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

More documents

Recommendations

Info

4 CHAPTER 1. INTRODUCTION1.2 Unbalanced Fermi-mixtures: a brief experimental overviewIn this section we present the experimental motivation for analyzing unbalanced Fermimixtureson optical lattices. In recent experiments [16] [17] the superfluidity of two-componentunbalanced Fermi-mixtures has been examined experimentally. Here we show brieflythe results obtained in the experiment done at Rice university [16]. In this experiment twocomponentFermi-mixtures with different proportions of the components were cooled downbelow the critical temperature of the superfluid phase transition. With the help of in-situimages, the spatial distribution of the majority and of the minority species were imaged. Theresults are shown graphically here:Figure 1.2: In-situ images of the spatial particle distributions are represented here. In the leftimage the population of the minority cloud is decreased from (a) to (f), while the temperatureis constant. In each part the upper picture shows the distribution of the majority species,the middle picture shows the distribution of the minority species and the lower picture showstheir difference. In the right image the parts (a)/(b) and (c)/(d) are measured at differenttemperatures. The parts (a) and (b) correspond to the lower temperature, which is the sameas in the left image. The parts (c) and (d) are measured at a higher temperature, but stillbelow the critical temperature of the superfluid phase transition.From Figure 1.2 we conclude that:- There is superfluidity in unbalanced Fermi-mixtures at low temperatures.- Phase separation takes place.- A superfluid core with balanced occupation is in the middle of the trap.- In the outer region we find the unpaired part of the majority cloud.- There is a second critical temperature beyond the superfluid-to-normal critical temperature.Between those critical temperatures we find a polarized superfluid phase.Hence, unbalanced Fermi-mixtures differ from balanced ones, where we find only one criticaltemperature and no phase separation, since the complete cloud is superfluid below the critical
1.2. UNBALANCED FERMI-MIXTURES: A BRIEF EXPERIMENTAL OVERVIEW 5temperature and it is normal above of it.Since these experiments were performed without the use of optical lattices and until todaytheory has looked mainly at these experiments [18] [19], we decided in this thesis to use theHubbard model to investigate unbalanced Fermi-mixtures loaded into optical lattices. Theresults we have obtained are presented in chapter 3.
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 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 and 38: 3.4. NUMERICAL RESULTS 31x-position
Page 39 and 40: 3.4. NUMERICAL RESULTS 33x-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
show all

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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?