Showing posts with label electrons. Show all posts
Showing posts with label electrons. Show all posts

Thursday, September 17, 2015

An exciting discovery

A discovery is not always a eureka moment where the a puzzle resolves itself in a burst of insight.  As I realized tonight, we had made a significant discovery of the gradual kind.

A graduate student Sean Mossman, collaborator Rick Lytel and I had been working on a problem for over a year.  We got what we believed was a significant result, so we submitted our work to the best optics journal called Optics Letters.  The reviews came back positive so we started to diligently work on the required revisions.  It was only then that it hit me that this might be a more significant discovery than we had originality imagined.

We have the disadvantage of working in an esoteric branch of a very applied field, so there aren't many people out there that understand or appreciate the work.  Last year I organized a small conference on WSU's campus to bring together people that have worked in this area and have an appreciation for its nuances.  This year, the second meeting in what is becoming an annual event, was held at Lehigh University and organized by a talented experimental physicist, Ivan Biaggio, who was an early appreciator of the power of the sum rules and the guidance they provide in understanding how to make better materials.  The next meeting will take place at Tufts University, and will be hosted by a young and energetic theorist named Tim Atherton.

It is our job to get the word out about our work so that others can reap its benefits and this paper is the first step in the process.

I am too excited to sleep, so to unwind, I am wiring this post.  Below is an email that I sent to my coauthors (typos and all!) of our paper.  I hope it gives my readers some appreciation of the joys associated with doing physics.  Such reward come rarely in the midst of persistent failures.

Goodnight!

Dear All,

First, let me say NICE JOB!  Usually after I read through a manuscript a zillion times, I start feeling more and more insecure about the significance of the work with each reading due to becoming desensitized; the sublime becomes the mundane.  However, this is not so with this work.  I truly think it is fantastic.


I have spent a considerable effort on revising the manuscript to address the reviewers' comments and to bring out the wonderful physics that I think was buried in there.  Though I was aware of it  all, as I now you were too, the significance of phase disruption did not strike me until I rewrote the last 4 paragraphs of the paper.


Let me summarize my thoughts.  First, we have shown that phase disruption is associated with a significantly enhanced nonlinear response.  If we go back to our fundamental understanding of a quantum wave function, a kink is only possible where there is an infinite change in the potential; the two classic examples are infinite walls, from which one makes perfect reflectors and ideal boxes to confine particles, and the delta function, which represents the ultimately-bound system.  All such systems are impractical.  That is most likely why researchers have had such difficulty in improving the nonlinear response.


In essence, we have played a great trick on nature by adding a branch that can divert a small electron flux.  As far as the main direction of flow is concerned, the effect on the wave function is the same as one would expect for a delta function.  But, this is easy to do in a nano wire by fabricating a little wart on its surface, or by asking a chemist to add a side group to the bridge that carries electrons between two parts of a molecule.


This may all seem an academic exercise because the original idea was implemented with one electron and there is another requirement that phase disruption must dominate the states near the ground state.  In the case of many electrons, this requires that the phase disruption be concentrated in the states near the Fermi level, which corresponds to the single partial states just below and above the Fermi level.  The problem is that an arbitrary quantum graph will not have this property.  However. all we need to do is to move the little side branch to the right place, and voila, we have a huge nonlinear-optical response.  All this time chemists have been synthesizing all sorts of structures made of all sorts of atoms, and it appears that all that we need to do is move one simple part.


Finally, we propose a very simple molecule that has the right properties to have a huge nonlinear response.  This makes it possible for our ideas to be tested.  I do not expect that the molecule we propose will end up being so great because we have not taken electron interactions into account.  It would indeed be a miracle if this one turned out to work given how everything needs to fine tune in just the right way.  But, with slight modifications of the prong position or length, a project for a seasoned synthetic chemist, and heavy duty calculations by quantum chemists, I think that the right geometry and topology can be identified and experimentally tested.


I will most likely have difficulty sleeping tonight, but I will try to hit the sack soon.  As for the paper, I am passing it along to you for your revisions.  Please keep in mind the ideas above, which I think should be stressed.  So if you make changes, please make sure that they preserve or enhance this narrative.


The response to the reviewers may need more work since I did not get a chance to proof it very carefully.  We need to make sure that we carefully answered all the reviewers comments in the way they intended.  Also, please make sure that our responses match up with the actual changes we made in the manuscript and that we didn't miss anything.


