The unreasonable effectiveness of a toy model

As I've mentioned before, often theoretical physicists like to use "toy models" - mathematical representations of physical systems that are knowingly extremely simple, but are thought to contain the essential physics ingredients of interest.  One example of this that I've always found particularly impressive also happens to be closely related to my graduate work.  Undergraduate physicists that take a solid state class or a statistical physics class are usually taught about the Debye theory of heat capacity.  The Debye model counts up the allowed vibrational modes in a solid, and assumes that each one acts like an independent (quantum) harmonic oscillator.  It ends up predicting that the heat capacity of crystalline (insulating) solids should scale like T³ at low temperatures, independent of the details of the material, and this does seem to be a very good description of those systems.  Likewise, undergrads learn about Bloch waves and the single-particle picture of electrons in crystalline solids, which ends up predicting the existence of energy bands.  What most undergrads are not taught, however, is how to think about the vast majority of other solids, which are not perfect single crystals.  Glass, for example.

You might imagine that all such messy, disordered materials would be very different - after all, there's no obvious reason why glass (e.g., amorphous SiO₂) should have anything in common with a disordered polymer (e.g., photoresist).  They're very different systems.  Yet, amazingly, many, many disordered insulators do share common low temperature properties, including heat capacities that scale roughly like T^1.1, thermal conductivities that scale roughly like T^1.8, and particular temperature dependences of the speed of sound and the dielectric function.  To give you a flavor for how weird this is, think about a piece of crystalline quartz.  If you cool it down you'll find a heat capacity and a thermal conductivity that both obey the Debye expectations, varying like T³.  If you take that quartz, warm it up, melt it, and then cool it rapidly so that it forms a glass, if you remeasure the low temperature properties, you'll find the glassy power laws (!), and the heat capacity at 10 mK could be 500 times what it was when the material was a crystal (!!), and you haven't even broken any chemical bonds (!!!).

Back in the early 1970s, Anderson, Halperin, and Varma postulated a toy model to try and tackle this mysterious universality of disordered materials.  They assumed that, regardless of the details of the disorder, there must be lots of local, low-energy excitations in the material to give the increased heat capacity.  Further, since they didn't know the details, they assumed that these excitations could be approximated as two-level systems (TLSs), with an energy difference between the two levels that could range from zero up to some high energy cutoff with equal probability.  Such a distribution of splittings naturally gives you a heat capacity that goes like T¹.  Moreover, if you assume that these TLSs have some dipole-like coupling to phonons, you find a thermal conductivity that scales like T².  A few additional assumptions give you a pretty accurate description of the sound speed and dielectric function as well.  This is pretty damned amazing, and it seems to be a remarkably good description of a huge class of materials, ranging from real glasses to polycrystalline materials to polymers.  

The big mystery is, why is this toy model so good?!  Tony Leggett and Clare Yu worked on this back in the late 1980s, suggesting that perhaps it didn't matter what complicated microscopic degrees of freedom you started with.  Perhaps somehow when interactions between those degrees of freedom are accounted for, the final spectrum of (collective) excitations that results looks like the universal AHV result.  I did experiments as a grad student that seemed consistent with these ideas.  Most recently, I saw this paper on the arxiv, in which Moshe Schechter and P. C. E. Stamp summarizes the situation and seems to have made some very nice progress on these ideas, complete with some predictions that ought to be testable.  This kind of emergence of universality is pretty cool.

By the way, in case you were wondering, TLSs are also a major concern to the folks trying to do quantum computing, since they can lead to noise and decoherence, but that's a topic for another time....

