So, you want to do science, uh? (Rants to Young Scientists Part I: Citations)

Sometimes, I wish someone had made that statement and followed with some advice, real world advice. I mean, Medawar's "Advice to a young scientist" was great in convincing me science was about inquiry, patience and common sense —the well-known adage of  1% inspiration and 99% perspiration— but, after a few years into the academia, I wished someone had told me about the dark side of research: citation engineering, steering and hiding just to mention some examples. I mean, all these lay inside the gray area between ethical and unethical behavior and a simple search brings up discussion forums on the topic in all the scientific communities from social to natural sciences.

I guess, right now, it is my frustration talking: I have seen a couple of recently published articles related to our late work that doesn't even bother to cite us even when we have introduced some basic concepts or techniques on the topic, our manuscript was published at a major journal and, also, a simple scholar search brings out our papers on the top of the list.

I'm curious about the motivation behind these practices. Discarding those cases when there's truly no knowledge about the previous work and results have been re-derived from the start — t happens, believe me—, I can imagine that some guys are so worried about fame and recognition, that they try to bring their work and only their work into the playground to increase the visibility of their papers above similar results from other groups. Some other guys may wish to engineer their metrics by increasing the citations to this or that paper, even in cases unrelated to the matter at hand, in order to fulfill requierements of evaluation agencies. Or maybe I'm completely wrong and don't understand the motivations behind us, human beings. 

So, you want to do science, right? Well, it's the best job you will have if you are into it. It's not as logical, ethical and "pure" as you would expect. Shit happens even in the ivory tower of academia but the good things is that the nice ethical guys are more than those in the gray side of the ethical/moral spectrum. The best part is: it depends on you to keep it that way. Cite, cite truthful, cite well. Sometimes your superior will have the last word —been there— just don't go down without raising the point, that will get you an explanation about how it is not unethical or amoral engineering or steering citations —it's up to you to buy it or not, I didn't—.

Our latest paper: The exact solution of generalized Dicke models via Susskind–Glogower operators

Our latest paper The exact solution of generalized Dicke models via Susskind–Glogower operators  has been published a day ago in J. Phys. A: Math. and Theor.  The Dicke Hamiltonian is a workhorse of Quantum Optics, it describes the interaction of a collection of identical two-level systems with a single mode electromagnetic field under the long wave and rotating wave approximations. Surely, you will be thinking: "well, that model conserves the total number of excitations and parity; then, it's trivial to find its proper values and states." Well, it is trivial to solve the system but, as far as I know, it's not that trivial to follow the dynamics of a large ensemble under this model. 

Actually, I was looking at recent solution to a nonlinear version of this model via the Bethe ansatz method and  I got frustrated that even by using this method it was hard to follow the dynamics of a qubit ensemble of size twenty. So, Héctor and I sat down and applied a right unitary method that we had used to follow the dynamics of a quantum Landau-Zener-Majorana Hamiltonian a few months ago. It was trivial to extend the approach from a single qubit to an ensemble but the solution was not elegant enough, as you can see in the first part of the latest paper. So, we tried an alternative, instead of thinking about transformations we just thought about algebraic manipulation of the Hamiltonian at hand. After a few tries, we realized that one particular arrangement allowed us to write the evolution operator as the transform operators acting on the evolution operator of a tridiagonal matrix in the ensemble basis that depended only on the number operator. From there, it was all downhill because calculating the evolution operator of such a semi-classical-like Hamiltonian is quite simple, numerically, even for very large matrices and applying the transform operators on the initial states was easier than applying them on the time evolution operator. 

At the time when we were writting the paper, I only had my dual-core i7 laptop with 8GB of RAM, but it only took a few hours to follow the dynamics of an ensemble consisting of twenty-five qubits interacting with a coherent field with as mean photon number of twenty five. Now, I have done some simulations in my eight-core i7 desktop with 64GB RAM and I can follow the dynamics of a hundred qubits overnight with a very inefficient program. I'm hoping hat I will be able to simulate four or five hundred qubits interacting with large coherent fields as soon as I have time to sit down to think about this problem again.

Oh, I forgot to tell you. Once we obtained a result for just the Dicke model we extended the approach to include independent nonlinearities in the field and the ensemble, an approach a little bit more general than that of the guys in the Bethe ansatz method.

So, I hope you like our approach, use it and cite us in the future. You can find the Journal version at JPAMG. If you don't have access, we have prepared a manuscript with the final published version but without the journal format and uploaded it to the arXiv.

Exact dynamics of finite Glauber-Fock lattices

Phys. Rev. A 84, 053845 (2011)

This is one of those papers that just pop out with a life of their own. Last year, there was a theoretical paper—one of the authors was Hector, my PhD supervisor—where they described the so-called Glauber-Fock lattice—a semi-infinite one-dimensional, coupled waveguide array with couplings varying as the square root of the position—. There, they showed that one could give an analytical close form evolution for classical fields by creatively mapping each waveguide to a number state and playing with the resulting algebra. Later, this year they published a nice experimental paper on the topic.

A few months ago—for reasons that now seem alien to me but I'm sure I will try it again and again in the future—I thought that studying the finite version of the system could be a good way to make new friends; I couldn't be further from the truth.

Anyway, I got fun with the math and the analysis of this system and in the end I collected my marbles and sent it to PRA. I  got the best reviewer I have ever had, he/she helped me a lot in clarifying the exposition and results.  Also the comments from Changsuk and Rafa help me a lot to get the paper to its latter form.

Experimental systems: I have my heart on photonic waveguides, they have already been built and tested by the Jenna group. It seems like Robert Keil and Alexander Szameit from Jena can build any configuration that one can think about.

