with several other gases, into the vacuum chamber. Once released from the getter, rubidium atoms will remain within the vacuum system for several days, residing most of the time on the walls of the chamber, and occasionally flying through the vacuum chamber. After several days, the rubidium atoms find their way to the ion pump where they become absorbed for good. The most reliable means of determining whether the chamber has a sufficient vapor pressure of rubidium is to operate the laser system and to scan the laser frequency very slowly across the rubidium resonance lines. For example, you might use the SRS DS345 to output a low frequency (0.1 Hz or so) sine wave, input that sine wave into the laser lockbox and use it to scan the PZT voltage so that the laser scans across the right frequency range. Viewing the inside of the chamber with the video camera, you should see dim fluorescence along the entire MOT laser beam path when the light is scanned across the Doppler-broadened resonance lines. If see no signs of rubidium vapor (you can ask a staff member just to be sure), you may need to replenish the chamber with rubidium. For this, you turn on the getter power supply and run about 5 amperes of current through the getter. Keep scanning the laser across resonance. Within 10’s of
Figure 8: Schematic of the servo controller. Input: A bias voltage is taken as the sum of an externally provided voltage and an internal variable voltage and is then subtracted from the detector input. Buffered monitors give the detector voltage before and after that subtraction. PZT branch: Following a variable voltage divider, to set the overall PZT feedback gain, the signal is sent through a circuit that can flip its sign. Next, an op-amp with variable input resistors and feedback capacitors determines the PZT feedback gain. A switch selects between the direct output of this op-amp, ground (switching off the PZT gain), or a notch-filtered (and inverted) version of the op-amp output. The voltage is then summed with the external sweep and a manually dialed offset voltage. Current branch: A two-op-amp circuit establishes the gain settings for the current feedback, with a rotary dial establishing three different gain settings. The signal is sent through another amplifier with variable gain. Following the current gain on/off switch, the signal is then added to the external sweep and output.
1-3). The goal of the second portion is to produce a stable MOT (Days 3-4) and provide qualitative and quantitative assessments of its characteristics (Days 4-5).
10.2 Task 1: Understanding Your Laser and Vacuum System
Your first task is to familiarize yourself with the equipment. As you read through the following description, you are asked to identify and start working with the various experimental components.
Before you leave each day, make sure to review the MOT equipment list (below) for details on which devices should be turned off and which should be powered on. This is incredibly important, as failure to turn off some equipment could damage the system permanently.
LEAVE ON THE FOLLOWING EQUIPMENT:
- Rb small Cell Heater power(under table)
- Ion Pump controller (under table)
- Ion Gauge Controller (under table, pressure should be about 4 × 10 −^8 torr)
- VCO Box (above table)
- Rb DAVLL Cell heater power (above table)
- Cold Trap Power (above table)
10.2.1 MOT Optics To do:
The optical setup for this experiment is, at first glance, rather complex, comprising many lenses, mirrors and other optical components, and possessing very many knobs with which to adjust and tune the optics.
Figure 9: Diagram of the pins of the vacuum feedthrough system and their corresponding Rb getters. The open circles represent pins that are connected, while the solid circles are not connected to any getters.
To understand the role of and relation between all these components, it is best to use an IR viewing card and to follow the path of laser light through the apparatus.
As you go through the optics and learn about what all the components do, you will be tempted to tweak the setup and see what happens. You should feel free to do so, but it would be wise to take note of what you are doing, and to return the setup to its original configuration when you are done with your tweaking, at least until you feel very confident that you know you are doing the right thing (say on the last day or two of the lab). Otherwise, you will find yourself trying to improve the optical setup but only making it more misaligned and poorly performing.
- Measure the optical power along the different beam paths. Repeat these measurements throughout the experiment to diagnose problems as they arise.
- At what frequency should the EOM be driven? Use a frequency meter to monitor the pre-amplifier microwave signal to see that the drive frequency is appropriate. Note also that the EOM has a narrow resonance; if you send in a microwave signal at the wrong frequency, that signal is reflected and directed, after attenuation, to the post-amplifier port of the microwave signal box. A hand-held frequency meter (a little black box from Elenco) provides a rough measurement of that reflected power (look for the signal bars below the frequency reading... and don’t worry about the frequency reading, as it’s outside the range for which the Elenco device is reliable). Tune the EOM input frequency to minimize this reflected power and note the center and width of the EOM resonance. If the EOM resonance seems to be at a microwave frequency far from what you need for the MOT, the EOM might need tuning. Ask a staff member for help.
[NOTE: As of April 13, 2010, the following settings of the rotatable quarter wave plates should give the proper circular polarization for a MOT: X-axis, rotation stage at 20 with numbers facing the incident beam; Y-axis, rotation stage at 268 with numbers facing the incident beam; Z-axis, rotation stage at 0 with numbers facing up]
Checkpoint Power:↑^ How does the power coming from each output port of the beamsplitter change as the preceding waveplate is rotated? Explain this quantitatively.
Checkpoint Two Quarter-Wave Plates:↑^ Explain how the two quarter-wave plates on the chamber level MOT beam path should be adjusted to provide the correct helicities for the op- eration of the MOT. What happens to the light polarization when the waveplates are rotated? Why is there no rotator on the second waveplate?
