Where does one start?

Here is a chatty overview of the construction and debugging of the experiment. We have spent a considerable amount of time doing things wrong over the last ten years, and we hope to enable you to shortcut most of that. This overview also serves as a sort of annotated table of contents to Heather Lewandowski's long JLTP article. Unless otherwise indicated, section numbers refer to the relevant sections of Heather's JLTP article, and citations refer to other publications, cited at the end of the JLTP article, which may provide useful instruction.

1. To get going, order (or construct [17,28,22]) the three lasers described in Section 3, and set up the necessary saturated absorption spectroscopy [18] to measure their frequencies and the servo circuitry [24] to control their frequencies. Order and set up mirrors, lenses, fibers, polarizers, optical isolators, density filters and associated mounts and posts necessary to control the alignment, polarization, diameter and spatial quality of the various laser beams for cooling and imaging the atoms.

2. In parallel with the optics alignment, construct, assemble and debug the vacuum chamber described in Section 4. Ideally by the time the chamber is first being pumped down, there will be at least one laser operational and able to scan back and forth over an absorption line, since observing the aborption on a laser beam passing though the MOT cell is the easiest way to know if the getters (Section 4.1) are working as they should. Sometimes it is necessary to zap the getter current up very briefly to a very high value (say 100% higher than normal operating current) to burn a layer of crust off them before they emit rubidium. You'll really want to know when the rubidium starts to come out because once the crust is gone, you can burn through a whole getter's worth of rubidium (and coat the inside of your glass cell with a fully opaque silvery sheen) in a few tens of minutes.

3. While waiting on the delivery of parts for steps 1 and 2, above, start setting up the electronics (Section 10) for computer control of the experiment. We have deliberately included relatively few details on this topic. In our experience, every experienced bench-top experimentalist thinks that he or she already knows the best way to implement a computer interface, and rarely welcomes advice on this topic. On request we will make available [24] (but will not provide support for) the under-documented LabView files we use to run our experiment. If nothing else, it will give a reasonable indication of the overall allocation of the various lines of TTL control lines to the various experimental functions.

4. Purchase and install the linear track (Section 6.3) that will move the quadrupole magnetic coils (Section 5) (which serve double purpose as the MOT coils and as the magnetic coils for a temporary quadrupole magnetic trap for transporting atoms from one chamber to another). Fabricate the coils, mount them on the track's slide, and set up the current supply and current servo (Section 5).

5. Set up and align the optics for the MOT [16,19], and turn it on! Set up the optics for collecting the fluorescence from the MOT, and try to figure out how many atoms you are collecting (Section 5.1, 5.2). The behavior tends to improve over the first two or three weeks after the vacuum system is first baked out. We think the getters gradually coat the inner surface of the MOT chamber with a few monolayers of rubidium (this surface coating is completely transparent), and the percentage of junk emanating from the getters gradually goes down as well.

6. Time to unpack that digital camera, plug it into the auxiliary computer you will be using to acquire and analyze images, set up an imaging lens, and see if you can take pictures of the MOT cloud (Section 6.2). You'll need this to optimize the behavior of the CMOT, and of the transfer of the atoms from the CMOT to the quadrupole magnetic trap. The temptation is to collect a large number of images under a variety of conditions, and then analyze them off-line, perhaps the next day. We have found that in order to make rapid progress it is much better to incorporate in the program that operates your camera a simple 2-d gaussian surface-fit routine that determines in real time (ie, the fit parameters for one image are displayed before the next image is acquired) the x- and y-widths of the cloud of atoms and its peak intensity.

7. This would be a fine time to set up your experimental control software. Make it run in a continuous loop -- set the lasers and quad coils to the MOT values; fill up the MOT for ten seconds; squeeze the atoms in a CMOT; then, click, off go the lasers and you pop the atoms in the magnetic trap; let the atoms sit in the trap for a while; finally, flash!, turn off the quadrupole magnetic trap, briefly strobe on the MOT beams, and acquire a digital image of the atoms in the magnetic trap (or more precisely, the atoms as they were just after they left the magnetic trap) (Section 6). Then loop back around again, every 40 seconds. Set up your loop so that each time through the loop you increment the time spent in the magnetic trap. As each image comes in, note the product of the x-width, the y-width and the peak intensity. This is roughly the number of atoms in the cloud after the particular length of time in the trap. What's the lifetime of the atoms in the quadrupole magnetic trap as it sits in the MOT cell?

