Tuesday, August 30 2022
14:15 - 15:30

IMSc Webinar

Entanglement entropy in generalized Landau system and squeezing in the three-wave mixing process

Sayan Kumar Pal

S. N. Bose National Centre for Basic Sciences, Kolkata

My talk will be primarily focused on the description of the
emergence of entanglement in a version of the Landau system and its
realization in terms of the squeezing phenomenon associated with the
three-wave mixing process that arises in quantum optics. This work has been
jointly done with Prof. Sibasish Ghosh along with my other collaborators as
a part of my Ph.D. thesis work.

We consider deformation of the standard symplectic algebra of position
coordinates and the associated momenta where in particular we consider
Moyal-type deformation i.e. the position coordinates of a two-dimensional
plane do not commute in this case. In this setting, we consider a 2D
harmonic oscillator living in the above-mentioned Moyal plane. We show that
the dynamics can be mapped to that of the Landau problem in an additional
2D oscillator potential. Next, we will show the existence of entanglement
in such a system by explicit computation of the von-Neumann entropy. Here
we reveal an Unruh-like physics in the system. Finally, we generalize our
system by considering the momenta to be non-commuting besides the
non-commuting coordinates. We then realize this dynamics in terms of
squeezing in the three-wave mixing process. Towards the end of my talk, I
will very briefly go through some of my other works along with my current
interests and proposals for future research works.

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