Cavity Optomechanics with Ultra Cold Atoms in Synthetic Abelian and Non-Abelian Gauge Field
Abstract
:1. Introduction
2. Cavity Optomechanics with Cold Atoms
2.1. Introduction to Cavity Optomechanics
2.1.1. Classical Treatment
2.1.2. Quantum Treatment
2.1.3. Two Level Atom in a Single Mode Cavity
2.1.4. Ultracold Atoms in a Cavity
3. Ultracold Atoms in Abelian and Non-Abelian Gauge Field
3.1. Abelian Gauge Field
3.2. Neutral Cold Atoms in Synthetic Abelian Gauge Field: Rotating Ultracold Condensate
3.3. Geometric Phase in Quantum Mechanics and the Related Gauge Fields
3.4. Ultracold Atoms in Non Abelian Gauge Field
3.4.1. Geometrically Created Non-Abelian Gauge Field
3.5. Synthetic Spin-Orbit Coupling for Ultracold Atomic Gases: Case of Non Abelian Gauge Field
3.6. Principle of Spin Orbit Coupling in Ultracold Bosonic Systems: NIST Method
4. Cavity Optomechanics of Ultracold Fermions in a Synthetic Gauge Field
4.1. Formalism
4.2. The Shubnikov de Hass Oscillation
5. Dynamically Created Spin-Orbit Coupling inside a Cavity
5.1. Synthetic SO Coupling in Ring-Cavity
6. Cavity Mediated Spin-Orbit Coupling
7. Spin-Orbit Coupled Ultracold Bosons in a Cavity
7.1. Formalism
7.2. Non-Interacting Limit
7.3. Interaction and Magnetic Order
Order | |
---|---|
zAFM | 0 |
Stripe | |
VX | |
3-Spiral | |
4-Spiral | |
zFM |
8. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Padhi, B.; Ghosh, S. Cavity Optomechanics with Ultra Cold Atoms in Synthetic Abelian and Non-Abelian Gauge Field. Atoms 2016, 4, 1. https://doi.org/10.3390/atoms4010001
Padhi B, Ghosh S. Cavity Optomechanics with Ultra Cold Atoms in Synthetic Abelian and Non-Abelian Gauge Field. Atoms. 2016; 4(1):1. https://doi.org/10.3390/atoms4010001
Chicago/Turabian StylePadhi, Bikash, and Sankalpa Ghosh. 2016. "Cavity Optomechanics with Ultra Cold Atoms in Synthetic Abelian and Non-Abelian Gauge Field" Atoms 4, no. 1: 1. https://doi.org/10.3390/atoms4010001