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

Physical Review A

Fermion-mediated BCS-BEC crossover in ultracold K40 gases: Mean-field theory and collective modes

J. M. Acton, Meera M. Parish, Benjamin D. Simons

Published Jun 16, 2005• 5 citations
Publisher

Abstract

Microscopic theories of Feshbach resonance phenomena in fermionic alkali-metal gases have, in the main, relied upon the intuition afforded by a ``Fermi-Bose'' theory which presents the Feshbach molecule as a featureless pointlike Bose particle. While this model may provide a suitable platform to explore the condensation phenomena in the $^{6}\mathrm{Li}$ system, it has been argued recently that its application to the $^{40}\mathrm{K}$ system, where the hyperfine structure is inverted, is inappropriate. Here, the formation of a Feshbach resonance involves the formation of a Feshbach molecule which shares a spin state with the open channel. In such an arrangement, the mechanism of condensate formation cannot escape the effects of Pauli exclusion. Building on a model three-state fermion Hamiltonian recently introduced by Parish et al. to describe the $^{40}\mathrm{K}$ system, we elucidate the mean-field structure of the model, investigate the internal structure of the condensate wave function in the crossover region, and develop a field theory of the transition.

DOI
10.1103/physreva.71.063606

Related papers

Fermion-Mediated BCS-BEC Crossover in Ultracold K40 Gases

Meera M. Parish, Bogdan Mihaila, Benjamin D. Simons +1 more

Studies of Feshbach resonance phenomena in fermionic alkali gases have drawn heavily on the intuition afforded by a Fermi-Bose theory which presents the Feshbach molecule as a featureless Bose particle. While this model may provide a suitable platform to explore the $^{6}\mathrm{Li}$ system, we argue that its application to $^{40}\mathrm{K}$, where the hyperfine structure is inverted, is inappropriate. Introducing a three-state Fermi model, where a spin state is shared by the open and closed channel states, we show that effects of ``Pauli blocking'' appear in the internal structure of the condensate wave function.

arXiv:cond-mat/0409756•Physical Review Letters•Jun 21, 2005•11 citations

Fermion-mediated BCS-BEC crossover in ultracold ${}^{40}$K gases

Meera M. Parish, Bogdan Mihaila, Benjamin D. Simons +1 more

Studies of Feshbach resonance phenomena in fermionic alkali gases have drawn heavily on the intuition afforded by a Fermi-Bose theory which presents the Feshbach molecule as a featureless Bose particle. While this model may provide a suitable platform to explore the Li-6 system, we argue that its application to K-40, where the hyperfine structure is inverted, is inappropriate. Introducing a three-state Fermi model, where a spin state is shared by the open and closed channel states, we show that effects of "Pauli blocking" appear in the internal structure of the condensate wave function.

APS March Meeting Abstracts•Mar 1, 2005•0 citations

BEC-BCS crossover with Feshbach resonance for a three-hyperfine-species model

Guojun Zhu, Anthony J. Leggett

We consider the behavior of an ultracold Fermi gas across a narrow Feshbach resonance, where the occupation of the closed channel may not be negligible. While the corrections to the single-channel formulas associated with the nonzero chemical potential and with particle conservation have been considered in the existing literature, there is a further effect, namely, the ``interchannel Pauli exclusion principle,'' associated with the fact that a single hyperfine species may be common to the two channels. We focus on this effect and show that, as intuitively expected, the resulting corrections are of the order of ${E}_{F}/\ensuremath{\eta}$, where ${E}_{F}$ is the Fermi energy of the gas in the absence of interactions and $\ensuremath{\eta}$ is the Zeeman energy difference between the two channels. We also consider the related corrections to the fermionic excitation spectrum, and briefly discuss the collective modes of the system.

arXiv:1202.4547•Physical Review A•Feb 25, 2013•1 citation

BCS,BEC states and Feshbach resonance in atomic Fermi gases

呂欣頤

To study the behavior of atomic Fermi gases in the vicinity of Feshbach resonance, M. Holland et al. [12] and S. J. J. M. F. Kokkelmans et al. [22] proposed resonance mean field theory in which the molecules formed by Feshbach resonance are considered in the many-body Hamiltonian. Motivated by microscopic scattering theory and resonance mean field theory, we develop a thermodynamic method to study this system. In this method we treat atomic Fermi gases near resoance as a atom-molecule mixture. We can use BCS Hamiltonian and Bose- Einstein statistics to describe the behavior of atoms and molecules respectively. Chemical equilibrium can be achieved between atoms and molecules due to hypefine interaction. We use this method to study the system behavior under different temperature and detuning energy and find that at low temperature a smooth BCS-BEC crossever can occure with decreasing detuning energy. We further calculate a measurable quantity, molecular condensation fraction, and find its behavior matches qualitatively with the experimental result [16].

