Applications of master equations in quantum optics:-
In Quantum Mechanics the evolution of the quantum state is described by the Schrodinger Equation
and it is a unitary evolution. In real word it is well known that it is not true. In general, when a
mixed state is appended with an environment evolve unitarily giving rise to dissipation.
A master equation is used to model the dissipation.
The master equation lies at the heart of quantum optics. It describes the evolution of the
dissipative systems. The master equation is used to model decoherence,
entanglement sudden death, has found many applications in quantum optics and open
quantum systems . In quantum information, they are used to model quantum channel
capacities.
A novel approach of solving master equation using thermo field dynamics is carried out.
Thermofield dynamics (TFD) is used to solve the master equation. This formalism has an important salient
features, the solving of master equation is reduced to solving a Schroedinger equation, thus all
the techniques available to solve the Schroedinger equation are applicable here. Hence, the
solving of master equation using TDF gives a very simple and elegant approach.
This methodology is applied to Entanglement in two-site Bose–Hubbard model with non-linear dissipation.
We are looking its applications to Cold atoms and Bose Einstein condensate (BEC).
I have being also interested in, Gisin’s theorem and quantum channel capacities.
Nonlinear coherent states : Interested in the Berry-Phase for coherent states of nonlinear su(2) and su(1, 1) algebras.
Thesis:
Baryogenesis (Cosmology) : The baryon asymmetry of the universe (BAU) problem is a challenging one in the
standard model of cosmology. It is characterised by the ratio η =nb/ nγ , where nb is the number
of baryons and nγ is the number of photons in the universe. The present value of the asymmetry
in the universe is η = 3 × 10−10 .
Three conditions postulated by Sakharov are sufficient to guarantee baryon asymmetry.
These are (i) Baryon number (B) violation, (ii) Charge (C) and Parity (CP) violation, (iii) the
presence of nonequilibrium processes.
There are several models explaining the value of η. I am interested in supersymmetric Affleck-Dine baryogenesis, gravitational baryogenesis and leptogenesis.
An Institute of Eminence
