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:1410.2577

Low-energy theory of the Nambu-Goldstone modes of an ultracold $^6Li-$ $^{40}K$ mixture in an optical lattice

Zlatko G. Koinov

Published Oct 9, 2014• 0 citations
arXivHTMLPDF

Abstract

A low-energy theory of the Nambu-Goldstone excitation spectrum and the corresponding speed of sound of an interacting Fermi mixture of Lithium-6 and Potassium-40 atoms in a two-dimensional optical lattice at finite temperatures with the Fulde-Ferrell order parameter has been formulated. It is assumed that the two-species interacting Fermi gas is described by the one-band Hubbard Hamiltonian with an attractive on-site interaction. The discussion is restricted to the BCS side of the Feshbach resonance where the Fermi atoms exhibit superfluidity. The quartic on-site interaction is decoupled via a Hubbard-Stratonovich transformation by introducing a four-component boson field which mediates the Hubbard interaction. A functional integral technique and a Legendre transform are used to give a systematic derivation of the Schwinger-Dyson equations for the generalized single-particle Green's function and the Bethe-Salpeter equation for the two-particle Green's function and the associated collective modes. The numerical solution of the Bethe-Salpeter equation in the generalized random phase approximation shows that there exist two distinct sound velocities in the long-wavelength limit. In addition to the long-wavelength mode (Goldstone mode), the two-species Fermi gas has a superfluid phase revealed by two rotonlike minima in the asymmetric collective-mode energy.

DOI
10.48550/arxiv.1410.2577

Related papers

Collective Modes of an Ultracold6Li-40K Mixture in an Optical Lattice

Zlatko G. Koinov

A low-energy theory of the Nambu-Goldstone excitation spectrum and the corresponding speed of sound of an interacting Fermi mixture of Lithium-6 and Potassium-40 atoms in a two-dimensional optical lattice at finite temperatures with the Fulde-Ferrell order parameter has been formulated. It is assumed that the two-species interacting Fermi gas is described by the one-band Hubbard Hamiltonian with an attractive on-site interaction. The discussion is restricted to the BCS side of the Feshbach resonance where the Fermi atoms exhibit superfluidity. The quartic on-site interaction is decoupled via a Hubbard-Stratonovich transformation by introducing a four-component boson field which mediates the Hubbard interaction. A functional integral technique and a Legendre transform are used to give a systematic derivation of the Schwinger-Dyson equations for the generalized single-particle Green’s function and the Bethe-Salpeter equation for the two-particle Green’s function and the associated collective modes. The numerical solution of the Bethe-Salpeter equation in the generalized random phase approximation shows that there exist two distinct sound velocities in the long-wavelength limit. In addition to low-energy (Goldstone) mode, the two-species Fermi gas has a superfluid phase revealed by two roton-like minima in the asymmetric collective-mode energy.

Advances in Condensed Matter Physics•Jan 1, 2015•3 citations

Collective modes of a spin-orbit-coupled superfluid Fermi gas in a two-dimensional optical lattice: a comparison between the Gaussian approximation and the Bethe-Salpeter approach

Zlatko G. Koinov, Rafael Mendoza

A functional integral technique and a Legendre transform are used to give a systematic derivation of the Schwinger-Dyson equations for the generalized single-particle Green's function and the Bethe-Salpeter equation for the two-particle Green's function and the associated collective modes of a population-imbalanced spin-orbit-coupled atomic Fermi gas loaded in a two-dimensional optical lattice at zero temperature. The collective-mode excitation energy is calculated within the Gaussian approximation, and from the Bethe-Salpeter equation in the generalized random phase approximation assuming the existence of a Sarma superfluid state. It is found that the Gaussian approximation overestimates the speed of sound of the Goldstone mode. More interestingly, the Gaussian approximation fails to reproduced the rotonlike structure of the collective-mode dispersion which appears after the linear part of the dispersion in the Bethe-Salpeter approach. We use the Gaussian approximation and the Bethe-Salpeter approach to investigate the speed of sound of a balanced spin-orbit-coupled atomic Fermi gas near the boundary of the topological phase transition driven by an out-of-plane Zeeman field. It is shown that within both approaches, the minimum of the speed of sound is located at the topological phase transition boundary, and this fact can be used to confirm the existence of a topological phase transition.

arXiv:1508.00712•Aug 4, 2015•0 citations

Speed of sound in a superfluid Fermi gas in an optical lattice

Zlatko G. Koinov

A system of equal mixture of $^6Li$ atomic Fermi gas of two hyperfine states loaded into a cubic three-dimensional optical lattice is studied assuming a negative scattering length (BCS side of the Feshbach resonance). When the interaction is attractive, fermionic atoms can pair and form a superfluid. The dispersion of the phonon-like mode and the speed of sound in the long-wavelength limit are obtained by solving the Bethe-Salpeter equations for the collective modes of the attractive Hubbard Hamiltonian.

