Sujit Sarkar

Physics of Dirac fermion and Majorana fermion in superconducting qubit systems:
We would like to study the one-dimensional superconducting charge qubit lattice. The superconducting charge qubits are connected through microwave resonator. We would like to study the different coupling strength of cavity-qubit to map this system to a quantum spin system. In this simulated quantum system, the degenerate ground state whose wave functions involve maximum quantum entanglement and we identify that they are equivalent to the Majorana fermions. We would also like to study the transition between the Dirac fermion modes to the Majorana fermion modes for the different coupling strengths of the system.
Physics of Dirac fermion and Majorana fermion in optical cavity QED systems:
We would like to study the low lying excitation of coupled optical cavity arrays. We would like to derive the Dirac equation for this system and explain the existence of Majorana fermion mode in the system. One can find quite a few analytical relations between the Rabi frequency oscillation and the atom-photon coupling strength to achieve the different physical situation of our study and also the condition for massless excitation in the system. We would like to study several analytical relations between the Majorana fields of this system, order and disorder operators for our systems. We would also like to show that the Luttinger liquid physics is one of the intrinsic concept in our system.
Superconducting Quantum Dots:
We study the quantum phase diagram of an ordered one-dimensional superconducting dots (mesoscopic grain) array which are connected through Josephson junctions. The average charge of the dots can be controlled through gate voltage. We study the interplay of long range Josephson tunneling and also long range charging energy of superconducting dots. Our quantum field theoretical studies predict different kind of phases like charge density wave, dimer order state, Luttinger liquid phase, and superconductivity in the vicinity of charge degeneracy point. Here we also predict the one dimensional counter part of two dimensional checker board phase. The dissipation physics of one dimensional mesoscopic superconducting quantum interference device array by using the field-theoretical renormalization group method. We observe length scale dependent superconductor- insulator quantum phase transition at very low temperature and the dual behavior of the system for the smaller and larger values of magnetic field. At a critical magnetic field, we also observe a critical behavior where the resistance is independent of length.
Topological Quantum Phase Transition and Local Topological Order in a Strongly Interacting Light-Matter System:
An attempt is made to understand the topological quantum phase transition, emergence of relativistic modes and local topological order of light in a strongly interacting light-matter system. We study this system, in a one dimensional array of non-linear cavities. Topological quantum phase transition occurs with massless excitation only for a finite detuning process.
We present few results based on the exact analytic calculations along with the physical explanations. We observe the emergence of massive Majorana fermion mode at the topological state, massless Majorana-Weyl fermion mode during the topological quantum phase transition and Dirac fermion mode for the non topological state. Finally, we study the quantized berry phase (topological order) and its connection to the topological number (winding number).