String theory (!) and "bad metals"

I saw a remarkable talk today by Hong Liu from MIT, about quantum gravity and what it has to say about high temperature superconductivity.  Yes, you read that correctly.  It was (at least for a nonexpert) a reasonably accessible look at a genuinely useful physics result to come from string theory.  I doubt I can do it justice, so I'll just give the bare-bones idea.  Within string theory, Maldacena (and others following) showed that there is a duality (that is, a precise mathematical correspondence) between some [quantum theories of gravity in some volume of d+1 dimensions] and some [quantum field theories w/o gravity on the d-dimensional boundary of that volume].  This sounds esoteric - what could it be good for?  Well, we know what we think the classical limit of quantum gravity should be:  Einstein's general relativity, and we know a decent number of solutions to the Einstein equations.  The duality means that it is possible to take what could be a very painful interacting many-body quantum mechanics problem (say, the quantum field theory approach to dealing with a large number of interacting electrons), and instead of solving it directly, we could convert it into a (mathematically equivalent) general relativity problem that might be much simpler with a known solution.  People have already used this approach to make predictions about the strongly-interacting quark-gluon plasma produced at RHIC, for example.


I'd known about this basic idea, but I always assumed that it would be of very limited utility in general.  After all, there are a whole lot of possible hard many-body problems in solid state physics, and it seemed like we'd have to be very lucky for the duals of those problems to turn out to be easy to find or solve.  Well, perhaps I was wrong.  Prof. Liu showed an example (or at least the results), in which a particular general relativity solution (an extremal charged blackhole) turns out to give deep insights into a long-standing issue in the strongly-correlated electron community.  Some conducting materials are said to be "bad metals".  While they conduct electricity moderately well, and their conductivity improves as temperature goes down (one definition of metal), the way that the conductivity improves is weird.  Copper, a good metal, has an electrical resistance that scales like T² at low temperatures.  This is well understood, and is a consequence of the fact that the low-energy excitations of the electrons in copper act basically like noninteracting electrons.  A bad metal, in contrast, has a resistance that scales like T, which implies that the low energy excitations in the bad metal are very complex, rather than electron-like.  Well, looking at the dual to the extremal black hole problem actually seems to explain the properties of this funny metallic state.  A version of Prof. Liu's talk is online at the KITP.  Wild stuff!  It's amazing to me that we're so fortunate that this particular correspondence exists.

Climate change talk

This afternoon we were fortunate enough to have our annual Rorschach Lecture, delivered by Ralph Cicerone, president of the US National Academy of Sciences.  The subject was climate change and its interaction with energy policy, and unsurprisingly to anyone who isn't willfully ignorant, this was a scary talk.  The atmospheric CO₂ data, the satellite-based measurements of accelerating Greenland and Antarctic ice loss, the amazing pace at which China is building coal-fire power plants (roughly 1 GW of electric generating capacity from coal coming on line every 10 days), are all very sobering.  The planet doesn't care, of course, but it sure looks like the human species had better get its act together, and the only way that's going to happen is if we come up with an energy approach that is cheap compared to coal (that includes the possibility of making coal more expensive, of course, but how do you persuade China and India not to burn their cheap, abundant coal?). 

Ahh, Air China

Posting from International Check-in at Beijing International Airport....

I was actually supposed to get home last night, but Air China had other plans.  At least I have quite the story out of it.  I'd originally booked a 2 hour 45 min layover in Beijing, figuring that would be plenty of time.  However, our Hangzhou-Beijing flight was delayed 2 hours.  Then, the pilot made two go-arounds at Beijing, very bumpy (cue the airsick bags and retching noises from fellow passengers), each time getting w/in about 30 feet of the ground, before giving up (due to high winds, I guess), and we diverted to Tianjin.  In Tianjin they kept us on the plane on the tarmac out at the end of their runway for close to 4 hours.  At least the AC worked there.  They ran out of water, and then orange juice.  Finally, they refueled and flew the plane back to Beijing, arriving only 8 hours late.  At least I wasn't alone (two other americans on the flight in the same situation as me), and Air China did, after some convincing, spring for a hotel for the night.

Clearly the simplest possible explanation for this is that I'm destined to make some universe-shattering discovery in the future, the echoes of which are rippling backward in time to try to prevent my return to the US. 

