Roy, Arunesh (2014) *Thermodynamics of Spin Orbit coupled Bose Einstein Condensate.* Masters thesis, Indian Institute of Science Education and Research Kolkata.

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## Abstract

In this thesis, we consider the Bose-Einstein condensation of ideal Bose gas in prsence of pseudo spin-orbit coupling. We take equal Rashba and Dresselhaus spin orbit coupling which give rise to degenerate minima at �nite momenta in the ground state eigenvalue and hence form an unconvensional condensate. In this work, we �rst considered the quantum mechanics of this system to calculate energy eigenvalues and the wave function both of which posses a signature of spin orbit coupling. Then we consider the statistical mechanical properties of these systems. In the case of homogeneous system, we �rst calculate the density of states and then the critical temperature of the system. The critical temperature shows a non-analytic point at a particular value of a certain parameter the Raman Coupling which is also known as the point of quantum phase transition in the case of interacting system. Critical temperature at point shows a cusp like structure and drops down to a minimum value at the same point. The critical temperature can be approximated analytically in two di�erent Raman coupling regime before and beyond the critical point from the density of state description. This description can be found by approximating the density of states with that of a free particle with reduced mass in the direction in which the spin orbit coupling takes place. We then consider the magnetization of the system an its variance with the change in the Raman coupling. The magnetization of the condensate vanishes at the same critical point. We next consider the spin orbit coupled Bose gas in a harmonic con�nement. The critical temeperature for this case will show a dip in around the same value of the critical point as in the previous case. But, in this case the drop in the critical temeperature is less sharp and smoothened due to the presense of an harmonic trap. Next we consider the natural extension of the spin bosons to a large spin and we show that it can be exactly mapped to the Dicke model. We can also estimate the critical temperature from this description in a similar fashion.

Item Type: | Thesis (Masters) |
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Additional Information: | Supervisor: Dr. Subhasis Sinha |

Uncontrolled Keywords: | Bose Einstein Condensate; Homogeneous Bose Gas; Thermodynamics; Spin Orbit |

Subjects: | Q Science > QC Physics |

Divisions: | Department of Physical Sciences |

Depositing User: | IISER Kolkata Librarian |

Date Deposited: | 14 Jan 2015 16:11 |

Last Modified: | 14 Jan 2015 16:11 |

URI: | http://eprints.iiserkol.ac.in/id/eprint/194 |

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