Files in this item
Files  Description  Format 

application/pdf Zhu_Guojun.pdf (1MB)  (no description provided) 
Description
Title:  BECBCS crossover with Feshbach resonance for threehyperfinespecies model 
Author(s):  Zhu, Guojun 
Director of Research:  Leggett, Anthony J. 
Doctoral Committee Chair(s):  Baym, Gordon A. 
Doctoral Committee Member(s):  Leggett, Anthony J.; DeMarco, Brian L.; Willenbrock, Scott S. 
Department / Program:  Physics 
Discipline:  Physics 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  superconductivity
crossover BoseEinstein condensation alkali gas 
Abstract:  The BECBCS crossover problem has been intensively studied both theoretically and experimentally largely thanks to Feshbach resonances which allow us to tune the effective interaction between alkali atoms. In a Feshbach resonance, the effective swave scattering length grows when one moves toward the resonance point, and eventually diverges at this point. There is one characteristic energy scale, $\delta_c$, defined as, in the negative side of the resonance point, the detuning energy at which the weight of the bound state shifts from predominatedly in the openchannel to predominated in the closedchannel. When the manybody energy scale (e.g. the Fermi energy, $E_{F}$) is larger than $\delta_c$, the closedchannel weight is significant and has to be included in the manybody theory. Furthermore, when two channels share a hyperfine species, the Pauli exclusion between fermions from two channels also needs to be taken into consideration in the manybody theory. The current thesis addresses the above problem in detail. A set of gap equations and number equations are derived at the meanfield level. The fermionic and bosonic excitation spectra are then derived. Assuming that the uncoupled boundstate of the closedchannel in resonance is much smaller than the interparticle distance, as well as the swave scattering length, $a_s$, we find that the basic equations in the singlechannel crossover model are still valid. The correction first comes from the existing of the finite chemical potential and additional counting complication due to the closedchannel. These two corrections need to be included into the meanfield equations, i.e. the gap equations and the number equations, and be solved selfconsistently. Then the correction due to the interchannel Pauli exclusion is in the order of the ratio of the Fermi energy and the Zeeman energy difference between two channels, $E_F/\eta$, which can be analyzed perturbatively over the previous corrections. Fermionic and bosonic excitation modes are studied. Similarly as the meanfield result, the basic structure follows that of the singlechannel model, and the correction due to the interchannel Pauli exclusion can be treated perturbatively with expansion parameter in the order of $E_F/\eta$. In the bosonic excitation, a new outofsync phase mode emerges for the twocomponent order parameters. It is nevertheless gapped at the the pairbreaking energy. 
Issue Date:  20120522 
URI:  http://hdl.handle.net/2142/31105 
Rights Information:  Copyright 2011 Guojun Zhu 
Date Available in IDEALS:  20120522 
Date Deposited:  201205 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois 
Dissertations and Theses  Physics
Dissertations in Physics