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.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.

Cambridge University Press eBooksJan 30, 20210 citations

BEC to basics

Ed Gerstner

Nature PhysicsSep 22, 20050 citations

STUDY OF BARDEEN COOPER STATE (BCS) TO BOSE EINSTEIN CONDENSATION (BEC) CROSSOVER

AMITESH KUMAR, R.K. VERMA

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.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 SCIENTIFIC TEMPERJul 25, 20190 citations

The BEC–BCS Crossover

R. Combescot

Cambridge University Press eBooksMar 10, 20220 citations

SNS junctions along the BCS-BEC crossover

Gautam Rai, Arman Babakhani, Ying Wang +2 more

We present a theory of SNS junctions, where a normal metal is in contact with two superconductors, along the crossover from the BCS to the BEC regime. Such systems can be realized experimentally by gate-controlled doping of thin film superconductors. We show that Andreev levels exist even in the BEC regime, as long as there is sufficient density of states in the normal metal. We derive the Josephson current through one-dimensional Sharvin contacts. We find that the Josephson current at zero temperature has no peak along the BCS-BEC crossover at $T=0\phantom{\rule{4.pt}{0ex}}\text{K}$ unless the order paramter $\mathrm{\ensuremath{\Delta}}$ is peaked, as it is the case for superconductors with one-dimensional density of states. At finite temperature, however, we find that the Josephson current is maximal at the BCS-BEC crossover for any dimension. We identify the mechanism for this phenomenon to be a decrease in the number of Andreev levels, accompanied by an increase in excitation energy to the unoccupied levels, along the BCS-BEC crossover. This makes it less likely that these states are thermally occupied. As a consequence, the Josephson current is more strongly reduced on the BCS side of the crossover, resulting in a maximal Josephson current at the BCS-BEC crossover. Furthermore, we find that the current phase relation changes along the BCE-BEC crossover with a slope which has a pronounced maximum on the BEC-side of the BCS-BEC crossover. This maximum becomes larger and sharper as the temperature is lowered.We present a theory of SNS junctions, where a normal metal is in contact with two superconductors, along the crossover from the BCS to the BEC regime. Such systems can be realized experimentally by gate-controlled doping of thin film superconductors. We show that Andreev levels exist even in the BEC regime, as long as there is sufficient density of states in the normal metal. We derive the Josephson current through one-dimensional Sharvin contacts. We find that the Josephson current at zero temperature has no peak along the BCS-BEC crossover at $T=0\phantom{\rule{4.pt}{0ex}}\text{K}$ unless the order paramter $\mathrm{\ensuremath{\Delta}}$ is peaked, as it is the case for superconductors with one-dimensional density of states. At finite temperature, however, we find that the Josephson current is maximal at the BCS-BEC crossover for any dimension. We identify the mechanism for this phenomenon to be a decrease in the number of Andreev levels, accompanied by an increase in excitation energy to the unoccupied levels, along the BCS-BEC crossover. This makes it less likely that these states are thermally occupied. As a consequence, the Josephson current is more strongly reduced on the BCS side of the crossover, resulting in a maximal Josephson current at the BCS-BEC crossover. Furthermore, we find that the current phase relation changes along the BCE-BEC crossover with a slope which has a pronounced maximum on the BEC-side of the BCS-BEC crossover. This maximum becomes larger and sharper as the temperature is lowered.

arXiv:2411.19396Physical review. B./Physical review. BApr 25, 20251 citation

BCS-BEC Crossover

Peking University-World Scientific advanced physics series/Peking University-World Scientific advance physics seriesNov 1, 20180 citations

\eta/s

bound.

T=0\phantom{\rule{4.pt}{0ex}}\text{K}

unless the order paramter $\mathrm{\ensuremath{\Delta}}$ is peaked, as it is the case for superconductors with one-dimensional density of states. At finite temperature, however, we find that the Josephson current is maximal at the BCS-BEC crossover for any dimension. We identify the mechanism for this phenomenon to be a decrease in the number of Andreev levels, accompanied by an increase in excitation energy to the unoccupied levels, along the BCS-BEC crossover. This makes it less likely that these states are thermally occupied. As a consequence, the Josephson current is more strongly reduced on the BCS side of the crossover, resulting in a maximal Josephson current at the BCS-BEC crossover. Furthermore, we find that the current phase relation changes along the BCE-BEC crossover with a slope which has a pronounced maximum on the BEC-side of the BCS-BEC crossover. This maximum becomes larger and sharper as the temperature is lowered.