Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

APS Division of Atomic, Molecular and Optical Physics Meeting Abstracts

A crossover model for BEC to BCS superconductivity in a resonant Fermi gas

J. N. Milstein, S. J. J. M. F. Kokkelmans, Murray Holland

Published May 1, 2002• 0 citations
OpenAlex

Abstract

The model which we have recently proposed to describe the behavior of a dilute Fermi gas in the presence of a Fechbach resonance (M. Holland, S.J.J.M.F. Kokkelmans, M.L. Chiofalo, and R. Walser, Phys. Rev. Lett. 87), 120406 (2001). (S.J.J.M.F. Kokkelmans, J.N. Milstein, M.L. Chiofalo, R. Walser, and M.J. Holland, e-print cond-mat/0112283.) has been extended to take into account the first order effects of pairing fluctuations. Within the context of a path integral formalism, we discuss a model which describes the crossover between the strong and weak coupling regimes of a dilute Fermi gas in the presence of a Feschbach resonance. With this model we are able to connect between the weak coupling BCS-regime and the strongly coupled BEC limits by modifying the detuning of the resonant state. Even though the scattering length goes through a singularity in the intermediate coupling regime, the curves connecting these regimes remains smooth.

Related papers

Interacting Fermi Gases and the BCS–BEC Crossover

Лев П. Питаевский, S. Stringari

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.

•Jan 1, 2016•1 citation

Aspects of BCS to BEC “Crossover” as illustrated by fulleride superconductivity

Richard H. Squire, Norman Henry March

Abstract The pioneering works by Eagles, Leggett, and Nozieres/Schmitt‐Rink [Eagles, Phys Rev, 1969, 186, 456; Leggett, In: Modern Trends in the Theory of Condensed Matter, Springer‐Verlag: Berlin, 1980; Nozieres and Schmitt‐Rink, Low Temp Phys, 1985, 59, 980] (reviewed and augmented by Randeria [Randeria, Bose‐Einstein Condensation, Cambridge University Press, Cambridge, 1995, p 255]) emphasize that in the limits of the models studied both at T = 0 and T ≠ 0, the “cross‐over” from a BCS‐type to a BEC‐type superconductor is continuous. The BCS and BEC “end points” seem to be well‐established. However, in the intermediate region—home to fulleride and high temperature superconductors—considerable extrapolation of the models must be done as there still is no exact theory. Yet, considerable current literature is devoted to what appears to be more “singular‐type phenomena” such as quantum critical points, “stripe” formation, insulator to superconductor phase transitions, loss of validity of the Fermi liquid theory, etc. Using a connection we have made with “cold” atom fermion‐boson crossover theory [Chen, Stajic, Levin, 2005, e‐print cond‐mat/0508603], we can establish that the resonance previously discussed [Squire and March, Int J Quant Chem, 2006, 106, 3343] is a result of the crossing of the fermion band by the boson band. While the ground state appears to remain continuous, the paired energy gap becomes transformed. We discuss features of the resonance and the experimentally observed pre‐formed “BEC Cooper pair” formation, essential to the boson‐fermion resonance theory. In addition some of the various singular phenomena discussed above can be put more into perspective. Finally, in both limits the relation of characteristic lengths to the inverse Fermi momentum is strongly emphasized, as is the role of the chemical potential near the pseudogap regime. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

International Journal of Quantum Chemistry•Jan 1, 2007•5 citations

Equation of state of a superfluid Fermi gas in the BCS- BEC crossover

H. Hu, Xia-Ji Liu, P. D. Drummond

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

•Jan 1, 2006•84 citations

Equation of state of a superfluid Fermi gas in the BCS-BEC crossover

H Hu, X.-J Liu, P. D. Drummond

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.

arXiv:cond-mat/0506046•Europhysics Letters (EPL)•Apr 11, 2006•177 citations

BCS-BEC Crossover and the Unitary Fermi Gas

Mohit Randeria, Edward Taylor

The crossover from weak coupling Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) of tightly bound pairs, as a function of the attractive interaction in Fermi systems, has long been of interest to theoretical physicists. The past decade has seen a series of remarkable experimental developments in ultracold Fermi gases that has realized the BCS-BEC crossover in the laboratory, bringing with it fresh new insights into the very strongly interacting unitary regime in the middle of this crossover. In this review, we start with a pedagogical introduction to the crossover and then focus on recent progress in the strongly interacting regime. While our focus is on new theoretical developments, we also describe three key experiments that probe the thermodynamics, transport and spectroscopy of the unitary Fermi gas. We discuss connections between the unitary regime and other areas of physics -- quark-gluon plasmas, gauge-gravity duality and high temperature superconductivity -- and conclude with open questions about strongly interacting Fermi gases.

arXiv:1306.5785•Jun 24, 2013•76 citations

Single-particle excitations in a trapped gas of Fermi atoms in the BCS-BEC crossover region. II. Broad Feshbach resonance

