1. Quantum Phase Transition of Light: A Renormalization Group Study
Dr. Sujit Sarkar
Poornaprajna Institute of Scientific Research, Bangalore
Acknowledgement:
Raman Research Institute Library
and
Prof. T. V. Ramakrishnan (Fellow of
Royal Society)

2. Out Line of the Talk:
(1). What is Optical Cavity QED? (2). Motivation. (3). Jaynes-Cumming Model and Basic Physics. (4). Interesting Experiments. (5). Model Hamiltonians. (6). Quantum Field Theoretical and RG Study. (7). Results and Discussions. (8). Summary and Conclusions.

9. In Cavity QED

12. Motivation:
(1). Interesting Experimental Findings. (2). Application of Quantum Many Body Physics and Quantum Field Theoretical Aspects in Cavity QED.

13. Light Crystallization:

20. Quantum Spin Physics in Janes-Cummings Hamiltonian

22. Photon Blocked
Two states atom coupled to a cavity mode. The underlying mechanism is the anharmonicity of the Janes.-Cummings ladder eigen states. Resonant absorption of photon

23. The Quantum Phase Transition:

24. Reference: Matrin B Plenio et al. (1)
Reference: Matrin B Plenio et al. (1). Laser and Photonics Reviews, August 19, (2). Phys. Rev. Lett 99, (2007). (3). Phys. Rev. Lett 99, (2007). (4). Nature Physics 2, 849 (2006).

25. Effective Spin Model

26. o0

35. (1) It is a continuous family of transformations of the
Renormalization Group Theory: (1). Quantum Field Theoretical, (2) Real Space and (3). Numerical
(1) It is a continuous family of transformations of the
coupling constants in correspondence to a change of the length scale of a physical system. There are various length scale in the system.
(2). Integrated out the higher degrees of freedom from
the system as a result of it coupling constants are change and some times new coupling constants
are generated.

36. Jordan-Wigner Transformations: Spin Operator to Spinless Fermionic Operators

39. Results Based on Abelian Bosonization Study

46. a2

51. Another BKT Transition:
In absence of z component of exchange interaction

54. Effect of Magnetic Field (laser field detuning)1.
Photon Blocked state to the Photonic Metallic State

56. Conclusions:
(1). We have presented Abelian bosonization study to extract different quantum phases for our system in the weak coupling limit. (2). We have presented three sets of RG equations for the different physical situations of the system. (3). Two sets of RG equations show BKT transition in the system. (4). We have predicted Photonic Metallic State, Photonic Superfluidity and Photon Blocked Phase. (5). We have predicted the Commensurate to Incommensurate transition in presence of laser field detuning.

57. Future Project:
(1). Quantum Optics from the perspective of Qubit Physics (quantum dots, superconducting Charge Qubit, Flux Qubit and Phase Qubit). This study will be from the perspective of Quantum Many Body Physics and Quantum Field Theoretical Methods. (2). Quantum Optics at Nanoscale: Single Molecule or Single Atom, Nano-Photonics. (3). Quantum Correlation Functions (Quantum Entanglement, Quantum Discord) for different Quantum Many Body System at Nanoscale.

58. My API Score is around 600 (according to the UGC rule 2010)
My API Score is around 600 (according to the UGC rule 2010). Most of the Associate Professor in different Universities, IIT’s and IISER’s and Research Institute not even able to touch 250 API Score.