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oai:www.ideals.illinois.edu:2142/31105 2023-07-10 col_2142_5131 col_2142_8859 com_2142_5130 com_2142_8858 com_2142_234

Leggett, Anthony J. Baym, Gordon A. Leggett, Anthony J. DeMarco, Brian L. Willenbrock, Scott S. Zhu, Guojun 2012-05-22T00:28:20Z 2012-05-22T00:28:20Z 2012-05 2012-05-22T00:28:20Z 2012-05 The BEC-BCS 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 s-wave 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 open-channel to predominated in the closed-channel. When the many-body energy scale (e.g. the Fermi energy, $E_{F}$) is larger than $\delta_c$, the closed-channel weight is significant and has to be included in the many-body 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 many-body theory. The current thesis addresses the above problem in detail. A set of gap equations and number equations are derived at the mean-field level. The fermionic and bosonic excitation spectra are then derived. Assuming that the uncoupled bound-state of the closed-channel in resonance is much smaller than the inter-particle distance, as well as the s-wave scattering length, $a_s$, we find that the basic equations in the single-channel crossover model are still valid. The correction first comes from the existing of the finite chemical potential and additional counting complication due to the closed-channel. These two corrections need to be included into the mean-field equations, i.e. the gap equations and the number equations, and be solved self-consistently. Then the correction due to the inter-channel 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 mean-field result, the basic structure follows that of the single-channel model, and the correction due to the inter-channel Pauli exclusion can be treated perturbatively with expansion parameter in the order of $E_F/\eta$. In the bosonic excitation, a new out-of-sync phase mode emerges for the two-component order parameters. It is nevertheless gapped at the the pair-breaking energy. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2012-01-03T20:29:57Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 3 0_deposit.zip: 3365985 bytes, checksum: 08a59e223486064e4867352fa28e0765 (MD5) newSlide.pdf: 738090 bytes, checksum: c3d15e56dea617d6ba734097aeb64e16 (MD5) Zhu_Guojun.pdf: 1111819 bytes, checksum: 7e6b74f2ec58a24da2cc3b2a8a959df1 (MD5) Made available in DSpace on 2012-05-22T00:28:20Z (GMT). No. of bitstreams: 3 Zhu_Guojun.pdf: 1113782 bytes, checksum: b574b695c0fdbb33a2fa5a5781c95c0d (MD5) 0_deposit.zip: 3365985 bytes, checksum: 08a59e223486064e4867352fa28e0765 (MD5) license.txt: 4057 bytes, checksum: 987d8a342319768a324903601e997509 (MD5) http://hdl.handle.net/2142/31105 en Copyright 2011 Guojun Zhu superconductivity crossover Bose-Einstein condensation alkali gas BEC-BCS crossover with Feshbach resonance for three-hyperfine-species model text Physics 1244 Physics 0240 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Physics -UIUC 10KS0240PHD