8. At this point, is the experiment behaving not at all the way you expect, as you vary the various parameters of the MOT, the CMOT, etc? On many occasions, we have caught ourselves spending too much time sitting in a comfy chair, naively believing the view of the world we get from our computer monitor. Get on up, arm yourself with a digital storage 'scope, a small pick-up coil, and a photo diode, and find out when the various magnetic fields and laser beams are really turning on and off. The timing of various steps (particularly during transfer from MOT to CMOT to magnetic trap, and during imaging) can be critical at the sub-ms level. Mechanical shutters (Section 3.2) have time lags and magnetic coils have inductances. Bear in mind also that while LabView is in principle willing to sequence your control voltages at your required level of temporal precision, it is allowed to do so after your computer's operating system has determined that there is absolutely nothing else the operating system itself would prefer to do (Section 10). Bear in mind also that common failure modes of mechanical shutters include sticking open, sticking closed, or "bouncing" -- reopening for a few ms after closing.

9. OK, let's take the atoms on a ride. After you have the atoms in a magnetic trap, let the linear track carry the atoms down through the conduction-limiting apertures into the science cell, then turn around and bring them right back to the MOT cell (Sections 4, 6). Image as before. Don't see anything? You'd like to have your experiment control software be flexible enough that in a few minutes you can set up the track to carry the quadrupole coils only a fraction of the way down to the science cell. You'll soon be able to figure out where the atoms are being lost. Are they going missing just as they pass through one of the two apertures? You'll need to tinker with the layout of the track, or perhaps adjust the average height of the two coils. On the other hand, maybe the atoms are vanishing suddenly, at some point still within the big glass MOT cell. Maybe just as the atoms are dragged across that spot, they can look out of your light baffling and see a big splotch of stray laser light on the wall of your lab (Section 6.3). On the other hand, if the atoms disappear always at a particular spot inside a stainless steel tube, recall that sometimes the welding process can turn a small patch of nominally nonmagnetic stainless steel into a ferromagnet. Pause for varying lengths of time as various spots along the way, to map out the magnetic trap lifetimes, and thus the quality of your ultra-high vacuum, or the quality of your shielding from stray light.

10. Vacuum and stray light under control? Now spend a happy week or three peaking up the transfer of atoms from the MOT into the quadrupole magnetic trap (Section 6.1, 6.2). Your goal is to have lots of atoms and as large a possible a collision rate in the magnetic trap.

11. Assemble your Ioffe-Pritchard (IP) magnetic trap (Section 6.4); verify, with a magnetometer probe, that the magnetic field profile within the trap is about what you hoped it would be; measure the resistances of all the coils carefully so that the later you will be able to quickly determine if an accidental coil overheating has led to an electrical short; tie the rf coil onto the science cell (Section 7.1); and then slide the IP assembly over the end of your glass science cell. There is very little clearance between the inner diameter of the trap assembly and the outer diameter of the glass cell. As you bolt the trap to its mount, it's really easy to snap the fragile glass science cell right off; the rapidly venting vacuum chamber will aspirate glass shards and other detritus, and it may be six weeks before you get back to this step to try again. It's a good idea to practice this step a few times with a hollow glass tube the same diameter as your science cell. This will give you also the opportunity to insert a tiny pick-up coil into mock up glass cell, to the place where your atoms will be, and get a rough feeling for the efficiency of your rf coil at various frequencies.

12. Now once again load atoms into the quadrupole trap and let the linear slide move the quadrupole coils down and around the IP assembly. The clearance between the inner surfaces of the quadrupole coils and the outer diameter of the IP assembly will be a little tight, but it is nothing one needs to check on ahead of time as we have found that the ground-ball screw track is powerful enough to shear off any protruding materials. On a related topic, be sure to develop a procedure such that the moving track is positively disabled before one does any work that involves having fingers or hair near the path of the moving coils. If you are using permanent magnets in your IP trap, you will need to slow the progress of the slide down to a crawl as the atoms enter the fringing fields of the permanent magnets and are heavily compressed. Work on optimizing the transfer into the IP trap (Section 6.5). At this point you are still dragging the atoms back down to the MOT cell for imaging, so you do the transfer in reverse order to go back to the quadrupole trap. Whatever loss in atom number or collision rate you see, remember you are really only doing half that badly, since in operation you will be leaving the atoms in the IP trap for evaporation. For now, set the currents in the axial coils of the IP trap so that you figure to have a longitudinal bias field of about 10 Gauss. This rather large value ensures that the bias field won't actually change direction anywhere. Later when your are able to image atoms in the IP trap you can feel your way down towards lower bias fields.