臺灣大學物理研究所學位論文•Jan 1, 2004•0 citations

The BCS - BEC Crossover in Ultracold Fermion Gases

Sebastian Diehl

The continuous crossover between a Bardeen-Cooper-Schrieffer (BCS)-type superfluid of fermion pairs and a Bose-Einstein condensate (BEC) of tightly bound bosonic molecules can be attributed to the spontaneous breaking of global $U(1)$ gauge symmetry which underlies both quantum condensation phenomena. Recently much attention has been paid to this problem, since Feshbach resonances allow for an experimental implementation of crossover physics in cold fermion gases. The strong interactions close to resonance call for an analysis beyond Mean Field Theory. We develop a systematic functional integral approach for the description of this phenomenon. Starting from a Yukawa-type atom-molecule model, a symmetry analysis allows to both construct the equation of state and to classify the thermodynamic phases in a unified way. The onset of superfluidity is signalled by the emergence of a massless Goldstone mode associated with the broken continuous U(1) symmetry. Beyond Mean Field, we include fluctuations of the molecule field self-consistently via the solution of suitable Schwinger-Dyson equations. The phase diagram is computed, and a variety of universal features are established. A new form of crossover from an exactly solvable narrow resonance limit to broad resonances or pointlike interactions is found. At low temperature our results agree well with quantum Monte Carlo simulations and recent experiments. Our approach is further developed in the frame of functional renormalization group equations. While the effective bosonic theory in the BEC regime shows the characteristics of a Bogoliubov theory for small temperatures, the phase transition is of second order.

•Jan 1, 2006•2 citations

BEC-BCS Crossover with Feshbach Resonance for Three-Hyperfine-Species Model

Zhu, Guojun

In a Feshbach resonance, the effective s-wave scattering length grows when one moves toward the resonance point, and eventually diverges at this point. There is one characteristic energy scale, $δ_c$, defined as, in the negative side of the resonance point, the detuning energy at which the weight of the bound state shifts from predominatedly in the open-channel to predominated in the closed-channel. When the many-body energy scale (e.g. the Fermi energy, $E_{F}$) is larger than $δ_c$, the closed-channel weight is significant and has to be included in the many-body theory. Furthermore, when two channels share a hyperfine species, the Pauli exclusion between fermions from two channels also needs to be taken into consideration in the many-body theory. The current thesis addresses the above problem in detail. A set of gap equations and number equations are derived at the mean-field level. The fermionic and bosonic excitation spectra are then derived. Assuming that the uncoupled bound-state of the closed-channel in resonance is much smaller than the inter-particle distance, as well as the s-wave scattering length, $a_s$, we find that the basic equations in the single-channel crossover model are still valid. The correction first comes from the existing of the finite chemical potential and additional counting complication due to the closed-channel. These two corrections need to be included into the mean-field equations, i.e. the gap equations and the number equations, and be solved self-consistently. Then the correction due to the inter-channel Pauli exclusion is in the order of the ratio of the Fermi energy and the Zeeman energy difference between two channels, $E_F/η$, which can be analyzed perturbatively over the previous corrections. Fermionic and bosonic excitation modes are studied.

