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

arXiv:cond-mat/0402448 · Physical Review Letters

Exactly Solvable Model of the BCS-BEC Crossover

Jean-Noël Fuchs, Alessio Recati, W. Zwerger

Published Aug 27, 2004• 167 citations
arXivHTMLPDF

Abstract

We discuss an integrable model of interacting fermions in one dimension that allows a complete description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2 fermions to the Lieb-Liniger model of repulsive bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from -infinity to +infinity while the system evolves from a BCS-like state through a Tonks-Girardeau gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and spin excitations, and the correlation functions. An experimental realization with cold atoms of such a one-dimensional BCS-BEC crossover is proposed.

DOI
10.1103/physrevlett.93.090408

Related papers

Boson-fermion resonance model in one dimension

Alessio Recati, Jean-Noël Fuchs, W. Zwerger

We discuss the BCS-BEC crossover for one-dimensional spin-$1∕2$ fermions at zero temperature using the boson-fermion resonance model in one dimension. We show that in the limit of a broad resonance, this model is equivalent to an exactly solvable single-channel model, the so-called modified Gaudin-Yang model. We argue that the one-dimensional crossover may be realized either via the combination of a Feshbach resonance and a confinement-induced resonance or using direct photoassociation in a two-component Fermi gas with effectively one-dimensional dynamics. In both cases, the system may be driven from a BCS-like state through a molecular Tonks-Girardeau gas close to resonance to a weakly interacting Bose gas of dimers.

arXiv:cond-mat/0410183•Physical Review A•Mar 28, 2005•21 citations

Solution of the BEC to BCS Quench in One Dimension

Colin Rylands, Pasquale Calabrese, Bruno Bertini

A gas of interacting fermions confined in a quasi one-dimensional geometry shows a BEC to BCS crossover upon slowly driving its coupling constant through a confinement-induced resonance. On one side of the crossover the fermions form tightly bound bosonic molecules behaving as a repulsive Bose gas, while on the other they form Cooper pairs, whose size is much larger than the average interparticle distance. Here we consider the situation arising when the coupling constant is varied suddenly from the BEC to the BCS value. Namely, we study a BEC-to-BCS quench. By exploiting a suitable continuum limit of recently discovered solvable quenches in the Hubbard model, we show that the local stationary state reached at large times after the quench can be determined exactly by means of the quench action approach. We provide an experimentally accessible characterization of the stationary state by computing local pair correlation function as well as the quasiparticle distribution functions. We find that the steady state is increasingly dominated by two-particle spin singlet bound states for stronger interaction strength, but that bound state formation is inhibited at larger BEC density. The bound state rapidity distribution displays quartic power-law decay suggesting a violation of Tan's contact relations.

arXiv:2209.00956•Physical Review Letters•Jan 12, 2023•18 citations

Four-Body Problem and BEC-BCS Crossover in a Quasi-One-Dimensional Cold Fermion Gas

Christophe Mora, A. Komnik, Reinhold Egger +1 more

The four-body problem for an interacting two-species Fermi gas is solved analytically in a confined quasi-one-dimensional geometry, where the two-body atom-atom scattering length a(aa) displays a confinement-induced resonance. We compute the dimer-dimer scattering length a(dd) and show that this quantity completely determines the many-body solution of the associated BEC-BCS crossover phenomenon in terms of bosonic dimers.

arXiv:cond-mat/0501641•Physical Review Letters•Aug 19, 2005•38 citations

Dimensional crossover in two-component Fermi gases with attractive interactions

Mathias Macêdo Lima

This work studies zero-temperature Fermi gases with short-ranged and attractive interactions with focus on the dimensionality aspects by confining the system from three to two dimensions. Interacting Fermi gases are superfluids characterized as being strongly correlated if the scattering length is much larger than the other scales present. In the many-body context, this category of systems requires a careful treatment since mean-field approaches are not expected to hold under the conditions which define the strong pairing. For this reason, we employ quantum Monte Carlo methods to study the dimensionality effects in two-component Fermi gases in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS-BEC) crossover. To be able to investigate such aspects, we consider a three-dimensional gas with periodic boundary conditions in the xy plane and a confining potential in the z direction capable of reducing the dimensionality of the system, which defines a dimensional BCS-BEC crossover. We calculate the equation of state as the energy per particle as a function of the dimensionality and as a function of the interaction parameter, which are characterized by the oscillator length in the z direction and the scattering length respectively. The greater confinement in the system lowers the interparticle distances, which increases the effects of the attractive interactions between antiparallel-spin fermions.We also calculate the density profile in the z direction over the crossover for different confinements and different interaction parameters to quantify their influence on the spatial distribution of the particles. This study connects the perspectives between theoretical and experimental works in low-dimensional ultracold Fermi gases by utilizing an approach that is similar to what it is realized in modern experiments.