Conference observations so far

This is a nice gathering of people, and the organizers have done a very good job.  More discussion would be nice - the program is very dense.  A few (not very serious) observations:

• I used to think that I was the only condensed matter physicist not working on graphene.  Now I realize I'm the only condensed matter physicist not working on graphene, iron pnictide superconductors, or topological insulators. 
• Chinese ring tones are different than US or European ringtones.
• One speaker inadvertently stumbled on a great, subtle psychological trick:  he used a font for most of his talk that is identical to the font (some Helvetica variant) used by the Nature publishing group for their titles and subtitles.  That font makes everything seem important :-).  He blew this aura of profundity it at the end, though, by switching to comic sans.
• The Chinese groups that have been charging on the iron pnictides must have enormous resources in terms of people and equipment - the rate at which they are cranking out material and data is remarkable.  US materials growers seem very undersupported by comparison.
  
• Laser-based angle-resolved photoemission, in its appropriate regime, is damned impressive.
  

In China this week

I'm off tomorrow for a week-long trip to China, to go to this workshop.  I've never been to China before, so this should be an interesting experience!  I may try to blog a little, but I don't know how internet access will work during the conference.  Hopefully the trip will go more smoothly than the travel arrangements beforehand.  If I ever hear Expedia's "on hold" music again, I may snap.

Update: The trip in was long but problem-free. Blogger access only works through VPN, thanks to the Great Firewall....

Fiber and CCDs

As you've all no doubt read by now, the 2009 Nobel in Physics was awarded to Charles K. Kao, for the development of truly low loss fiber optics (a technology that you're all using right now, unless the internet backbone in your country consists of smoke signals or semaphore flags), and Willard Boyle + George Smith for the invention of the CCD (charge-coupled device, which is the basis for all digital cameras, and has revolutionized spectroscopy).  

The CCD portion makes a tremendous amount of sense.  CCDs work by using local gates on a doped semiconductor wafer to capture charge generated by the absorption of light.  The charge is then shifted to an amplifier and the resulting voltage pulses are converted into a digital signal that can be interpreted by a computer.  The description given in the supporting document (pdf) on the Nobel website is very good.  CCDs have revolutionized astronomy and spectroscopy as well as photography, and the physics that must be understood and controlled in order to get these things to work well is quite rich (not just the charge generation process, but the solid state physics of screening, transport, and carrier trapping).

The fiber optic portion is more tricky, since many people have worked on the development of fiber optic communications.  Still, Kao had the insight that the real limitation on light propagation in fiber came from particular types of impurities, understood the physics of those impurities, guided a program toward clean material, and had the vision to see where this could all lead.  

Certainly there will be grumbling from some that these are <sneer>engineering</sneer> accomplishments rather than essential physics, as if having a practical impact with your science that leads to technology and helps society is somehow dirty, second-rate, or a sign of intellectual inferiority.  That is a terrible attitude, and I'm not just saying that because my bachelor's degree is in engineering.  Trust me:  some engineers have just as much raw intellectual horsepower as high energy theoretical physicists.  Finding intellectual fulfillment in engineering is not some corruption of pure science - it's just how some very smart people prefer to spend their time.  Oh, by the way, the actual will of Alfred Nobel refers to accomplishments that "shall have conferred the greatest benefit on mankind", and specifically mentions "the person who shall have made the most important discovery or invention [my emphasis] within the field of physics".

Finally, this provides yet another data point on just how transformative Bell Labs (and other remarkable industrial R&D labs, including IBM, GE, and others) really was in the physical sciences.  The withering of long-term industrial research will be felt for a long, long time to come.


 

Single atoms in semiconductors

One last post before the obligatory Nobel post tomorrow.

