RESEARCH STATEMENT

 

Alberto G. Rojo

 

            My research focuses on properties of correlated electrons and electron transport at low temperatures. This work, unified under the theme of quantum fluctuations, addresses important unresolved issues at the frontier of condensed matter theory. In this research statement I highlight my recent contributions to this field within the last three years, and indicate some future directions.  I am particularly interested in emphasizing my research program in the area of nanotechnology, where several problems of fundamental as well as applied interest are emerging, and where one finds growing funding opportunities.

 

            1. Many electron properties in two layer systems

 

In 1992, together with G. D. Mahan, I discovered the effect of non-dissipative drag (NDD) on superconductors and mesoscopic systems. I plan to continue this line of research, exploring various applications of this fascinating effect. My work in this area has stimulated significant experimental and theoretical activity. NDD results from the coupling of the zero point charge fluctuations between two systems with no tunneling from one to the other. I have discussed and summarized its current status and its relation with the dissipative current drag in my recent review article[1]. In collaboration with my graduate student Joe Baker I have studied both analytically and by two different numerical methods the effect of disorder on NDD in order to make contact with experiments[2].

            A related effect that has bearing on the coupling between non-tunneling systems is the eddy current coupling between a superconductor and a normal, highly conducting system. I am involved in an ongoing collaboration with the experimental group of C. Thomsen and A. Goñi at the Technische Universität in Berlin, where the effect was observed for the first time in the InSb/GaAs system. The experimental results are in quantitative agreement with my theoretical predictions.[3]  I am seeking external funding to strengthen the collaboration in which we will explore further ramifications of this very interesting and significant effect.

 

 

            2. Squeezing and control of quantum noise

 

            Another project that has been particularly successful since my arrival at Michigan was my work on phonon squeezing, a field that falls within my interest in zero point fluctuations. In preliminary calculations I had identified the mechanism of pulses acting on harmonic systems as a means of producing squeezing. For the case of phonons the effect corresponds to a time modulation of the amplitude of the zero point fluctuations in the atomic positions within the solid. I started collaboration with R. Merlin’s group, who measured the effect using ultra fast optical pulses. The experiment[4] constituted the first observation of the squeezing effect in condensed matter, and could have exciting future applications in device physics and in several areas where, in general, a “stroboscopic” control over the quantum noise might be necessary. A very important question to be addressed in the future is: what other excitations can be squeezed in condensed matter, and what are the possible applications? Part of my future research effort will be devoted to answering these questions.

 

 

            3. Role of confinement in high temperature superconductivity

 

            Before arriving in Michigan I did some important work on high temperature superconductors. Since my arrival I have continued working on some problems within this field. With my former graduate student Mathew Reilly, I solved the two-magnon Raman scattering problem,[5] showing that some recent experiments can be understood using a spin-phonon model without disorder in the non-adiabatic approximation. The study of High Tc superconductors has motivated an intense study of spin systems and Heisenberg, e.g. spin ladders, where the issue of a gapless versus gapped spectrum of excitations is the subject of experimental and theoretical study. I contributed to that subfield by providing a proof, extending the Lieb-Mattis theorem, that spin ladders with an odd number of legs are gapless.[6]

            My recent work on confinement on c-axis transport[7] addresses the fundamental issue of whether correlations can give rise to a “confined” phase in which transport is coherent in two spatial directions, and incoherent in the third. This is an unresolved many-body problem, the detailed study of which originates in P. W. Anderson’s conjecture that the ideas and paradigms of one-dimensional non-Fermi liquids can be extended to two and three-dimensional systems. In collaboration with C. Balseiro from Bariloche (Argentina) I considered the strongly correlated anisotropic system, proposed and solved a model using a new slave-fermion scheme, and showed that a confinement transition emerges naturally from the solution. This collaboration is funded by the National Science Foundation through its international program, and has proven very fruitful. We have also approached two other significant problems within High Tc superconductivity: the effect of disorder on d-wave pairing,[8] and the problem of resistance at the melting point of a vortex lattice.[9]

            I plan to continue studying the issue of confinement. This will be the subject of the Ph.D. thesis of a graduate student in Bariloche who is studying finite anisotropic systems using the Lanczos method.

