Dr. Sujit SarkarPoornaprajna Institute of Scientific Research,

Bangalore-560 080

Acknowledgement: Raman Research Institute Library

And CCMT of Phys. Dept of IISc Bangalore

Emergent Majorana Fermion in Cavity QED Lattice

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.

Majorana Fermion?

Majorana Fermions in Quantum Condensed Matter System

(1). QH system with filling fraction 5/2. (2). Kitaev: Majorana Fermions modes in onedimensional model.(3). Edge state of 1D system: Electrostatic defect linesin superconductor and quasi one dimensional

superconductor.(4). Cold atoms trapped in one-dimension.(5). Topological quantum computation.

What is about Cavity QED?

Majorana Fermion in Superconductor

Motivation:

(1). Interesting Experimental Findings.

(2). Application of Quantum Many Body Physics andQuantum Field Theoretical Aspects in Cavity QED.

Light Crystallization:

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

o0

Luttinger Liquid Physics Intrinsic in Cavity QED Lattice

Cavity QED Lattice Physics in XY Model

Conclusions:(1). We express cavity QED lattice system in integrablequantum 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 frequencyoscillations and coupling strengths where the physics ofTransverse Ising model and anisotropic XY model are the same.

Thank You