Recently, there has been progress in examining the electronic transport properties of individual dopant atoms in semiconductors.  There are several motivations for this.  First and probably foremost, with increasing miniaturization we are rapidly approaching the limit when the active channel in semiconductor devices will contain, statistically, only a small number of dopants; it makes sense to figure out how these systems work and whether they have any intrinsically useful properties.  Second, these systems are the ultimate small-size limit of quantum dots, even smaller than single-molecule transistors.  Third, since the host materials are extremely well-studied, and quantum chemistry calculations can handle the relevant volumes of material, there is the possibility of realistic, detailed theoretical treatments.  This paper is a great example of treating an individual phosphorus donor in Si as a quantum dot.  This other paper looks at a single arsenic donor, and can see Kondo physics involving the unpaired electron on the donor site interacting with the (valley degenerate) Si conduction electrons.  Very cool stuff!

The return of the embarassing news story.

As mentioned previously, the news story about NSF upper level staff surfing for porn while on the job is back.  This would be funny if it weren't so pathetic and sad.  Obviously this is inappropriate behavior, and NSF clearly needs to get their IT staff up to snuff, since it's certainly possible in a corporate environment to detect and stop this kind of activity.  Still, it seems unfair to single out NSF like this.  I'd be surprised if this didn't go on in all large, computer-heavy organizations at some rate.

First principles vs. toy models

One of the hot topics at the workshop I attended was the proper role of "first principles" calculations in trying to understand electronic conduction at the atomic and molecular scale.  In this business, there tend to be two approaches.  The first, which I call for lack of a better term the "toy model" paradigm, constructs models that are highly idealized and minimalistic, and you hope that they contain the essential physics needed to describe real systems.  An example of such a model would be the single-level Anderson-Holstein model of transport through a molecule.  Instead of worrying about all of the detailed electronic levels of a molecule and the many-electron physics there, you would concentrate on a single electronic level that can either be empty, singly occupied, or doubly occupied.  Instead of worrying about the detailed band structure of the electrodes, you would treat them as ideal electronic reservoirs, and there would be some couplings that allows electrons to hop between the level and the reservoirs.  Instead of considering all of the possible molecular vibrations, you would assume a single characteristic vibrational mode that "lives" on the molecule, and there would be some additional energy cost for having that vibration excited while there is an electron occupying the level.  While this sounds complicated, it is still a comparatively idealized situation that can be described by a handful of characteristic energies, and it contains rich physics.

On the other hand, one can consider trying to model a specific molecule in detail, worrying about the precise electronic and vibrational levels appropriate for exactly that molecule bonded in a particular configuration to a specific kind of metal electrode surface.  While this sounds in some ways like it's what you "really" ought to do, this "first principles" approach is fraught with challenges.  For example, just solving for the electronic levels of the molecule and their relative alignment with the electronic levels in the electrodes is extremely difficult in general.  While there are impressive techniques that can work well in certain situations (e.g., density functional theory), very often the circumstances where those methods work best (quasi-equilibrium, far away from resonances, in situations where electron correlation effects are minimal) are often not too interesting. 

It's interesting to watch the gradual convergence of these approaches.  As computing power grows and increasingly sophisticated treatments are developed, it looks like first-principles calculations are getting better.  One direction that seems popular now, as our condensed matter seminar speaker yesterday pointed out, is using such calculations as guidelines for correctly estimating the parameters that should be fed into the essential physics toy models.  Interesting times are on the horizon.

AAAS and advertising

I've received three pieces of fundraising advertising from AAAS in the last two days via US Mail.  This makes me wonder about a few things.  First, in this day and age, why can't they get a mailing database set up that can tell that Douglas Natelson and Dr. Douglas Natelson at the same address are actually the same person? Second, do they really think that I pay a lot of attention to bulk-mailed fundraising appeals? Third, how much money are they spending, how much energy is consumed, and how much pollution is generated in sending out these tree-killing mailings, when they claim to be environmentally conscious and already have my email address as a subscriber to Science? Fourth, this many appeals in one week smacks of desperation - is there something we should know? 

