On May 24th, Prof. Tan Shina from Georgia Institute of Technology had delivered a lecture entitled "From ultraviolet divergence to some exact relations for a strongly interacting quantum gas" in Wuhan Institute of Physics and Mathematics (WIPM, CAS).
In the research of ultracold atomic gases (i.e. two component ultracold Fermi gases), the properties in the strongly interacting regime has always been an attractive topic. Since the temperature and particle density is very low, the characteristic length scales and scattering length are both sufficiently large compared to the typical interaction range between the particles, we could safely employ s-wave contact pseudopotential to describe these interactions. Prof.Tan's lecture concentrated on some exact universal properties of such a strongly interacting Fermi gas. Due to the utility of the zero-range contact pseudopotential, the system's wavefunction will diverge near the origin point in the coordinate space, which would turn into the well-known ultraviolet divergence after transforming into the momentum space. To properly treat this problem, Prof.Tan defined two new generalized functions, and by rewriting the Hamiltonian of the system using the special characters of these generalized functions, he got a universal yet simple expression for the system energy. Meanwhile, by taking the momentum distribution into account, he introduced a new thermodynamic quantity called Contact, which plays a center role in the systems. Moreover, when the scattering length is large enough, it can be shown that various physical quantities including pair correlation function, adiabatic changes and two-body loss rate could be calculated using simple formulae all include the Contact. These formulae are the well-recognized Tan Relations bearing Prof.Tan's name. Prof. Tan also introduced some recent experimental progresses in the test of these relations and pointed out the probable challenges in the future experimental implementations. At the end of the lecture, Prof.Tan gave a summary of the validity of the theory and posted some research topics in the area, i.e. finding nontrivial constraints on the strongly interacting systems to solving the ground states via the approach resembling the successful DFT method.
The lecture had attracted experts and students both in experimental and theoretical research, and Prof.Tan carried out productive communication and discussion with research staff and students on the validity, mathematical derivation, physical essence of the model and possible experimental schemes.
Prof. Tan obtained his PhD from the University of Chicago and he had done post-doctoral research at University of Washington and Yale university. Now he is an assistant professor at the School of Physics, Georgia Institute of Technology. His main research interest lies on the quantum many-body and few-body theory of ultracold atomic and molecular systems. In recognition of his breakthrough contribution to the field as a young researcher, he was awarded the 2010 APS George E. Valley Prize. Prof.Tan will be on a two-month stay in WIPM and carry out academic cooperation with the research staff in Cold Atom physics．Prof.Tan is a member of the Research Center for Cold Atoms and has established long-term cooperation with WIPM.