I am willing to read through it all before we resubmit unless you both are comfortable with the final product.  Given that grading is piling up, meetings continue to chew up my time, and I still need to do quite a bit of work for my presentation in DC, any relief from proofing burdens is greatly appreciated!


All the best!

-- 
Mark G. Kuzyk
Regents Professor of Physics
Meyer Distinguished Professor of Sciences
Washington State University
Pullman, WA 99164-2814

Phone: 509-335-4672
Fax: 509-335-7816

Web Page: www.NLOsource.com

Friday, March 22, 2013

Monopoles, electric dipoles, and the inverse square potential


Research is a fulfilling enterprise, especially when it takes us on an unexpected path that leads to new insights even when others may have crossed the same path.

A couple years ago on Christmas eve, I was toying with a calculation based on my realization that a potential of the form V(x) = xq captures all of the interesting toy models of quantum mechanics such as the harmonic oscillator (q=2), the particle in a box (q = ∞), and the hydrogen atom (q= -1). I wanted to derive a general analytical expression for the energy spectrum as a function of q so that I could analyze the nonlinear-optical properties of all such systems. To my delight, I was able to get such an expression using a mathematical trick. I was am certain that I was not the first to do so, but I nevertheless felt satisfied.

A plot of my results showed a removable singularity at q=0, which corresponds to a free particle that has no bound states (bound states are needed for my calculation of the nonlinear-optical properties), and a divergence at q = -2. I dutifully wrote up the results and left them sitting on my computer for a couple years. The work was given new life when I handed it over to new graduate student.

After working on the problem for a summer and part of a semester, he found a huge literature on the x-2 potential, the location of the divergence in my plot. It turns out that this potential has all sorts of interesting mathematical problems. It has a continuum of bound states -- very unusual and in fact an impossibility; and, the wave functions and their duals do not span the same space -- a peculiar state of affairs. The known fix, as the student found in the literature, is to exclude a small region near x = 0 and then solve the problem in the limit as this small region tends to zero. Doing so fixes the problems by essentially removing the point-like properties of the dipole. 

The x-2 potential describes the influence of an electric dipole moment on a point charge. Certainly nature must reconcile these funny mathematical difficulties given that dipoles and point charges exist. But how?

Nature is very clever by not allowing true point electric dipoles to exist.  Instead, all dipoles are extended dipoles where the potential deviates from x-2 at close range, thus removing the pathological behavior. In fact, this may be the reason why an ideal point dipole is not observed in any particle. If it existed, serious paradoxes would ensue.

The electron has a very tiny electric dipole moment beyond the limits of measurability with today's technology, and arises from the CP-violating part of the CKM matrix in the standard model. The moment is tiny because CP violation involves quarks that are created as virtual particles, interact with the electron, and then are annihilated. As a result, the dipole moment is not a point dipole but is due to a sea of virtual quarks. All elementary particles have only small electric dipole moments with an extended charged cloud, so nature avoids potential pathologies by forbidding point dipoles.

Magnetic dipoles, which are a consequence of moving charges through spin and orbital angular momentum, are a different story. Spin angular momentum does not originate from spread out charge that spins in physical space.The spin anguar momentum lives in its own space so the associated magnetic dipole moment is pointlike, and will lead to pathologies when interacting with a magnetic monopole. Nature has apparently avoided such problems by forbidding the existence of magnetic monopoles. While there are theories that allow for magnetic monopoles, searches for them have come up short and I don't think they will be found.

In summary, the interaction of a point dipole that interacts with a point charge leads to all kinds of pathologies that can only be resolved by demanding that the dipole be an extended object that avoids being a true x-2 potential. Nature seems to have solved the problem by allowing point electric charges but no point electric dipoles. Magnetic point dipoles, on the other hand exist; but, there are no magnetic monopoles with which they can interact.  The symmetry between the electric and magnetic parts of Maxwell's equations is broken to avoid unphysical behavior.

I cannot claim to be the first person to have this idea and wouldn't be surprised if this argument is common knowledge. Or, my argument may be faulty.  This does not make my musings any less exciting to me. I continue to be in awe of the power of physics, which allows us to ponder domains that are far removed from our daily experiences. My job not only allows me to think of such things, but encourages it; it is indeed a wonderful life

In studying the complex ramifications of the simple x-2 potential when applied to nonlinear optics leads to insights into why point electric dipoles and magnetic monopoles can't exist.  How can I sleep tonight!