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Cambridge University Press eBooks

The Fermi Superfluid

Hui Zhai

Published Jan 30, 2021• 0 citations
Publisher

Abstract

1. Compare the difference between the two-body problem in a vacuum and on top of the Fermi sea. 2. Introduce the BCS mean-field theory and the BCS ground state wave function and its excitation. 3. Introduce the physical picture of BCS pairing. 4. Introduce the concept of contact using the BCS state as an example. 5. Discuss how the BCS state responds to the Zeeman field. 6. Discuss different pairing symmetries. 7. Discuss how the BCS-BEC crossover mean-field equation recovers features in both the BCS and the BEC limit. 8. Discuss different behaviors of the excitation spectrum in the BCS and the BEC regimes and determine superfluid critical velocity from the excitation spectrum. 9. Discuss how the superfluid transition temperature changes from the BCS regime to the BEC regime. 10. Introduce a list of experimental observations on the BCS-BEC crossover. 11. Discuss the challenging issues in studying the unitary Fermi gas. 12. Introduce the concept of holographic duality and the prediction of the $\eta/s$ bound.

DOI
10.1017/9781108595216.007

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Cambridge University Press eBooks•Jan 30, 2021•0 citations
  1. Compare the difference between the two-body problem in a vacuum and on top of the Fermi sea. 2. Introduce the BCS mean-field theory and the BCS ground state wave function and its excitation. 3. Introduce the physical picture of BCS pairing. 4. Introduce the concept of contact using the BCS state as an example. 5. Discuss how the BCS state responds to the Zeeman field. 6. Discuss different pairing symmetries. 7. Discuss how the BCS-BEC crossover mean-field equation recovers features in both the BCS and the BEC limit. 8. Discuss different behaviors of the excitation spectrum in the BCS and the BEC regimes and determine superfluid critical velocity from the excitation spectrum. 9. Discuss how the superfluid transition temperature changes from the BCS regime to the BEC regime. 10. Introduce a list of experimental observations on the BCS-BEC crossover. 11. Discuss the challenging issues in studying the unitary Fermi gas. 12. Introduce the concept of holographic duality and the prediction of the η/s\eta/sη/s bound.
Abstract This is the first of a series of chapters devoted to interacting Fermi gases, with special focus here on the effects of superfluidity. It starts with a brief discussion of the ideal Fermi gas and then focuses on the properties of dilute interacting Fermi gases. Topics include the weakly repulsive Fermi gas; the gas of composite bosons; the BCS limit of a weakly interacting Fermi gas; the strongly interacting, but still dilute, unitary Fermi gas where the scattering length is much larger than the average interatomic distance; the BCS–BEC crossover; and the Bogoliubov–de Gennes approach. A discussion of the main physical quantities predicted by mean-field theory and by quantum Monte Carlo simulations, including, in particular, the equation of state, the momentum distribution, and the condensation of pairs, is also presented.
PACS. 03.75.Hh – Static properties of condensates; thermodynamical, statistical and structural properties. PACS. 03.75.Ss – Degenerate Fermi gases. PACS. 05.30.Fk – Fermion systems and electron gas. Abstract. – We present a theory for a superfluid Fermi gas near the BCS-BEC crossover, including pairing fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink for the normal phase. In the strong coupling limit, our theory is able to recover the Bogoliubov theory of a weakly interacting Bose gas with a molecular scattering length very close to the known exact result. We compare our results with recent Quantum Monte Carlo simulations both for the ground state and at finite temperature. Excellent agreement is found for all interaction strengths where simulation results are available. The recent experimental realization of strongly interacting Fermi gases of 6 Li and 40 K atoms near a Feshbach resonance has opened up the exciting possibility of investigating the crossover from a Bardeen-Cooper-Schrieffer (BCS) superfluid to a Bose-Einstein condensate (BEC) [1–5]. In these systems, the inter-atomic interaction strength can be varied by tuning
The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the sss-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.
We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at T=0 using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. Results on Tan's contact parameter associated with short-range physics are also reported along the BCS-BEC crossover.
1. Introduce quantum phase transition in the Bose-Hubbard model. 2. Emphasize vanishing energy scales and universality at the quantum critical point. 3. Introduce microscopic theories to describe the quantum phase transition, and explicitly show the vanishing of energy scales and the critical exponents. 4. Illustrate the emergent Lorentz symmetry and the Higgs mode at the quantum critical point of the Bose-Hubbard model with the particle-hole symmetry. 5. Discuss an experimental probe of the superfluid to the Mott insulator phase transition. 6. Show that the repulsive and the attractive Fermi-Hubbard models are related by the particle-hole symmetry. 7. Discuss the origin of antiferromagnetic order in the repulsive Fermi-Hubbard model at half-filling. 8. Introduce the enlarged SO(4)SO(4)SO(4) symmetry of the Fermi-Hubbard model at half-filling and zero spin imbalance and its physical concequence. 9. Introduce important unsolved challenge issues in the Fermi-Hubbard model. 10. Introduce the concept of eigenstate thermalization hypothesis and many-body localization as opposite to thermalization. 11. Introduce a few metrics to characterize the many-body localization. 12. Emphasize the role of entanglement entropy in characterizing quantum thermalization, and discuss how to measure entanglement entropy in ultracold atom systems.