arXiv:1006.1392•Jun 7, 2010•0 citations

Superfluidity of fermion atoms loaded in a deep optical lattice: the existence of two rotonlike modes

Zlatko G. Koinov

We present theoretical calculations of collective modes of the one-band attractive Hubbard model which is widely used to study the s-wave superfluid phases of atomic Fermi gases of two-hyperfine states loaded in a deep optical lattice. To make our theory applicable for both superconductivity and superfluidity, we assume the more general $t-U-J$ Hamiltonian. Using the functional differentiation we derive Schwinger-Dyson equations for the single-particle Green's functions. The method of Legendre transform is used to give a systematic derivation of the Bethe-Salpeter (BS) equation for the two-particle Green's function and the associated collective modes. The numerical solution of the BS equation in the limit $J\rightarrow 0$ shows the existence of two rotonlike collective modes with different low-energy Goldstone dispersions and different positions of the rotonlike minima. The two rotonlike modes lie outside of the region determined by the lower boundary of the particle-hole continuum, and therefore, the two modes are not damped and they should be experimentally observable. In the presence of superfluid flow at a certain critical flow momentum, the minimum of the first rotonlike mode reaches zero energy, but this occurs before the minimum of the second mode and the lower boundary of the particle-hole continuum do, i.e. there are two critical flow momenta related to the existence of two rotonlike excitations.

arXiv:1302.5494•Feb 22, 2013•0 citations

Speed of sound in an optical lattice

Zlatko G. Koinov

Abstract A system of equal mixture of 6Li atomic Fermi gas of two hyperfine states loaded into a cubic three‐dimensional optical lattice is studied assuming a negative scattering length (BCS side of the Feshbach resonance). When the interaction is attractive, fermionic atoms can pair and form a superfluid. The dispersion of the phonon‐like mode and the speed of sound in the long‐wavelength limit are obtained by solving the Bethe‐Salpeter equations for the collective modes of the attractive Hubbard Hamiltonian.

Annalen der Physik•Jul 30, 2010•5 citations

Rotonlike Fulde-Ferrell Collective Excitations of an Imbalanced Fermi Gas in a Two-Dimensional Optical Lattice

Zlatko G. Koinov, Rafael Mendoza, Mauricio Fortes

We address the question of whether superfluidity can survive in the case of fermion pairing between different species with mismatched Fermi surfaces using as an example a population-imbalanced mixture of 6Li atomic Fermi gas loaded in a two-dimensional optical lattice at nonzero temperatures. The collective mode is calculated from the Bethe-Salpeter equations in the general random phase approximation assuming a Fulde-Ferrell order parameter. The numerical solution shows that, in addition to low-energy (Goldstone) mode, two rotonlike minima exist, and therefore, the superfluidity can survive in this imbalanced system.

