Hubbard Model for Asymmetric Ultracold Fermionic ... - KOMET 337

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32 CHAPTER 3. UNBALANCED FERMI-MIXTURESx-position107.52.551.5246z-position10.58 0nDiff.0.0040.0030.0020.00102.55x-position7.5102468z-position∆0.20.150.10.0502.55x-position7.5102468z-positionFigure 3.15: Spatial distribution of the parameters n, (n ↑ −n ↓ ) = nm and ∆ in the x-z-planeat trap parameters: {U = −3, t = 1, µ 0 = 0, B = −0.05, Ω = Diag(0.05,0.3,0.1)}.
3.4. NUMERICAL RESULTS 33x-position6421.5246z-position810.510 0nDiff.0.0020.00150.0010.000502x-position46246810z-positionFigure 3.16: Spatial distribution of the parameters n and (n ↑ − n ↓ ) = nm in the x-z-planeat trap parameters: {U = −2, t = 1, µ 0 = 1, B = −0.01, Ω = Diag(0.2,0.3,0.1)}. The orderparameter ∆ vanishes in the whole system and is not shown.We will now discuss the numerical results presented in Figures 3.14 - 3.16. These Figuresdemonstrate that:1. Phase separation occurs: at different lattice sites different phases are found.2. The superfluid polarized phase never occurs.3. We see a shell structure of non-superfluid magnetized and superfluid non-magnetizedrings.4. In Figure 3.14 we have the magnetized phase in the center of the trap, the superfluidring sorrounding it and a magnetized phase in the outer region.5. In Figure 3.15 the magnetized phase in the center is missing, we have a superfluid phasein the center sorrounded by a magnetized phase.6. In Figure 3.16 superfluidity breaks down in the whole system. There is only the magnetizedphase left.
Page 1: Hubbard Model for AsymmetricUltraco
Page 4 and 5: coupling regime. The trapping poten
Page 6 and 7: 4.5 Critical temperatures . . . . .
Page 8 and 9: 2 CHAPTER 1. INTRODUCTIONlattice si
Page 10 and 11: 4 CHAPTER 1. INTRODUCTION1.2 Unbala
Page 12 and 13: 6 CHAPTER 1. INTRODUCTION
Page 14: 8 CHAPTER 2. FORMALISM AT WEAK COUP
Page 17 and 18: 2.3. SELF-CONSISTENCY EQUATIONS 11w
Page 19 and 20: 2.3. SELF-CONSISTENCY EQUATIONS 13w
Page 21 and 22: 2.4. PROPERTIES OF THE SELF-CONSIST
Page 25 and 26: Chapter 3Unbalanced Fermi-mixturesI
Page 33 and 34: 3.3. NUMERICAL METHOD 27- In Figure
Page 35 and 36: 3.3. NUMERICAL METHOD 29Input of
Page 37: 3.4. NUMERICAL RESULTS 31x-position
Page 41 and 42: Chapter 4Model with spin-dependent
Page 43 and 44: 4.2. SUPERFLUIDITY AWAY FROM HALF F
Page 45 and 46: 4.3. NUMERICAL METHOD FOR THE PROBL
Page 47 and 48: 4.4. NUMERICAL RESULTS FOR THE GROU
Page 49 and 50: 4.5. CRITICAL TEMPERATURES 430.4∆
Page 51 and 52: 4.5. CRITICAL TEMPERATURES 454.5.2
Page 53 and 54: Chapter 5Strong coupling limitIn th
Page 55 and 56: 5.2. GENERAL PROCEDURE 49with an an
Page 57 and 58: = ∑ ijlσ= − ∑ ijlσ= ∑ ijl
Page 59 and 60: 5.4. LOW TEMPERATURE LIMIT 53At fir
Page 61 and 62: 5.4. LOW TEMPERATURE LIMIT 555.4.2
Page 63 and 64: Summary and OutlookIn this thesis w
Page 65 and 66: Bibliography[1] C. Wieman and E. Co
Page 67 and 68: DanksagungAn erster Stelle möchte

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