Center for Computation, Modelling and Simulation

Computational studies of atomic & molecular processes in noisy environments

Anil Shaji

Precise experimental control over aggregates of a few atoms ranging from the tens to thousands in number is rapidly becoming a reality in the laboratory. There is a lot of interesting physics as well as potential applications hiding in this mesoscopic scale which needs to be explored in depth. The Hilbert space structure of quantum mechanics precludes efficient simulation of the states and dynamics of composite systems made of many quantum particles. When the number of atoms is very large, emergent phenomena become dominant and statistical treatment of the system becomes quite accurate. However in the mesoscopic regime mentioned above this is not the case and to understand the full dynamics, integration of the full, manybody, Schrodinger equation is needed. For doing this substantial computational power of the type proposed in this project is required. Of particular interest to me is numerically solving the evolution of Bose-Einstein condensates (BEC) with a few to several thousand atoms held in dynamic and specifically shaped trapping potentials. The BEC can be used as a probe in a quantum limited measurement scheme in which the measurement uncertainty can potentially scale faster than the “Heisenberg-limited scaling” of 1/N which still is widely regarded as the best possible scaling of uncertainty with resources in any measurement scheme allowed by the rules of quantum physics. The challenge is to examine to what extent the non-ideal conditions present in a lab will potentially affect the scaling of the measurement uncertainty in a measurement scheme using the BECs. Apart from attempting a full quantum simulation of single and two mode BECs with a few thousand atoms, numerical integration of the Gross-Pitaevski equations and extensions to it is also required to understand all the aspects of the proposed quantum metrology scheme.

Closely connected to the line of research on master equations is the study of energy transfer in complex molecular complexes. In collaboration with faculty members in the school of chemistry we are working on designing and studying small groups of molecules each with tens of atoms which exchange energy. The focus is on studying the role of quantum coherence in the energy transfer mechanisms with the long term view of understanding the role of such coherence in critical natural processes like photosynthesis. In parallel, framing of accurate quantum master equations describing the time evolution of both the energy donor and acceptor molecule will be attempted. To find the electronic configuration of the complex molecules both in their ground and excited states, extensive use of standard quantum chemistry packages like Gaussian and QChem are needed preferably running in a high performance computing cluster.

A very different line of research for which substantial computing power is needed is to try and answer the open question of how the spatial patterns of leaves and flowers in plants are determined. In collaboration with faculty members in the school of Biology we are working on understanding how molecular factors including growth inducing hormones, proteins that facilitate the transport of the hormones, active and passive transport of the hormones and proteins etc can explain the patterns. The modelling of the molecular factors at a cellular level is done with input from both in vitro and in vivo experiments and observations. The aim to see how changing the parameters of the model, in ways that can be mirrored in the lab also, changes the observed patterns so that one can go back to the lab and do the corresponding changes to the parameter and see if the predicted patterns indeed appear. The problem of pattern formation in plants has been addressed by many people including the likes of DaVinci over several hundred years but still as completely satisfactory explanation is not forthcoming. What has changed in recent years is the degree of control at the molecular and genetic levels that is possible in the lab. With such control data can be obtained with the specific aim of fixing each term in a mathematical model of the same. Typically with such detail the model that is obtained is a rather complex set of differential equations which requires substantial computing power to solve and explore.