Curve fitting

Very often in experimental physics, we're interested in comparing some data to a physical model that may involve a number of unknown parameters, and we want to find the set of parameters that gives the best fit.  Typically "best fit" means minimizing a "cost" function, often the sum of the squares of the deviations between the model and the data.  The challenge is that many models can be very complicated, with nonlinear dependences on the parameters.  This often means that finding the optimal parameters can be very difficult - the cost function in parameter-space can have lots of shallow, local minima, for example.  The cost function may also be extremely sensitive to some parameters (the "stiff" ones) and comparatively insensitive to others (the "sloppy" ones).  In arxiv:0909.3884, James Sethna and Cornell colleagues take a look at this dilemma using the tools of differential geometry, and they propose an improvement to standard techniques based on geodesics on the relevant hypersurface in parameter space.  This looks really cool (if mathematical!), and I wish they'd included an example of an actual minimization problem that they'd done with this (instead of leaving it for an "in preparation" reference).  Any prospect for real improvements in nonlinear fitting is exciting.

Ahh, KLM.

Stuck in Schipol, forced to fly back to Houston via BRE-AMS-DET-IAH, since mechanical difficulties cancelled my early BRE-AMS flight (thus causing me to miss my AMS-IAH direct flight).  The other AMS-IAH direct flight on their schedule is really just a psychological torture device, since it's really a charter that's 100% business class and un-bookable except as a cash purchase (which would set me back $4K on top of everything I've already paid).

Could be worse.  There was another guy on the original BRE-AMS flight that got involuntarily rebooked through Paris.  After hanging out at the Bremen airport for four hours, he got to have his BRE-Paris flight also cancelled due to mechanical difficulties.

At least the workshop was extremely good.

Draconian ISP.

The ISP (netopsie) for my hotel here in Bremen, Germany has apparently decided to block access to all "blogspot.com" domains.  If I try to view my blog, I get redirected to a page that says "Banned Site.  You are seeing this error because what you attempted to access appears to contain, or is labeled as containing, material that has been deemed inappropriate."  Ironically, I can post new entries since that is done from a blogger.com page.   I can't view the blog, however, or see comments.  Idiots.  Makes me wonder what they find objectionable on blogs in particular, or whether they are complete puritans and block lots of stuff.

This week in cond-mat

Three quick blurbs from the arxiv this week.  I'm going to a workshop in Germany next week and have a bunch to do in the meantime, so blogging will likely be light.

arxiv:0909.0628 - Bocquet and Charlaix, Nanofluidics, from bulk to interfaces
This paper is an outstanding overview of fluids confined to the nanoscale.  I will definitely be referring to this the next time I teach my graduate course that touches on this topic.  Two of the central questions that comes up when thinking about fluids at the nanoscale are, when do large-scale assumptions about hydrodynamics (e.g., that fluid right at the walls of a container is at rest relative to the walls, even when the fluid away from the walls is flowing - the so-called "no slip" boundary condition) break down, and when does the continuum picture of the fluid (i.e., that fluid may be modeled as a homogeneous medium with some density, rather than a collection of strongly coupled particles) fall apart?  This article looks at these issues in detail, with many useful references.

arxiv:0909.0951 - Saikin et al., On the chemical bonding effects in the Raman response: Benzenethiol adsorbed on silver clusters
This one is of interest to me because of its relevance to some of the research done in my group.  Raman scattering is inelastic light scattering, where light can lose (or gain) energy to a molecule by exciting (or de-exciting) molecular vibrations.  It's been known for more than 30 years that the Raman scattering process can be greatly (many orders of magnitude) enhanced on nanostructured metal surfaces.  This happens for two reasons.  First, nanostructured metals support local plasmon modes, so that the metal acts like a little optical antenna, helping the molecule to "receive" (and "transmit") light.  This is called electromagnetic enhancement.  Second, there can be additional enhancing effects due to resonances involving charge transfer between the molecule and the nearby metal.  This latter effect is called chemical enhancement, and this paper takes a detailed look at how this can arise, considering specific configurations of molecules on Ag clusters.  It is very challenging to do calculations like this and get realistic results!

arxiv:0909.1205 - Martineau et al, High crystalline quality single crystal CVD diamond
I picked this one because (a) the fact that it is possible to grow high quality single crystal diamond by chemical vapor deposition is just plain cool, as well as of great technological potential; and (b) the x-ray topographs in this paper showing crystallographic defects in the crystals are very pretty.

