Quantum Phase Transition of Light: A Renormalization Group Study Dr. Sujit Sarkar Poornaprajna Institute of Scientific Research, Bangalore-560 080 Acknowledgement: Raman Research Institute Library and Prof. T. V. Ramakrishnan (Fellow of Royal Society)

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.

In Cavity QED

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

Light Crystallization:

Quantum Spin Physics in Janes-Cummings Hamiltonian

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

The Quantum Phase Transition:

Reference: Matrin B Plenio et al. (1) Reference: Matrin B Plenio et al. (1). Laser and Photonics Reviews, August 19, 2008. (2). Phys. Rev. Lett 99, 103601 (2007). (3). Phys. Rev. Lett 99, 160501 (2007). (4). Nature Physics 2, 849 (2006).

Effective Spin Model

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(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.

Jordan-Wigner Transformations: Spin Operator to Spinless Fermionic Operators

Results Based on Abelian Bosonization Study

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

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

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.

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.

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