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研究生:呂欣頤
研究生(外文):Hsin-I Lu
論文名稱:在費米原子氣裏的BCS、BEC態與Feshbach共振
論文名稱(外文):BCS,BEC states and Feshbach resonance in atomic Fermi gases
指導教授:張慶瑞
指導教授(外文):Ching-Ray Chang
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:物理研究所
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:54
中文關鍵詞:超流費米原子氣超導共振態
外文關鍵詞:Feshbach resonanceBECBCSatomic Fermi gases
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To study the behavior of atomic Fermi gases in the vicinity of Feshbach resonance, M. Holland et al. [12] and S. J. J. M. F. Kokkelmans et al. [22] proposed
resonance mean field theory in which the molecules formed by Feshbach resonance are considered in the many-body Hamiltonian. Motivated by microscopic scattering theory and resonance mean field theory, we develop a thermodynamic
method to study this system. In this method we treat atomic Fermi gases near resoance as a atom-molecule mixture. We can use BCS Hamiltonian and Bose-
Einstein statistics to describe the behavior of atoms and molecules respectively. Chemical equilibrium can be achieved between atoms and molecules due to hypefine interaction. We use this method to study the system behavior under different temperature and detuning energy and find that at low temperature a smooth BCS-BEC crossever can occure with decreasing detuning energy. We
further calculate a measurable quantity, molecular condensation fraction, and find its behavior matches qualitatively with the experimental result [16].
1 Introduction 1
2 Low-energy Feshbach resonances 5
2.1 Low Energy Potentail Scattering . . . . . . . . . 6
2.1.1 The Lippmann-Schwinger Equation . . . . . . . 6
2.1.2 Partial Wave Analysis and Scattering Length . 7
2.2 Low-energy Feshbach resonance . . . . . . . . . . 10
2.2.1 coupled-channel scattering problem . . . . . 10
2.2.2 Low-energy Feshbach resonance . . . . . . . .11
2.3 Feshbach resonances in cold atom system . . . . . .16
2.3.1 Two-body interaction . . . . . . . . . . . . 16
3 Resonance Mean Field Theory 19
3.1 Effective interaction . . . . . . . . . . . . . . .20
3.1.1 Coupled-channel scattering problem with contact potential . . . . . . . . . . . . . . . . . . . .20
3.1.2 Scattering length and the effective interaction strength . . . . . . . . . . . . . . . . . . 24
3.2 Resonance Mean field theory . . . . . . . . . . . 26
3.2.1 Many-body Hamiltonian . . .. . . . . . . . . 26
3.2.2 Mean fields . . . . . . . . . . . .. . . . . 27
3.2.3 Determination of mean fields . . . . . . . . 29
3.2.4 Determination of the transition temperature. 30
4 Thermodynamic method 35
4.1 Formalism . . . .. . . . . . . . . . . . . . . . . 36
4.2 Self-consistent equations . .. . . . . . . . . . . 37
4.3 Numerical solutions . . . . . .. . . . . . . . . . 38
4.3.1 Setting T = 0.4TF and changing ν . . . . . . 38
4.3.2 Setting T = 0.1TF and changing ν . . . . . . 39
4.3.3 Setting ν = -0.65εF and changing T . . . . . 46
5 Summary 51
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