If you're reading this, you're probably pretty net-savvy.

Perhaps this feature has always been available, but I just noticed the other night that Google Analytics can tell me stats about what kind of web browsers people use to access this page.  Far and away the number one browser used was Firefox (57%), followed by Safari (16%), Internet Explorer (15%), and Chrome (8%).  Interestingly, the breakdown for those accessing my group webpage was quite different, with IE having more like 30% of the total.  Very educational.  No one using lynx, though.

Two nanoscience tidbits

Since nearly everyone else in the science blogging world has touched on this (see here, here, here, here, and here, to name a few), I might as well do so, also.  Leo Gross and coworkers at IBM Zurich have used an atomic force microscope to do something incredibly impressive:  They have been able to image the bonding orbitals in individual pentacene molecules with better than atomic resolution, using the very short-range forces that contribute to the "hard core repulsion" between atoms.  Atoms tend to be attracted to each other on nanometer scales, even in the absence of strong chemical interactions, due to the van der Waals interaction, which comes from the fluctuating motion of their electron clouds.  At very short distances, though, atoms effectively repel each other extremely strongly, both from the Coulomb interaction (electrons don't like each other overly much) and the effects of the Pauli Exclusion Principle.  Gross and colleagues accomplished this feat by working in ultrahigh vacuum (around 10^-15 of atmospheric pressure) and at 5 K, and by deliberately attaching a single CO molecule to their conducting atomic force microscope (AFM) tip.  It's a heck of a technical achievement for AFM.  Atomic resolution has been demonstrated before, but this kind of sensitivity is remarkable.  (FWIW, I once heard one of the major coauthors, Gerhard Meyer, speak at a meeting about the same group's ultrahigh resolution STM work.  He seemed very low key about their obviously impressive achievements - amazingly so.  I hope he got excited about this!)

Also, a group at Berkeley has made a laser based on a CdS nanowire, and like the result mentioned last week, this gadget uses plasmons (this time in a Ag film) to act as an effective cavity.  Clearly using the extreme confinement of some plasmon modes to do photonics is going to be a growth industry.

Industrial R&D

I've felt for a long time that the current business climate, which punishes rather than rewards long-term research investments by companies, is misguided. When most stock is owned and traded by institutional investors and large funds who don't have any interest in holding particular companies for the long term, and when executive compensation massively overvalues year-over-year growth (because we all know that 40% annual growth in cell phone sales is sustainable forever, right? There's no such thing as market saturation, is there?), you end up where long-term investment is viewed by company boards as a misuse of resources. This article in Business Week makes some interesting arguments on ways to try and fix this. Unfortunately I think most of these ideas are not very compelling or likely. Norm Augustine had an interesting suggestion: scale the capital gains tax rate inversely with the amount of time one owns a stock. If someone holds a stock less than a year, tax the capital gains at 90%. If they own the stock 10 years or more, tax the capital gains at nearly 0%. Interpolate appropriately. The idea here is to set up a system that incentivizes long-term investment, which in turn is more likely to support industrial research. Hard to see how such an overhaul would ever get passed in Congress, though. I imagine the financial industry would crush it like a bug, since anything that slows down trading is viewed as interference in the free market, or, more cynically, interference in their enormous transaction fee profits.