13. To get started on making evaporation work [20] (Section 7) turn on the rf and see if you can get rid of some or all of the atoms while they are in the Ioffe-Pritchard trap. As a place to start, try sweeping down across the entire relevant frequency range. You'd like to see most of the atoms vanish. At what frequency should you start? Well you have already measured the temperature of the atoms in the magnetic quadrupole trap back at step 10 above. You know the gradient strengths of your IP trap. Assume (dubiously) that the transfer from quadrupole magnetic trap to IP trap is fully adiabatic and calculate the expected initial temperature in the IP trap. Multiply by Boltzmann's constant, and by six, and divide by Planck's constant, and you will be in the right range. Don't worry if you can't get to quite that high a frequency. For the lower end of the sweep, take your expected longitudinal bias field and multiply by 700 KHz/Gauss. Take a series of shots in which you stop the rf ramp at various points short of the final frequency. Map out the number of atoms remaining as a function of that final frequency. If you see sharp features in this curve, you may have discovered unwelcome resonances in your rf circuitry, or you might have learned that there is something special about, say the particular frequency of 20 MHz, such that when your rf synthesizer changes from from 20.01 MHz to 19.99 MHz, it dips precipitously down to 10 MHz for a few milliseconds before recovering to the desired value.

14. Play around a little with some evaporative ramps (Section 7.2). Don't worry if you can't get too cold -- the process of moving the atoms back to the MOT region will prevent you from seeing particularly cold clouds. In fact, if the atoms get too cold you will lose them through spin-flips at the field null at the center of the quadrupole trap as the atoms move back down to the MOT region. Once the images you are collecting back in the MOT cell are convincing you that you are getting at least some cooling, it's time to set up absorption imaging in the science cell (Section 8). Move the camera down to the other end of the vacuum system, and line up the probe beam through the IP assembly, through the cell, back out through the IP assembly, through the objective lens, through a secondary lens, and into the camera. If evaporation is starting to work, the cloud will actually be easier to image once it has been cooled by a factor of ten or twenty. The optical depth of the cloud gets larger and the effect of the field gradients is smaller.

15. You are just about there. You will find that it is hard to focus the camera without a really cold cloud of atoms to look at, and hard to get the atoms really cold when the camera is far out of focus. Optimization of evaporation (Section 7) and imaging (Section 8) is often an iterative process. In Section 8 we describe an elaborate method for getting high-accuracy images in the fields of the permanent magnets; this will not be relevant if you are using electromagnetic coils to generate the transverse fields in your IP trap. In any case by this time you have earned the right to a little immediate gratification, so go look for a BEC! Try just jumping the IP bias field up to as large a field as you can reach. The cloud will expand in the radial direction, and you can calculate about how long it will take to reach its outer turning point. Then just image on an F=1 to an upperstate transition (you'll need to calculate the Zeeman shift to know where to look in frequency space). The atoms will be optically pumped into a dark state soon enough, but you should be able to see them if you image with a short, low-intensity laser pulse. When one is imaging in this way, the BEC transition is marked by the appearance of a two-component density profile, most easily seen by integrating the density profile in the radial direction and looking at the axial distribution.

16. Congratulations on your condensate! Your next priority depends on your particular scientific and technological goals, but you will almost surely want to spend a few weeks working on optimizing the number of atoms in your condensate, and learning to better understand the behavior of your imaging system. For most applications, the reproducibility of condensate number is at least as important as its average value. With some work, you can expect to have a condensate number variation of less than 10% rms shot-to-shot, at least over the short term. Arrange for the evaporative ramp to end just at the critical temperature. Do the images fluctuate shot-to-shot between large numbers of atoms with no condensate on the one hand and small numbers of atoms with a condensate on the other? Then you need to work on the stability of the longitudinal bias field in your IP trap. But that is not the only possible culprit. End the evaporative ramp at a point at which you typically see a small condensate and a large noncondensed cloud. Shot-to-shot, do you see the ratio of condensate to noncondensate atoms remain constant, but the total number of atoms fluctuate? Then you don't really have irreproducibility in your atom sample at all -- the irreproducibility is in your imaging, probably shot-to-shot frequency fluctuation of your probe laser, or perhaps timing jitter in your shutters. Or perhaps instead you see the same temperature and number in your thermal cloud each shot, but widely varying number in your condensate? The problem may start way back with inconsistent number of atoms in your MOT fill, or in the details of the MOT-CMOT-quadrupole trap transfer.

17. You can get a very nice overall check on the overall accuracy of your image acquisition and analysis procedure (Section 9) by verifying that the total number of atoms in the trap, the temperature of the noncondensed atoms, and the condensate fraction is consistent with the predictions of thermodynamics. A second overall check with somewhat different dependencies of potential systematics is to verify that the spatial extent of the condensate is what is predicted by simple mean-field theory, given the measured number of atoms in the condensate fraction. See sections IV and V of "Theory of Bose-Einstein condensation in trapped gases" by Dalfovo F, Giorgini S, Pitaevskii LP, Stringari S Rev. Mod. Phys. 71, 463-512 (1999). Achieving accuracy at the 30% level, referred to number of atoms, or at the 5% level, referred to spatial extent of the atom cloud, is doing pretty well.

18. When it works, drop us a line [24]. If it doesn't work, let us know that, too. We may write an updated version of this paper after collecting some reader feedback.