The Making of "Squeezed States in a Bose-Einstein Condensate"

Yesterday's write-up of my Science paper ended with a vague promise to deal some inside information about the experiment. So, here are some anecdotes that you would need to have been at Yale in 1999-2000 to pick up. We'll stick with the Q&A format for this, because why not?

Why don't we start with some background? How did you get involved in this project, anyway? I finished my Ph.D. work at NIST in early 1999, graduating at the end of May. I needed something to do after that, so I started looking for a post-doc by the don't-try-this-at-home method of emailing a half-dozen people I knew were doing interesting work, and asking "Do you have any post-doc spots available?" (The six were: Wolfgang Ketterle at MIT, John Doyle at Harvard, Dave Weiss at Berkeley (now at Penn State), Thad Walker at Wisconsin, Tom Gallagher at Virginia, and Mark Kasevich at Yale. I actually did a semi-formal application for Ketterle, because an email had gone around about the possibility of a post-doc there; the others were just cold emails.) Mark was the only one who had a job open (though I got one "I wish you'd asked three months ago, because I would rather have hired you than the guy we did get," which was kind of nice), and it sounded like an interesting project, so I took the position. Which worked out really well, because Kate got into Yale Law School, so we were able to continue living in the same city...

Other than this being the only job available, what drew you to the project? BEC was still relatively new at that point, and a lot of the experiments that people were doing with it seemed to be just using the condensate as a big clump of atoms. They were studying things that were basically single-atoms physics, where you were just mapping out the wavefunction by taking a picture of a million individual atoms.

There were a few experiments using the weirder quantum properties of the BEC state-- the NIST group was doing a four-wave mixing experiment at the time, and out in Boulder they were starting to look at vortices-- and this was in that vein. The squeezed state results couldn't be obtained just by solving the Gross-Pitaevski equation, which was most of what people were doing at the time, and I liked that idea. I've always been a fan of weird quantum phenomena (doo doo, de-doo doo!), and the squeezed state stuff was right up my alley.

So, how did joining this project go? When I got to New Haven, basically nothing worked. Brian Anderson (now a professor at Arizona) had built the BEC apparatus as a grad student at Stanford, disassembled it and moved it across the country when Mark moved to Yale, then got it back together and did a really nice experiment on putting a BEC in an optical lattice. He had moved on to a post-doc at JILA, though, and things had slowly degraded to the point where the apparatus wasn't reliably making condensates, let alone putting them in lattices. I started in late August of 1999, and spent 6-8 months taking everything apart and putting it back together again. By June of 2000, we were reliably getting condensates in a lattice, and we spent the summer and early fall in intense data-taking. At one point, we were running around the clock, with me and two grad students (Ari Tuchman and Matt Fenselau, co-authors on the paper) taking eight-hour shifts in the lab until the apparatus exploded.

Literally exploded? Literally exploded. Part of it, anyway. I forget exactly how many fires we had, but it blew up at least four or five times before we got all the data we needed. By September 2000, we were ready to start writing things up. I remember it because I went to a conference in France in mid-September, and I had a draft of the squeezed state paper before I left.

The actual paper wasn't published until March 2001. That must've been some tough editorial process. No, we didn't submit it in September. I just had a first draft then. As is often the case, the writing and internal review process uncovered a lot of stuff that needed to be re-analyzed, and re-re-analyzed, and new data needed to be taken, and on and on. We submitted it in early December 2000, and it was accepted in February 2001.

That seems like kind of a long time. Yes and no. At the time, it felt to me like the slowest process in the history of slow processes. Three months isn't actually all that unreasonable a time to spend on writing things up, though, and I think I hold the all-time record for fastest publication out of the Kasevich group.

Why is that? Mark's a bit of a perfectionist, and wants absolutely everything to be nailed down before he'll send anything off. He also had a wide range of projects going on, and isn't a huge fan of the writing process generally. Getting him to read drafts of the paper and give me comments was kind of difficult. I ended up making a huge nuisance of myself, stopping by his office several times a day, interrupting meetings of other groups within the lab, and that kind of thing.

That sounds kind of dickish. Why so intense? Well, I was in the second year of my post-doc, and applying for faculty jobs. I had nothing to show from the project to that point, though, other than a handful of invited talks, so I really wanted a publication to bolster my CV. I knew this was going to be pretty big, and wanted to be able to list a Science paper on my applications. I ended up settling for "submitted to Science," and shipping out my applications in mid-December 2000, late enough that I missed a couple of deadlines. So I was kind of a giant ball of stress for the entire process.

You do realize that lots of people do multiple post-docs before getting a tenure-track job, right? And end up with less than a Science article on their CV's? Yeah, intellectually, I knew that. But I had come out of the Phillips group at NIST, where post-docs just didn't fail to get good jobs after two years. My view of things was kind of skewed. But look, this isn't about my arrogant job search, OK?

Fine. So, can you give an example of some stuff that came up during the editing process? Well, for example, one of the key points of the analysis ended up turning on a happy accident. We were trying to figure out how to address the inhomogeneous broadening problem beyond the ramp-up-ramp-down experiment, which is complicated enough that people were a little dubious about just that. At some point, I remembered, though, that in doing a different experiment-- looking at the dynamics of the squeezed states following a sudden change-- I had ended up having one of the students do a few runs where we held the atoms in the lattice for a long time at level where the state was a little bit squeezed, but not all that much.

I had glanced at the data from that, but was disappointed by the fact that the contrast of the images was kind of crappy, and didn't produce what I wanted regarding the dynamics, so I put it aside. During the writing-up, though, I realized that that showed exactly what we needed-- that when we started with a state that was a little bit squeezed, it stayed a little bit squeezed. If we'd been dealing with just messed-up phases from some technical glitch, that would've gotten worse over the hundred-odd milliseconds we held it for. That became one of the key points in the argument that we really had squeezing.

