Within the framework of quantum field theory, we find that uniform Bose atomic gases with noncontact interaction can undergo a Bardeen–Cooper–Schrieffer (BCS) condensation below a critical temperature. In the BCS condensation state, bare atoms with opposite wave vectors are bound into pairs, and unpaired bare atoms are transformed into a new kind of quasi-particle, i.e., the dressed atom. The atom-pair system is a condensate or a superfluid and the dressed-atom system is a normal fluid. At absolute zero temperature the condensate possesses a lowest negative energy. The critical temperature and the effective mass of dressed atoms are derived analytically. The transition from the BCS condensation state to the normal state is a first-order phase transition.
We find that uniform Bose atomic gases with weak attraction can undergo a Bardeen—Cooper—Schrieffer (BCS) condensation below a critical temperature. In the BCS condensation state, bare atoms with opposite wave vectors are bound into pairs, and unpaired bare atoms are transformed into a new kind of quasi-particles, i.e. the dressed atoms. The atom-pair system is a condensate or a superfluid and the dressed-atom system is a normal fluid. The critical temperature and the effective mass of dressed atoms are derived analytically. The transition from the BCS condensation state to the normal state is a first-order phase transition.
This thesis focuses on the analysis of Bardeen-Cooper-Schrieffer (BCS) \nto Bose-Einstein condensation (BEC) evolution in ultracold superfluid \nFermi gases when the interaction between atoms is varied. The tuning of \nattractive interactions permits the ground state of the system to evolve from a weak \nfermion attraction BCS limit of loosely bound and largely overlapping Cooper pairs \nto a strong fermion attraction limit of tightly bound small bosonic molecules \nwhich undergo BEC. \nThis evolution is accompanied by anomalous behavior of many superfluid \nproperties, and reveals several quantum phase transitions. \nThis thesis has two parts: \nIn the first part, I analyze zero and nonzero orbital angular momentum \npairing effects, and show that a quantum phase transition occurs for \nnonzero angular momentum pairing, unlike the
s-wave case where the BCS \nto BEC evolution is just a crossover. \nIn the second part, I analyze two-species fermion mixtures with mass and \npopulation imbalance in continuum, trap and lattice models. In contrast with \nthe crossover physics found in the mass and population balanced mixtures, \nI demonstrate the existence of phase transitions between normal and \nsuperfluid phases, as well as phase separation between superfluid (paired) \nand normal (excess) fermions in imbalanced mixtures as a function of scattering \nparameter and mass and population imbalance.
This study presents a simple idea and a conceptual understandingof the crossover from the Bardeen Cooper (BCS) state of weakly-correlatedpairs of fermions to the Bose{Einstein condensation (BEC) of diatomicmolecules in the atomic Fermi gas. In the context of ultra cold Fermi gases,a BCS-BEC crossover means that by tuning the interaction strength, onegoes from a BCS state to a BEC state without encountering a phase transition.BEC state is a Bose-Einstein condensate of two-atom molecules (boundfermions), while the BCS state is made up of pair of atoms. The differencebetween the pairs and the molecules is that the molecules are localized inthe real space, whereas the BCS pairs are made of two particles with oppositemomenta in the momentum space.
The use of Feshbach resonances in the field of ultracold gases has received a lot of attention recently. In first instance it was realized that these resonances can be used to alter the interaction strength in an atomic gas, by means of tuning an external magnetic field. Furthermore, by sweeping the magnetic field from one side of the resonance to the other, a degenerate gas of bosonic molecules can be created, a significant accomplishment. By making the interactions between fermionic atoms strongly attractive, a fermionic superfluid was recently made, a feat that has drawn a lot of attention in the physics community and from the media. We present work that describes these many-particle systems near a Feshbach resonance in a comprehensive way by using the concept of dressed molecules. These dressed molecules are essentially two-particle states that are a superposition of a tightly bound bare molecule, and two unbound bare atoms. This description reduces to the correct paired wave-function in the two-body limit. Moreover it gives a physically correct description of all the phenomena mentioned above: the Bose-condensation of a gas near a Feshbach resonance, that contains molecules, is more correctly interpreted as a Bose-condensation of dressed molecules. The fermionic superfluid contains a condensate of bosonic pairs, normally called Cooper pairs, that can be understood as the dressed molecules. For the latter case, the dressed-molecule picture also gives an elegant characterization of the crossover between a Bose condensate of pure molecules on one side of the resonance, to a fermionic Bardeen-Cooper-Schrieffer superfluid on the other side. Then, the dressed molecules change continuously from being mostly a bare molecule, to being mostly a loose pair of two atoms. It is clear that the nature of the dressed molecules is much determined by the probability for it to be in the bare-molecular state. This probability we denote with a single parameter Z. We present various ways of calculating it, and study how it affects the macroscopic physics.
We analyze the evolution of superfluidity for nonzero orbital angular momentum channels from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) limit in three dimensions. First, we analyze the low-energy scattering properties of finite range interactions for all possible angular momentum channels. Second, we discuss ground-state
(T=0) superfluid properties including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, atomic compressibility, ground-state energy, and low-energy collective excitations. We show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the
s-wave case where the BCS to BEC evolution is just a crossover. Third, we present a Gaussian fluctuation theory near the critical temperature
(T=Tc), and we analyze the number of bound, scattering, and unbound fermions as well as the chemical potential. Finally, we derive the time-dependent Ginzburg-Landau functional near
Tc, and compare the Ginzburg-Landau coherence length with the zero-temperature average Cooper pair size.
We consider the evolution of superfluid properties of a three-dimensional p-wave Fermi gas from a weak coupling Bardeen-Cooper-Schrieffer (BCS) to strong coupling Bose-Einstein condensation (BEC) limit as a function of scattering volume. At zero temperature, we show that a quantum phase transition occurs for p-wave systems, unlike the s-wave case where the BCS to BEC evolution is just a crossover. Near the critical temperature, we derive a time-dependent Ginzburg-Landau (GL) theory and show that the GL coherence length is generally anisotropic due to the p-wave nature of the order parameter, and becomes isotropic only in the BEC limit.