How we fund grad students

As new grad students flood onto campuses across the US, I just got around to reading this piece in Science from a few of weeks ago about Roald Hoffman's idea for changing the way we support grad students in the sciences and engineering. Most S&E grad students in the US are supported by a mix of teaching assistantships (TAs), research assistanceships (RAs), and fellowships. A typical S&E grad student at an American university shows up and is supported during their their first year by a mix of university funds and pay for teaching. They then often make the transition to being supported as an RA by research funds obtained by their advisor through research grants. (Some remain as TAs - this is more common at large, public institutions with large undergraduate teaching needs.) Some relatively small fraction of S&E grad students are supported instead by fellowships, awarded competitively by agencies like NSF, DOE, DOD, NIH, etc. or by private foundations such as the Hertz Foundation.

Prof. Hoffman suggests that we should move to a system where all grad student support is fellowship-based. The idea is that this will (a) fund only the best students; (b) allow students much greater independence since an advisor will no longer be able to say "You have to do boring experiment #23 because that's what the grant that's paying your salary says we're going to do"; (c) result in better mentoring b/c faculty will no longer view students as "hands". Now, there's basically no way to see how such a drastic change in the system would ever happen, but it's worth looking at the idea.

As someone lucky enough to have a fellowship in grad school, I understand the appeal from the student side. Independence is great - it means that you and your advisor are freed from the stress of worrying that your grant won't get renewed when you're in year 3 of your program. It means that you are a free agent.

However, I think Hoffman's idea would be a disaster, for two main research-related reasons (not to mention the challenge of how you'd handle TA duties at large places that suddenly had many fewer grad students). First, there is little doubt that this would skew an already tilted system even further in favor of the top, say, 20 institutions in the country. Right now it's possible for good researchers at second tier universities to write grants, hire students, and do research. Imagine instead if the only source of student support were competitive external fellowships. It's all well and good to talk about overproduction of PhDs, and say that drastically reducing the number of grad students would be good for employment and salaries. There is a point to that. However, you would effectively end research as an enterprise at many second and third-tier schools, and there are a fair number of really good programs that would go away. Second, since federally funded fellowships would presumably only go to US citizens, this idea would drastically reduce international PhD students in S&E. That, too, would be a mess. Some of our best students are international students, and whether or not they stay in the US after their degrees, training these people is a valuable service that the current US system provides.

It is worth considering other funding schemes, though. I know that in the UK students are supported through their PhD, rather than on a schedule set by external grant deadlines. Perhaps some of my UK readers could comment on the pluses and minuses of this approach.

plasmons instead of cavities

Sorry for the delay in posts. The beginning of the new academic year is a hectic time.

This paper is a very exciting new result. Unfortunately there does not appear to be a publicly accessible version available. Ordinarily, lasing (that is, light amplification by the stimulated emission of radiation) requires a few things. One needs a "gain medium", some kind of optically active system that has (at least one) radiative transition. In this paper, the medium is a dielectric oxide containing dye molecules known to fluoresce at a wavelength of 520 nm. This medium needs to be pumped somehow, so that there are more optically active systems in the excited state than in the ground state. This is called "population inversion". (It is possible to get lasing without inversion, but that's a very special case....) Finally, one generally needs a cavity - an optical resonator of high enough quality that an emitted photon stays around long enough to stimulate the emission of many more photons. The cavity has to be somewhat leaky, so that the laser light can get out. However, if the cavity is too leaky, the optical gain from stimulated emission in the pumped medium can't outpace the cavity losses. The usual approach is to have a rather high quality cavity, made using either dielectric mirrors, total internal reflection, or some other conventional reflectors.

In this paper, however, the authors take a different tactic. They use the near-field from the plasmon resonance of the gold core (not coincidentally, at around 520 nm wavelength) of Au-core-dielectric-shell nanoparticles. Plasmon resonances are often quite lossy, and this is no exception - the Q of the plasmon resonance is around 14. However, the enhanced near field is so large, and the effective mode volume (confinement) is so small, that gain still outpaces loss. When the dye is optically pumped, it is possible to make these nanoparticles lase. This paper is likely to spawn a great deal of further work! It's cool, and there are many clear directions to pursue now that this has been demonstrated.