Major result: By using the method of minors, the polynomial related to the eigenvalue problem is shown to be the N-th Hermite polynomial—where N is the size of the finite lattice. Once the spectra is found, the j-th component of the k-th eigenvectors is easily calculated as the j-th Hermite polynomial evaluated at the k-th eigenvalue.

With the analytical solution at hand, it is possible to calculate whatever you want. 

The Physics: The evolution given by the aforementioned result is such that the system acts like an almost perfect mirror for input close to the zeroth waveguide. This is shown in the paper explicitly for single photon single- or multi-waveguide input as well as two-photon single- or multi-waveguide input—the graphics are damn big, sorry for that—.

Curious things I learned:

• If one is patient, it is possible to write an analytical closed form—a radical form—for all the roots of the first ten Hermite polynomials. If one gets Mathematica, one can get the roots of higher order polynomials in radical form.
• For some reason that I still don't understand but that I documented extensively numerically, the last component of  all the normalized eigenvectors is always the same.
• PRA copyeditors don't like passive voice, they changed all my "(...) was shown." Sorry, I promise I will stop using it.

Non-Academic things I learned:

• My mother was right when she told me: "Fool me once, shame on you. Fool me twice, shame on me."
• I'm still and idealistic fool that believes in people and I will keep being one. Great people are by far a majority in academy.

Well, I hope you can find some use for the results in the paper and, as always, drop me a line, I am always glad to discuss or try to help whenever possible. Citations are welcome! 

Do you want to read more about this or other papers of mine? Visit my Publication List.

Solution to the Landau–Zener problem via Susskind–Glogower operators

Phys. Lett. A 375, 3770-3774 (2011) 

In this paper, we try to show what happens when you consider the Jaynes-Cummings model in the case of a linear time-dependent detuning between the two-level system and the field.

Experimental systems: I have my heart on circuit-QED, it is the simplest thing I can think of and our result may be helpful for modular processes. A more complicated model may or may not be of relevance in BEC physics.

Our major result: By using a right unitary transform involving Susskind-Glogower operators—these are the ones introducing the right unitary characteristic—it is possible to show that the Hamiltonian is exactly solvable; specifically, the Hamiltonian is diagonalizable in the Fock state basis of the field. Moreover, the time evolution for the Hamiltonian can be written in an exact closed form given in terms of solutions to Weber Differential Equation, which are related to the exact solutions to the Landau-Zener-Majorana-Stuckelberg problem. 

With the analytical solution at hand, it is possible to calculate whatever you want. 

Minor results: It was curious for me to find out that in the case where the rotating wave approximation cannot be made it is still possible to diagonalize the Hamiltonian in the two-level system basis. Then, one can do numerics for small number of photons in the field. 

I was surprised to find that it was very simple to write a script that generates code to solve a system of some thousand coupled differential equations. 

The Physics: (Everybody always asks me about "the physics", so far I still don't have a clue what that question is really about but here's an attempt to an answer) Just for the sake of giving an example, in the article we present the physics in cases similar to those dealt by Landau, Zener and Majorana, to obtain the transition probability at the end of times for a system initially in the ground state at the beginning of time. Basically, the number of photons in the quantum field enhances the coupling between the two-level system and the field; this you can see at the level of the right unitary application.

Curious things: I learned the following,

• Majorana worked on the problem and published his results at the same time than Landau and Zenner. His formulation is closer to a full quantization of the Rabi problem. I found this while reviewing the literature on the topic.
• Stuckelberg worked in the problem, I haven't been able to get my hands on his paper so I have no clue what he said about the problem. I found this while attending the QIPC Zurich 2011 and someone gave a talk and mentionend the Landau-Zener-Stuckelberg-Mechanism.
• I should read Wikipedia at least once before finalizing a paper because in its entrance for Landau-Zener it clearly states the cites to Stuckelberg and Majorana's works.

Well, I hope you can find some use for the results we present in the paper and, as always, drop me a line, I am always glad to discuss or try to help whenever possible.

Solution to the Landau-Zener problem via Susskind-Glogower operators

We just uploaded a short, simple manuscript showing how to deal with a time dependent Jaynes-Cummings Hamiltonian where the time dependence is linear and you end up with a quantum Landau-Zener-Majorana (LZM)-like Hamiltonian.

This LZM-like Hamiltonian, under the rotating wave approximation, is simple to diagonalize in the field basis and the solutions to the classical Landau-Zener problem holds; that is, you can express the time evolution of the state in terms of Parabolic Cylinder or Hypergeometric functions.

As it goes, the Hamiltonian without the rotating wave approximation is also simple to diagonalize in the two-level system basis. The evolution of the initial state can be reduced all the way to two-uncoupled infinite sets of first order differential equations; of course, I have no clue how to solve these or else I would not be calling this a simple manuscript *wink* hehehe.

If you want, you can learn more about this by reading the Arxiv preprint.

Edit: If someone knows a reference for equation 16, please tell me about it. I cannot believe no-one has used it before, but I haven't found anything about it in the literature so far.

Spiderbeam!

I got sick and tired of head-butting into walls. I have decided to realize some ideas that have been on my mind for a while. So, I sat down and tried to teach myself Python to solve a problem regarding manipulation of matter with light.

After leaving the program running overnight at the workstation, I got to the office and ran the visualization program... What did I see? I saw SPIDERBEAM:

Lyx was the one that realized the similitude with Spiderman logo and Daniel got me this jpeg of the Spiderman 3 movie:

Note: I don't intend to violate any copyright. I tried to find the link for the jpeg but couldn't find it so I posted the jpeg that my friend made for me.