We also spent a week or so going back and re-doing that part of the experiment, when Mark learned that the whole thing turned on two data points from June.

OK, that's a nice bit of serendipity. Anything that went wrong during this process? There was a point in... late October, I think, when Mark talked to Subir Sachdev, a theorist at Yale, about the condensed matter version of this, and got really fired up to re-interpret everything in terms of a quantum phase transition from a superfluid state to a Mott insulator. There was a week or so when he wanted to basically scrap everything that we had written and start over on the whole thing.

I tried to run with it for a while, but could just see the whole thing unspooling endlessly into the future, and eventually insisted that we run with the original interpretation, to get the paper out. That was probably a mistake, in retrospect, in that the Mott insulator angle on this problem really took off a year or so later, and is the language everybody uses to talk about this stuff, now. Had we re-written things in that language, our paper might be better remembered.

You're bitter that you only have 540-odd citations? Not really, because the original Mott insulator stuff by Immanuel Bloch and Markus Greiner is a really spectacular experiment, and does some thing that are different. They used a 3-d lattice rather than the 1-d lattice we had, which meant that they had 1-2 atoms per site, and the effects are a lot cleaner. Our stuff was never going to be as sharp as that, no matter how we re-analyzed it, so we were better off getting it into print and staking out priority.

I do think that we probably had hit the Mott insulator transition, but we wouldn't've been able to prove it. For one thing, one of the factors we were using to convert the lattice depth to the parameters we needed to compare to theory was just wrong, but that error didn't turn up until a couple of years later. I think Ari nailed it all down when he wrote up his thesis, but I don't remember where my copy of that got to.

In my darker moments, I occasionally think that we ought to get more credit than we do for being first, but there's a reasonable case to be made that the regime we were working in is sufficiently different from Bloch and Greiner's stuff that they really deserve the credit. Also, they've continued to build on those results, where we really didn't, and that makes a big difference. And, really, it's kind of churlish to be bitter about what was by any reasonable standard a spectacular success.

So, once you submitted it, did anything interesting happen? Mark handled the communication with Science, so I don't know much about the editorial process. I don't remember the referee comments particularly, which suggests they were all perfectly reasonable. There was a tiny bit of drama when it turned out that I had made a mistake in normalizing the data for the cool images, but that was a cosmetic thing only, and we cleared it up on resubmission.

When it got accepted, we made a bid for the cover of Science, putting together the 3-d plot that's the "featured image" at the top of this post, but they had had enough of those by that time, and passed on it. We did get a nice news write-up with a dreadful headline, and were mentioned in the breakthroughs of the year article, so I can't really complain about that.

So, what happened after this got published? Well, the other thing we were working on with this system was the dynamics after a rapid change. We would ramp the lattice up to make a number-squeezed state, then drop the lattice down to a much lower level, hold for a while, and release the atoms to get the contrast of the image. When you do that, the system evolves in a way that causes oscilations in the number uncertainty-- you go from a number-squeezed state with low contrast to state that gives very high contrast. You can even, with the right choice of parameters, come up with a phase-squeezed state.

This was the thing we were really interested in, in some sense-- the process is basically analogous to sending a squeezed state of light into a beamsplitter, and is the first step toward doing squeezed state interferometry. And Mark's all about atom interferometry. We spent ages taking oscillation data, some of which I'll reproduce here from an old talk slide:

Oscillation of the interference contrast after a sudden change in the lattice.

Keep in mind, each point on that graph represents one five-minute date-taking cycle, not counting the analysis time, so that's close to three hours of work right there. But it looks pretty nice.

And yet, this isn't in the paper. So what gives? Well, we got tons of oscillation data, but interpreting it turned out to be a miserable slog. This was my one foray into doing theory for an extended period, months of grinding away at Matlab, trying to match the experimental data. We could mostly explain the frequency of the oscillation, and how it depended on the basic parameters, but there was this damping of the contrast oscilaltions that we couldn't quite figure out. And simulating it was a nightmare-- the experimental situation violated all of the nice simplifying assumptions you would like to make. If you only had two wells, the theory was easy, and if you had an effectively infintie number it was easy, but we had about a dozen, which is neither two nor infinite, and turns out to be a nasty problem. Which would be tractable if you had the same number of atoms in each lattice site, except we didn't, because the number of atoms dropped off to zero at the edges of the condensate, and again, rules out a whole bunch of simplifying approximations. I never really got anywhere with the simulations, and about the only thing I learned was that I shouldn't do theory.

So, nothing came of it? Not nothing, no. They kept poking at it after I left, and it eventually ended up as a Rapid Communication in Physical Review A (arxiv version). They eventually recruited a real theorist to do the simulations, and got satisfactory explanations for most of it. Mark and Ari moved on to other projects, though, so it wasn't a real high priority. The final publication came when I was up for tenure, and sent Ari email asking "Hey, whatever happened to that?" That prompted them to submit the final version, years after I left the group.

I think there's some cool stuff there, but it turns out to be way harder to work with than we appreciated at the time. Which is why it got pulled out of the squeezed state paper into its own thing. There's an outside chance that we could've made more of it, but I had gotten a job, and was coming down from being a giant ball of stress for about six solid months (and Mark and I were getting on each other's nerves), so it never came together. I suspect, though, that where it ended up is about as good as it was going to get, because Ari did a great job tying up all the loose ends, and it's just a messy, hard problem.

Any final comments? And keep in mind that this is already over 2500 words... Not really, no. It was a great experience in a lot of ways, and a miserable slog in others. I have to say, I've never felt smarter than I did when we put all this together-- that was a high point of my research career that I'm exceedingly unlikely to ever match again.