Aspects of non-equilibrium many-body phenomena in quantum matter and light

Non-equilibrium quantum and classical systems have been of tremendous
interest in both fundamental and applied physics. Recent experimental
breakthroughs in atomic, condensed matter physics and quantum optics
have given birth to new paradigms for studying out-of-equilibrium
quantum systems. Understanding such phenomena requires a
cross-disciplinary approach uniting ideas from these diverse
fields. In this talk, I will address non-equilibrium aspects in both
isolated and driven-dissipative systems.

I will present a nonlinear hydrodynamic theory of a strongly
interacting Fermi gas, which showed remarkable agreement with
experiments [1,2]. For Bosonic systems, using high-performance
computing and analytical results, I will present a deep connection
between the Nonlinear Schrodinger equation (Gross-Pitaevskii equation)
and Kardar-Parisi-Zhang universality class of stochastic dynamics
[3,4,5]. Given the wide range of phenomena described by these
equations, our results have implications in fields ranging from cold
gases to nonlinear optics.

I will then discuss a driven-dissipative system consisting of a
quantum gas placed in an optical cavity and pumped by a laser [6]. I
will describe the non-trivial dissipative properties near the critical
point of the open quantum phase transition [7], which explained recent
mysterious experimental findings [8]. I will also propose protocols to
prepare entangled quantum states by engineering drive and dissipation
in hybrid light-matter systems. Our work shows that
far-from-equilibrium many-body physics is an extremely rich field
where theory and experiments across several disciplines thrive
together.

(1) J. Joseph, J. E. Thomas, M. Kulkarni, A. G. Abanov, Phys. Rev. Let
t.  106, 150401  
(2) M. Kulkarni, A. G. Abanov, Phys. Rev. A, 86, 033614 
(3) M. Kulkarni, A. Lamacraft, Phys. Rev. A 88, 021603, Rapid
Communication 
(4) M. Kulkarni, D. A. Huse, H. Spohn (in preparation, 2014)  
(5) M. Kulkarni, Journal of Statistical Physics  (invited article,
2014) 
(6) R. Mottl, F. Brennecke, K. Baumann, R. Landig, T. Donner, and
T. Esslinger, Science 336, 1570 (2012) 
(7) M.Kulkarni, B. Oztop and H. E. Tureci, Phys. Rev. Lett, 111,
220408 
(8) F. Brennecke, R. Mottl, K. Baumann, R. Landig, T. Donner,
T. Esslinger, PNAS July 16, 2013 110, 11763.