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**Emergent Majorana Fermion in Cavity QED Lattice**

Dr. Sujit Sarkar Poornaprajna Institute of Scientific Research, Bangalore Acknowledgement: Raman Research Institute Library And CCMT of Phys. Dept of IISc Bangalore

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Out Line of the Talk: (1). What is Majorana Fermion? (2). What is Optical Cavity QED? (3). Motivation. (4). Interesting Experiments. (5). Model Hamiltonians. (6). Results and Discussions. (7). Conclusions.

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Majorana Fermion?

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**Majorana Fermions in Quantum Condensed Matter System**

(1). QH system with filling fraction 5/2. (2). Kitaev: Majorana Fermions modes in one dimensional model. (3). Edge state of 1D system: Electrostatic defect lines in superconductor and quasi one dimensional superconductor. (4). Cold atoms trapped in one-dimension. (5). Topological quantum computation. What is about Cavity QED?

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**Majorana Fermion in Superconductor**

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

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**Light Crystallization:**

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**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).

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Effective Spin Model

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**Luttinger Liquid Physics Intrinsic in Cavity QED Lattice**

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**Cavity QED Lattice Physics in XY Model**

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Conclusions: (1). We express cavity QED lattice system in integrable quantum spin system. (2). Elementary excitation of the cavity QED lattice is the Majorana fermions. (3). We have derived the Dirac equation for the cavity QED lattice and the condition for the massless excitations. (4). We have derived the condition in terms of Rabi frequency oscillations and coupling strengths where the physics of Transverse Ising model and anisotropic XY model are the same.

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Thank You

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