•Mar 30, 2026•0 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

Theoretical results of strongly interacting quasi-one-dimensional Fermi gases in the BCS–BEC crossover

Zhou Li, Hang Dong, Yong-li Ma

We present a quasi-one-dimensional (Q1D) Bose–Fermi mixture model of strongly interacting Fermi gases through the confinement-induced resonance (CIR) to describe 3D fermions trapped in a Q1D geometry along the z axis. Based on the 1D Bethe ansatz method, we analyse the ground and excited states of the Q1D system and derive their integral equations in terms of the momentum distributions in the thermodynamic limit. By applying a Legendre expansion method, the crossover from the BCS superfluid of singlet pairs to the BEC of molecules is calculated in the ground and excited states. We then obtain the dependence of several physical quantities on the inverse of a dimensionless coupling parameter a ⊥ / a with a dimensionless density parameter na ⊥ of Q1D where is the transverse size and ω ⊥ is the 2D harmonic trap frequency in the xy plane. Our results can go back to the smooth 1D crossover when na ⊥ → 0. The theoretical results quantitatively show that the strongly coupling Fermi gas in the Q1D behaves as a Bose–Fermi mixture near the crossover.

Journal of Statistical Mechanics Theory and Experiment•Dec 16, 2014•1 citation
We discuss an integrable model of interacting fermions in one dimension that allows a complete description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2 fermions to the Lieb-Liniger model of repulsive bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from -infinity to +infinity while the system evolves from a BCS-like state through a Tonks-Girardeau gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and spin excitations, and the correlation functions. An experimental realization with cold atoms of such a one-dimensional BCS-BEC crossover is proposed.
We discuss the BCS-BEC crossover for one-dimensional spin-1∕21∕21∕2 fermions at zero temperature using the boson-fermion resonance model in one dimension. We show that in the limit of a broad resonance, this model is equivalent to an exactly solvable single-channel model, the so-called modified Gaudin-Yang model. We argue that the one-dimensional crossover may be realized either via the combination of a Feshbach resonance and a confinement-induced resonance or using direct photoassociation in a two-component Fermi gas with effectively one-dimensional dynamics. In both cases, the system may be driven from a BCS-like state through a molecular Tonks-Girardeau gas close to resonance to a weakly interacting Bose gas of dimers.
A gas of interacting fermions confined in a quasi one-dimensional geometry shows a BEC to BCS crossover upon slowly driving its coupling constant through a confinement-induced resonance. On one side of the crossover the fermions form tightly bound bosonic molecules behaving as a repulsive Bose gas, while on the other they form Cooper pairs, whose size is much larger than the average interparticle distance. Here we consider the situation arising when the coupling constant is varied suddenly from the BEC to the BCS value. Namely, we study a BEC-to-BCS quench. By exploiting a suitable continuum limit of recently discovered solvable quenches in the Hubbard model, we show that the local stationary state reached at large times after the quench can be determined exactly by means of the quench action approach. We provide an experimentally accessible characterization of the stationary state by computing local pair correlation function as well as the quasiparticle distribution functions. We find that the steady state is increasingly dominated by two-particle spin singlet bound states for stronger interaction strength, but that bound state formation is inhibited at larger BEC density. The bound state rapidity distribution displays quartic power-law decay suggesting a violation of Tan's contact relations.
This work studies zero-temperature Fermi gases with short-ranged and attractive interactions with focus on the dimensionality aspects by confining the system from three to two dimensions. Interacting Fermi gases are superfluids characterized as being strongly correlated if the scattering length is much larger than the other scales present. In the many-body context, this category of systems requires a careful treatment since mean-field approaches are not expected to hold under the conditions which define the strong pairing. For this reason, we employ quantum Monte Carlo methods to study the dimensionality effects in two-component Fermi gases in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS-BEC) crossover. To be able to investigate such aspects, we consider a three-dimensional gas with periodic boundary conditions in the xy plane and a confining potential in the z direction capable of reducing the dimensionality of the system, which defines a dimensional BCS-BEC crossover. We calculate the equation of state as the energy per particle as a function of the dimensionality and as a function of the interaction parameter, which are characterized by the oscillator length in the z direction and the scattering length respectively. The greater confinement in the system lowers the interparticle distances, which increases the effects of the attractive interactions between antiparallel-spin fermions.We also calculate the density profile in the z direction over the crossover for different confinements and different interaction parameters to quantify their influence on the spatial distribution of the particles. This study connects the perspectives between theoretical and experimental works in low-dimensional ultracold Fermi gases by utilizing an approach that is similar to what it is realized in modern experiments.
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 quasi-one-dimensional (Q1D) Bose–Fermi mixture model of strongly interacting Fermi gases through the confinement-induced resonance (CIR) to describe 3D fermions trapped in a Q1D geometry along the z axis. Based on the 1D Bethe ansatz method, we analyse the ground and excited states of the Q1D system and derive their integral equations in terms of the momentum distributions in the thermodynamic limit. By applying a Legendre expansion method, the crossover from the BCS superfluid of singlet pairs to the BEC of molecules is calculated in the ground and excited states. We then obtain the dependence of several physical quantities on the inverse of a dimensionless coupling parameter a ⊥ / a with a dimensionless density parameter na ⊥ of Q1D where is the transverse size and ω ⊥ is the 2D harmonic trap frequency in the xy plane. Our results can go back to the smooth 1D crossover when na ⊥ → 0. The theoretical results quantitatively show that the strongly coupling Fermi gas in the Q1D behaves as a Bose–Fermi mixture near the crossover.