 

 

            4. Bose-Einstein condensation

 

            The field of Bose-Einstein condensation is one of the most exciting problems in physics. Due to its observation in supercooled atomic systems, the problem combines knowledge from condensed matter and atomic physics. For example, a condensate can be produced of Rb atoms in two internal states, which invites analogies with anisotropic magnetic systems. I have proven an interesting theorem that establishes the regimes of phase separation for these kind of condensates.[10] Also, in collaboration with P. Berman (Atomic Physics) at the University of Michigan, I studied the so-called Talbot oscillations, already well known for independent atoms, and their modification in the presence of a Bose-Einstein condensate.[11] Our goal was to understand the effects that atom-atom interactions will have on the Talbot oscillations. Since the atom-atom interaction makes the problem an unsolved many-body problem, one has to resort to approximations. To approach this problem I have proposed a simplified version that can be solved exactly. The simplification consists of treating the problem in one dimension, and mapping strongly interacting (hard-core) bosons to free fermions. This trick, originally introduced by M. Girardeaux, can be proven to work in this case and we describe the interplay of collision and quantum coherence in an exact framework. Our work has already attracted some attention and has motivated interesting extensions.

 

            5. Funding

 

My research was funded by the National Science Foundation ("Studies of Strongly Disordered Anisotropic Superconductors and Non-Adiabatic Spin-Phonon Effects", US-Argentina collaboration) and General Motors Corporation/DARPA (CoPI with C. Uher) "Hybridization-Gap Semiconductors and Intermediate Valence compounds in Thermoelectric Cooling Applications". Also I have support from the Alfred P. Sloan Foundation to support minority graduate students. I plan to actively search for new funding sources in the area of nanotechnology.

 

 

                6. Summary of future directions

 

            The field of solid state physics is facing very interesting challenges. Novel experimental capabilities provide access to regimes of operation of electronic and mechanical devices where quantum mechanics plays a relevant role. In general I plan to continue my research effort in fundamental coherent many body effects and zero point fluctuations, focusing in the nanoscale.

 In the near future I plan to build upon the research program that started with my work on non-dissipative drag. The first extension in that direction is already under way, and has produced the interesting eddy current coupling mechanism between a superconductor and a normal metal. A further extension will be the study of drag (longitudinal and transverse) between a normal metal (2DEG) and a superconducting film, a problem that has not yet attracted much experimental attention. The goal in this project is to understand whether there is an observable Hall drag effect due to eddy-current coupling between spontaneously generated vortices in the superconducting film and the 2DEG.   I also plan to investigate realizations of the NDD in coupled systems of quantum dots. These systems can exhibit coherent many body effects as shown in recent experimental breakthroughs that report a Kondo regime in dots embedded in mesoscopic multiply connected systems. Therefore, the coulomb coupling between several dots embedded in different mesoscopic rings could give rise to an observable NDD effect.         

In addition, I will continue my studies of phonon squeezing and new possible ways of controlling zero point noise by applying pulses. More specifically, for nanomechanical devices the ultimate limit is operation at or even beyond, the quantum limit. In fact, some of today’s systems already verge on the quantum limit at temperatures of 100mK and one must appeal to the quantum theory of measurement to understand and optimize force and displacement measurements. A natural question that arises is whether quantized amplitude jumps can be observed in such devices. As pointed out by M.L.Roukes, for such jumps to be observed the device must be in a “number” or “Fock” state and the transducers that couple to the device should measure only the mean-squared position. It is interesting that the sensitivity of current magnetomotive detectors is only a factor of ten below resolution of individual quantum jumps. Once this domain is reached it should be possible to squeeze the quantum limited mechanical states to achieve force and displacement measurements that exceed the quantum limit imposed by the uncertainty principle.  A substantial part of my research plan will be devoted to study schemes of squeezing and quantum non-demolition force and displacement measurements in nanomechical devices.