This CAREER award supports theoretical research aimed at developing new analytical and numerical tools to treat strongly correlated many-body dynamics in nanostructures and low-dimensional systems. The main focus of the proposal is to understand general properties of many-body dynamics of strongly correlated systems out of equilibrium. The proposal concentrates on the investigation of systems that can be described by effective models of impurities coupled to a continuum of modes, as illustrated by the case of a quantum dot coupled to leads. Most of the specific projects will be addressed using techniques introduced by the PI directed towards the description of impurity-type models and their generalizations. In particular, the following directions will be pursued:
(i) The Kondo effect in nanostructures. The ultimate goal of this research direction is to obtain new analytical results for the non equilibrium dynamical properties of nanostructures in the Kondo regime, such as nonlinear conductance through the quantum dot.
(ii) Strongly correlated quantum optics. Preparation and control of strongly correlated states of photons by coupling them to quantum dots will be considered.
(iii) Non equilibrium dynamics of ultracold gases on nanofabricated chips. Ultracold gases provide a fertile ground to investigate non-equilibrium phase transitions, thermalization and transition from integrable to chaotic behavior in an isolated quantum system.
(iv) Two-dimensional Fermi-Luttinger liquids. A universal approach to dynamical properties of two-dimensional quantum liquids will be developed, bridging the gap between one-dimensional Luttinger liquids and three-dimensional Fermi liquids.
The educational part of this award involves advising undergraduate students and the development of a new graduate course on the physics of ultracold atoms, which will span a wide range of topics in conventional atomic and molecular optics, condensed matter physics, and quantum optics. Such a course will integrate PI's research program and his educational activities, and will contribute to the training of future leaders in this rapidly developing line of research. The outreach component of this award will take advantage of PI's extensive experience in organizing physics contests and coaching high school students for the Physics Olympiads during his college years. The PI will develop an open-access website with a collection of online instruction materials for use by high-school teachers and students. The website will focus on preparing talented high-school students for Physics Olympiads. Such effort will also take advantage of Rice University's unique location to reach underrepresented and minority students.
NON-TECHNICAL SUMMARY
This CAREER award supports theoretical research aimed at understanding the properties of systems of interacting electrons and atoms in confined geometries at very low temperatures, a regime where quantum mechanics plays a major role. When the motion of these quantum particles is spatially confined, their collective behavior changes drastically compared to their bulk form which is described relatively well by conventional theories. The resulting motion of the constituent particles is strongly correlated. The PI will focus on understanding general dynamical properties of such strongly correlated systems, in particular when they are driven out of equilibrium. To achieve this goal, the PI will adopt a strategy of investigating particular systems in connection with current experiments and focus on calculating concrete observable quantities and making predictions that can be verified in laboratories. Successful implementation of the research project will significantly advance our fundamental understanding of strongly correlated phenomena and will be of importance to current experimental efforts on systems of dimensions that are some millionth the size of the human hair and/or systems confined in some of the spatial dimensions. In the long run, the research supported by this award may contribute to the development of new devices for high-precision measurements at the quantum level, spin-dependent transport and electronics, and quantum computation.
The educational part of this award involves advising undergraduate students and the development of a new graduate course on the physics of ultracold atoms, which will span a wide range of topics in conventional atomic and molecular optics, condensed matter physics, and quantum optics. Such a course will integrate PI's research program and his educational activities, and will contribute to the training of future leaders in this rapidly developing line of research. The outreach component of this award will take advantage of PI's extensive experience in organizing physics contests and in coaching high school students for the Physics Olympiads during his college years. The PI will develop an open-access website with a collection of online instruction materials for use by high-school teachers and students. The website will focus on preparing talented high-school students for Physics Olympiads. Such effort will also take advantage of Rice University's unique location to reach underrepresented and minority students.