arXiv:1212.6691•Dec 30, 2012•1 citation
Microscopic theories of Feshbach resonance phenomena in fermionic alkali-metal gases have, in the main, relied upon the intuition afforded by a ``Fermi-Bose'' theory which presents the Feshbach molecule as a featureless pointlike Bose particle. While this model may provide a suitable platform to explore the condensation phenomena in the 6Li^{6}\mathrm{Li}6Li system, it has been argued recently that its application to the 40K^{40}\mathrm{K}40K system, where the hyperfine structure is inverted, is inappropriate. Here, the formation of a Feshbach resonance involves the formation of a Feshbach molecule which shares a spin state with the open channel. In such an arrangement, the mechanism of condensate formation cannot escape the effects of Pauli exclusion. Building on a model three-state fermion Hamiltonian recently introduced by Parish et al. to describe the 40K^{40}\mathrm{K}40K system, we elucidate the mean-field structure of the model, investigate the internal structure of the condensate wave function in the crossover region, and develop a field theory of the transition.
Studies of Feshbach resonance phenomena in fermionic alkali gases have drawn heavily on the intuition afforded by a Fermi-Bose theory which presents the Feshbach molecule as a featureless Bose particle. While this model may provide a suitable platform to explore the 6Li^{6}\mathrm{Li}6Li system, we argue that its application to 40K^{40}\mathrm{K}40K, where the hyperfine structure is inverted, is inappropriate. Introducing a three-state Fermi model, where a spin state is shared by the open and closed channel states, we show that effects of ``Pauli blocking'' appear in the internal structure of the condensate wave function.
Fermion-mediated BCS-BEC crossover in ultracold 40{}^{40}40K gases
Studies of Feshbach resonance phenomena in fermionic alkali gases have drawn heavily on the intuition afforded by a Fermi-Bose theory which presents the Feshbach molecule as a featureless Bose particle. While this model may provide a suitable platform to explore the Li-6 system, we argue that its application to K-40, where the hyperfine structure is inverted, is inappropriate. Introducing a three-state Fermi model, where a spin state is shared by the open and closed channel states, we show that effects of "Pauli blocking" appear in the internal structure of the condensate wave function.
We consider the behavior of an ultracold Fermi gas across a narrow Feshbach resonance, where the occupation of the closed channel may not be negligible. While the corrections to the single-channel formulas associated with the nonzero chemical potential and with particle conservation have been considered in the existing literature, there is a further effect, namely, the ``interchannel Pauli exclusion principle,'' associated with the fact that a single hyperfine species may be common to the two channels. We focus on this effect and show that, as intuitively expected, the resulting corrections are of the order of ${E}_{F}/\ensuremath{\eta}$, where EF{E}_{F}EF​ is the Fermi energy of the gas in the absence of interactions and $\ensuremath{\eta}$ is the Zeeman energy difference between the two channels. We also consider the related corrections to the fermionic excitation spectrum, and briefly discuss the collective modes of the system.
To study the behavior of atomic Fermi gases in the vicinity of Feshbach resonance, M. Holland et al. [12] and S. J. J. M. F. Kokkelmans et al. [22] proposed resonance mean field theory in which the molecules formed by Feshbach resonance are considered in the many-body Hamiltonian. Motivated by microscopic scattering theory and resonance mean field theory, we develop a thermodynamic method to study this system. In this method we treat atomic Fermi gases near resoance as a atom-molecule mixture. We can use BCS Hamiltonian and Bose- Einstein statistics to describe the behavior of atoms and molecules respectively. Chemical equilibrium can be achieved between atoms and molecules due to hypefine interaction. We use this method to study the system behavior under different temperature and detuning energy and find that at low temperature a smooth BCS-BEC crossever can occure with decreasing detuning energy. We further calculate a measurable quantity, molecular condensation fraction, and find its behavior matches qualitatively with the experimental result [16].
The continuous crossover between a Bardeen-Cooper-Schrieffer (BCS)-type superfluid of fermion pairs and a Bose-Einstein condensate (BEC) of tightly bound bosonic molecules can be attributed to the spontaneous breaking of global U(1)U(1)U(1) gauge symmetry which underlies both quantum condensation phenomena. Recently much attention has been paid to this problem, since Feshbach resonances allow for an experimental implementation of crossover physics in cold fermion gases. The strong interactions close to resonance call for an analysis beyond Mean Field Theory. We develop a systematic functional integral approach for the description of this phenomenon. Starting from a Yukawa-type atom-molecule model, a symmetry analysis allows to both construct the equation of state and to classify the thermodynamic phases in a unified way. The onset of superfluidity is signalled by the emergence of a massless Goldstone mode associated with the broken continuous U(1) symmetry. Beyond Mean Field, we include fluctuations of the molecule field self-consistently via the solution of suitable Schwinger-Dyson equations. The phase diagram is computed, and a variety of universal features are established. A new form of crossover from an exactly solvable narrow resonance limit to broad resonances or pointlike interactions is found. At low temperature our results agree well with quantum Monte Carlo simulations and recent experiments. Our approach is further developed in the frame of functional renormalization group equations. While the effective bosonic theory in the BEC regime shows the characteristics of a Bogoliubov theory for small temperatures, the phase transition is of second order.
In a Feshbach resonance, the effective s-wave scattering length grows when one moves toward the resonance point, and eventually diverges at this point. There is one characteristic energy scale, δcδ_cδc​, defined as, in the negative side of the resonance point, the detuning energy at which the weight of the bound state shifts from predominatedly in the open-channel to predominated in the closed-channel. When the many-body energy scale (e.g. the Fermi energy, EFE_{F}EF​) is larger than δcδ_cδc​, the closed-channel weight is significant and has to be included in the many-body theory. Furthermore, when two channels share a hyperfine species, the Pauli exclusion between fermions from two channels also needs to be taken into consideration in the many-body theory. The current thesis addresses the above problem in detail. A set of gap equations and number equations are derived at the mean-field level. The fermionic and bosonic excitation spectra are then derived. Assuming that the uncoupled bound-state of the closed-channel in resonance is much smaller than the inter-particle distance, as well as the s-wave scattering length, asa_sas​, we find that the basic equations in the single-channel crossover model are still valid. The correction first comes from the existing of the finite chemical potential and additional counting complication due to the closed-channel. These two corrections need to be included into the mean-field equations, i.e. the gap equations and the number equations, and be solved self-consistently. Then the correction due to the inter-channel Pauli exclusion is in the order of the ratio of the Fermi energy and the Zeeman energy difference between two channels, EF/ηE_F/ηEF​/η, which can be analyzed perturbatively over the previous corrections. Fermionic and bosonic excitation modes are studied.