Physical Review Letters•Mar 7, 2011•13 citations
Low-energy theory of the Nambu-Goldstone modes of an ultracold 6Li−^6Li-6Li− 40K^{40}K40K mixture in an optical lattice
A low-energy theory of the Nambu-Goldstone excitation spectrum and the corresponding speed of sound of an interacting Fermi mixture of Lithium-6 and Potassium-40 atoms in a two-dimensional optical lattice at finite temperatures with the Fulde-Ferrell order parameter has been formulated. It is assumed that the two-species interacting Fermi gas is described by the one-band Hubbard Hamiltonian with an attractive on-site interaction. The discussion is restricted to the BCS side of the Feshbach resonance where the Fermi atoms exhibit superfluidity. The quartic on-site interaction is decoupled via a Hubbard-Stratonovich transformation by introducing a four-component boson field which mediates the Hubbard interaction. A functional integral technique and a Legendre transform are used to give a systematic derivation of the Schwinger-Dyson equations for the generalized single-particle Green's function and the Bethe-Salpeter equation for the two-particle Green's function and the associated collective modes. The numerical solution of the Bethe-Salpeter equation in the generalized random phase approximation shows that there exist two distinct sound velocities in the long-wavelength limit. In addition to the long-wavelength mode (Goldstone mode), the two-species Fermi gas has a superfluid phase revealed by two rotonlike minima in the asymmetric collective-mode energy.
A low-energy theory of the Nambu-Goldstone excitation spectrum and the corresponding speed of sound of an interacting Fermi mixture of Lithium-6 and Potassium-40 atoms in a two-dimensional optical lattice at finite temperatures with the Fulde-Ferrell order parameter has been formulated. It is assumed that the two-species interacting Fermi gas is described by the one-band Hubbard Hamiltonian with an attractive on-site interaction. The discussion is restricted to the BCS side of the Feshbach resonance where the Fermi atoms exhibit superfluidity. The quartic on-site interaction is decoupled via a Hubbard-Stratonovich transformation by introducing a four-component boson field which mediates the Hubbard interaction. A functional integral technique and a Legendre transform are used to give a systematic derivation of the Schwinger-Dyson equations for the generalized single-particle Green’s function and the Bethe-Salpeter equation for the two-particle Green’s function and the associated collective modes. The numerical solution of the Bethe-Salpeter equation in the generalized random phase approximation shows that there exist two distinct sound velocities in the long-wavelength limit. In addition to low-energy (Goldstone) mode, the two-species Fermi gas has a superfluid phase revealed by two roton-like minima in the asymmetric collective-mode energy.
A functional integral technique and a Legendre transform are used to give a systematic derivation of the Schwinger-Dyson equations for the generalized single-particle Green's function and the Bethe-Salpeter equation for the two-particle Green's function and the associated collective modes of a population-imbalanced spin-orbit-coupled atomic Fermi gas loaded in a two-dimensional optical lattice at zero temperature. The collective-mode excitation energy is calculated within the Gaussian approximation, and from the Bethe-Salpeter equation in the generalized random phase approximation assuming the existence of a Sarma superfluid state. It is found that the Gaussian approximation overestimates the speed of sound of the Goldstone mode. More interestingly, the Gaussian approximation fails to reproduced the rotonlike structure of the collective-mode dispersion which appears after the linear part of the dispersion in the Bethe-Salpeter approach. We use the Gaussian approximation and the Bethe-Salpeter approach to investigate the speed of sound of a balanced spin-orbit-coupled atomic Fermi gas near the boundary of the topological phase transition driven by an out-of-plane Zeeman field. It is shown that within both approaches, the minimum of the speed of sound is located at the topological phase transition boundary, and this fact can be used to confirm the existence of a topological phase transition.
A system of equal mixture of 6Li^6Li6Li atomic Fermi gas of two hyperfine states loaded into a cubic three-dimensional optical lattice is studied assuming a negative scattering length (BCS side of the Feshbach resonance). When the interaction is attractive, fermionic atoms can pair and form a superfluid. The dispersion of the phonon-like mode and the speed of sound in the long-wavelength limit are obtained by solving the Bethe-Salpeter equations for the collective modes of the attractive Hubbard Hamiltonian.
We present theoretical calculations of collective modes of the one-band attractive Hubbard model which is widely used to study the s-wave superfluid phases of atomic Fermi gases of two-hyperfine states loaded in a deep optical lattice. To make our theory applicable for both superconductivity and superfluidity, we assume the more general t−U−Jt-U-Jt−U−J Hamiltonian. Using the functional differentiation we derive Schwinger-Dyson equations for the single-particle Green's functions. The method of Legendre transform is used to give a systematic derivation of the Bethe-Salpeter (BS) equation for the two-particle Green's function and the associated collective modes. The numerical solution of the BS equation in the limit J→0J\rightarrow 0J→0 shows the existence of two rotonlike collective modes with different low-energy Goldstone dispersions and different positions of the rotonlike minima. The two rotonlike modes lie outside of the region determined by the lower boundary of the particle-hole continuum, and therefore, the two modes are not damped and they should be experimentally observable. In the presence of superfluid flow at a certain critical flow momentum, the minimum of the first rotonlike mode reaches zero energy, but this occurs before the minimum of the second mode and the lower boundary of the particle-hole continuum do, i.e. there are two critical flow momenta related to the existence of two rotonlike excitations.
Abstract A system of equal mixture of 6Li atomic Fermi gas of two hyperfine states loaded into a cubic three‐dimensional optical lattice is studied assuming a negative scattering length (BCS side of the Feshbach resonance). When the interaction is attractive, fermionic atoms can pair and form a superfluid. The dispersion of the phonon‐like mode and the speed of sound in the long‐wavelength limit are obtained by solving the Bethe‐Salpeter equations for the collective modes of the attractive Hubbard Hamiltonian.
We address the question of whether superfluidity can survive in the case of fermion pairing between different species with mismatched Fermi surfaces using as an example a population-imbalanced mixture of 6Li atomic Fermi gas loaded in a two-dimensional optical lattice at nonzero temperatures. The collective mode is calculated from the Bethe-Salpeter equations in the general random phase approximation assuming a Fulde-Ferrell order parameter. The numerical solution shows that, in addition to low-energy (Goldstone) mode, two rotonlike minima exist, and therefore, the superfluidity can survive in this imbalanced system.