- PZT CAPACITOR: A four-position dial varies the capacitor on the feedback branch of the op-amp.
- RESET: Switches the low-frequency PZT feedback between being an integrator and having propor- tional gain. Down means the integrator is off.
- BYPASS/OFF/NOTCH: There is a notch filter to extinguish the response of the PZT feedback around the resonance frequency of the PZT (around 2.4 kHz). This is a three-pole switch, for which the settings are: up = notch is bypassed, PZT feedback is on; middle = PZT feedback is off; down = notch is used, PZT feedback is on.
- OFFSET: You can add a constant voltage to the PZT output, controlled by the offset knob and switch.
Current feedback branch:
- CURRENT RESISTOR: A three-position dial that controls the magnitude of the current gain.
- CURRENT GAIN: Controls the current gain.
- CURRENT GAIN SWITCH: switches the current gain on/off.
Sweep:
- SWEEP GAIN: Varies the strength of the sweep.
- SWEEP SWITCH: A three-pole switch that selects whether to send the sweep input onto the current modulation (up), the PZT modulation (down), or to neither output (middle). NOTE: Even in the middle position, there is a small (∼part in a thousand) contamination of the sweep input onto the PZT and current modulation that can affect the stability of the laser. When you’re not using the sweep, you might want to disconnect the sweep input or at least set the amplitude of the sweep to zero.
10.3.3 Outputs
- PZT MOD: Control signal sent to the laser controller through a 10:1 voltage divider to vary the PZT setting in the laser head.
- CURRENT MOD: Control signal sent to the laser controller to vary the current supplied to the laser.
- DETECTOR MONITOR: A low-pass, buffered replica of DETECTOR INPUT. When the laser is locked with the integrator, you can read this signal to determine what is the laser frequency according to your prior calibration.
- BIASED MONITOR: A low-pass, buffered replica of the error signal after the analog INTERNAL BIAS and EXTERNAL BIAS have been subtracted out. When the system is locked with the integrator, this output should be near zero.
10.3.4 Generating the error signal
Observe the Doppler-broadened absorption spectrum:
- Input a low-frequency sweep (triangle wave, 10s of Hz) from the SRS DS345 generator into the SWEEP INPUT port of the laser controller and direct the sweep (using the front-panel switch) to the PZT output. We use a triangle-wave so that the variation in the PZT voltage is linear in time, making it easier to interpret the signals on the scope. Be mindful that the PZT will ring slightly at the ends of your triangle-wave sweep; we mitigate that problem somewhat by sweeping very slowly.
- Now monitor the output of the spectroscopy setups on a scope as you vary the offset voltage, either on the servo controller or the laser controller. For this, you may want to use the DS345 SYNC output to trigger the scope.
- Expand the sweep range so that you see four broad dips in the transmission through the spectroscopy setup (PD2). The hyperfine splitting of the excited state is unresolved for the Doppler broadened signals. Look up [13, 6] and identify these with the four ground-state hyperfine manifolds of 85 Rb and (^87) Rb. Note the frequency splitting between these Doppler-broadened absorption lines. You can now monitor the PZT MOD signal on the scope (using a BNC Tee), and thus make a first determination of the low-frequency transfer function (MHz/V) of the PZT controller. Later on, when you focus on the DAVLL error signal right around the line used for laser cooling, you will use this transfer function to know how to relate the voltage of your error signal to the frequency offset of the laser.
Figure 10: A sweep of the 4 Rb spectrum lines as will be seen on the scope along with the sweep of the function generator. Notice the mirroring on the down sweep.
Checkpoint Four Peaks:↑^ Once you get your response from the photodetector as the picture shown above show your GSI the signal on the scope and point at the four peaks that correspond to the two different states of Rb^85 and Rb^87 respectively (don’t forget to mention which transition is which).
Note that the digital storage scope used for this experiment is connected to a computer, so that you can record data for analysis and your lab report.
Obtaining the DAVLL signal:
- Turn on DAVLL heater and leave it on. The heater should reliably supply rubidium into the cell at 1 volt and 4 amps, slight adjustments should not be necessary. Do not exceed 5 Amps without consulting the laboratory staff.
- Narrow the sweep onto the 85 Rb F = 3 and the 87 Rb F = 2 absorption lines. You should see the rubidium fluoresce within the beam paths on the video monitor. Examine both the spectroscopy signal (PD2) and the DAVLL signal (PD1a-PD1b) simultaneously. Now, block each of the two DAVLL- setup photodiodes in turn. You should see the Rb-cell absorption lines for σ+^ and σ−^ laser light, respectively (recall that you’re looking at the output of a difference op-amp circuit, the DAVLL error box, PD1a-PD1b signal). Ignore this next sentence: Notice that the line centers of these different absorption lines are shifted from the field-free lines seen in the saturated absorption cell. From this difference, determine what is the magnetic field inside the DAVLL vapor cell.
- Now allowing light into both PD1a and PD1b, you should see the DAVLL error signal. Explain why it has the form that it does.