Yoji Ohashi, Adam Griffin

We apply the formulation developed in a recent paper [Y. Ohashi and A. Griffin, Phys. Rev. A 72, 013601 (2005)] for single-particle excitations in the BCS-BEC crossover to the case of a broad Feshbach resonance. At $T=0$, we solve the Bogoliubov--de Gennes coupled equations taking into account a Bose condensate of bound states (molecules). In the case of a broad resonance, the density profile $n(r)$, as well as the profile of the superfluid order parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}(r)$, are spatially spread out to the Thomas-Fermi radius, even in the crossover region. This order parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}(r)$ suppresses the effects of low-energy Andreev bound states on the rf tunneling current. As a result, the peak energy in the rf spectrum is found to occur at an energy equal to the superfluid order parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}(r=0)$ at the center of the trap, in contrast to the case of a narrow resonance, and in agreement with recent measurements. The local density approximation is found to give a good approximation for the rf-tunneling spectrum.

arXiv:cond-mat/0508213•Physical Review A•Dec 5, 2005•25 citations
The model which we have recently proposed to describe the behavior of a dilute Fermi gas in the presence of a Fechbach resonance (M. Holland, S.J.J.M.F. Kokkelmans, M.L. Chiofalo, and R. Walser, Phys. Rev. Lett. 87), 120406 (2001). (S.J.J.M.F. Kokkelmans, J.N. Milstein, M.L. Chiofalo, R. Walser, and M.J. Holland, e-print cond-mat/0112283.) has been extended to take into account the first order effects of pairing fluctuations. Within the context of a path integral formalism, we discuss a model which describes the crossover between the strong and weak coupling regimes of a dilute Fermi gas in the presence of a Feschbach resonance. With this model we are able to connect between the weak coupling BCS-regime and the strongly coupled BEC limits by modifying the detuning of the resonant state. Even though the scattering length goes through a singularity in the intermediate coupling regime, the curves connecting these regimes remains smooth.
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.
Abstract The pioneering works by Eagles, Leggett, and Nozieres/Schmitt‐Rink [Eagles, Phys Rev, 1969, 186, 456; Leggett, In: Modern Trends in the Theory of Condensed Matter, Springer‐Verlag: Berlin, 1980; Nozieres and Schmitt‐Rink, Low Temp Phys, 1985, 59, 980] (reviewed and augmented by Randeria [Randeria, Bose‐Einstein Condensation, Cambridge University Press, Cambridge, 1995, p 255]) emphasize that in the limits of the models studied both at T = 0 and T ≠ 0, the “cross‐over” from a BCS‐type to a BEC‐type superconductor is continuous. The BCS and BEC “end points” seem to be well‐established. However, in the intermediate region—home to fulleride and high temperature superconductors—considerable extrapolation of the models must be done as there still is no exact theory. Yet, considerable current literature is devoted to what appears to be more “singular‐type phenomena” such as quantum critical points, “stripe” formation, insulator to superconductor phase transitions, loss of validity of the Fermi liquid theory, etc. Using a connection we have made with “cold” atom fermion‐boson crossover theory [Chen, Stajic, Levin, 2005, e‐print cond‐mat/0508603], we can establish that the resonance previously discussed [Squire and March, Int J Quant Chem, 2006, 106, 3343] is a result of the crossing of the fermion band by the boson band. While the ground state appears to remain continuous, the paired energy gap becomes transformed. We discuss features of the resonance and the experimentally observed pre‐formed “BEC Cooper pair” formation, essential to the boson‐fermion resonance theory. In addition some of the various singular phenomena discussed above can be put more into perspective. Finally, in both limits the relation of characteristic lengths to the inverse Fermi momentum is strongly emphasized, as is the role of the chemical potential near the pseudogap regime. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
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
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 crossover from weak coupling Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) of tightly bound pairs, as a function of the attractive interaction in Fermi systems, has long been of interest to theoretical physicists. The past decade has seen a series of remarkable experimental developments in ultracold Fermi gases that has realized the BCS-BEC crossover in the laboratory, bringing with it fresh new insights into the very strongly interacting unitary regime in the middle of this crossover. In this review, we start with a pedagogical introduction to the crossover and then focus on recent progress in the strongly interacting regime. While our focus is on new theoretical developments, we also describe three key experiments that probe the thermodynamics, transport and spectroscopy of the unitary Fermi gas. We discuss connections between the unitary regime and other areas of physics -- quark-gluon plasmas, gauge-gravity duality and high temperature superconductivity -- and conclude with open questions about strongly interacting Fermi gases.
We apply the formulation developed in a recent paper [Y. Ohashi and A. Griffin, Phys. Rev. A 72, 013601 (2005)] for single-particle excitations in the BCS-BEC crossover to the case of a broad Feshbach resonance. At T=0T=0T=0, we solve the Bogoliubov--de Gennes coupled equations taking into account a Bose condensate of bound states (molecules). In the case of a broad resonance, the density profile n(r)n(r)n(r), as well as the profile of the superfluid order parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}(r)$, are spatially spread out to the Thomas-Fermi radius, even in the crossover region. This order parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}(r)$ suppresses the effects of low-energy Andreev bound states on the rf tunneling current. As a result, the peak energy in the rf spectrum is found to occur at an energy equal to the superfluid order parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}(r=0)$ at the center of the trap, in contrast to the case of a narrow resonance, and in agreement with recent measurements. The local density approximation is found to give a good approximation for the rf-tunneling spectrum.