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Bulletin of the American Physical Society

Excitation spectrum of two-dimensional cold fermionic gases in the dilute limit

Christophe Berthod, Corinna Kollath, Thierry Giamarchi, Michael S. Feld, Bernd Fr ohlich, Marco Koschorreck, Enrico Vogt, Michael K ohl

Published Mar 2, 2012• 0 citations
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Crossover of the pair excitation spectrum in the ground state of a dilute two-dimensional Fermi gas is studied as a function of the attraction strength $\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}$, where ${\ensuremath{\varepsilon}}_{0}$ is the two-fermion binding energy and ${\ensuremath{\varepsilon}}_{F}$ is the Fermi energy. It is shown that at $\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}\ensuremath{\simeq}\frac{1}{4}$ the spectrum changes its character from the continuous one in the strong-coupling, or "Bose-gas," limit ($\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}\ensuremath{\gg}1$) to that which consists of two different types of excitations in the weak-coupling ($\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}\ensuremath{\ll}1$) regime: (i) long-wavelength soundlike mode with the cutoff at momentum ${q}_{c}\ensuremath{\sim}\frac{1}{{\ensuremath{\xi}}_{0}}$, and (ii) pair excitations with $q\ensuremath{\ge}\sqrt{8m\ensuremath{\mu}}$.

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Collective excitations in the ground state of a two-dimensional attractive Fermi gas

Sergei V. Traven

The spectrum of collective (pair) excitations in the ground state of a dilute twodimensional (2D) attractive Fermi-gas is studied within the functional integral formalism. The linearized equations for the fluctuations about the non-trivial saddle point are analyzed for all coupling regimes, which are characterized by the ratio ε 0 /ε F , where ε 0 is the two-fermion binding energy and ε F is the Fermi energy. The approximation takes into account propagation of the fluctuations and their interaction with the condensate. In the strong-coupling, or ‘;Bosegas’, regime (ε 0 /ε F > 1) the spectrum is continuous and has the Bogolubov form, but in the weak-coupling limit (ε 0 /ε F «1) there are two types of excitations (different from the two-fermion scattering states): (i) long-wavelength sound-like excitations with the cut-off at momentum q c ≃ l/ξ 0 (where ξ 0 is the Cooper pair size), and (ii) pair excitations with q ≃ (8 m μ) ½ , where μ is the chemical potential and m is the fermion mass. The crossover between weakand strong-coupling behavior of the excitation spectrum is found to occur at the value of the coupling parameter ε 0 /ε F ≃¼. Introduction Since the discovery of high- T c superconductivity there has been growing interest in studying 2D Fermi gases with attractive interaction, especially in the crossover regime, when the pair size ξ 0 is of the order of the interparticle distance. The importance of such a model, which can be regarded as a semiphenomenological model of a 2D superconductor, is highlighted by experimental evidence that the high- T c superconductors, most of which have a layered structure, have a short coherence length, so that k F ξ 0 ≃1, where k F is the Fermi momentum.

Cambridge University Press eBooks•Sep 7, 1995•0 citations
We suggest that collective oscillation frequencies of cold trapped gases can be used to test predictions from quantum many-body physics. Our motivation lies in both rigid experimental tests of theoretical calculations and a possible improvement of measurements of particle number, chemical potential or temperature. We calculate the effects of interaction, dimensionality and thermal fluctuations on the collective modes of a dilute Bose gas in the hydrodynamic limit. The underlying equation of state is provided by the non-perturbative Functional Renormalization Group or by Lee–Yang theory. The spectrum of oscillation frequencies could be measured by response techniques. Our findings are generalized to bosonic or fermionic quantum gases with an arbitrary equation of state in the two-fluid hydrodynamic regime. For any given equation of state P (μ, T ) and normal fluid density n n (μ, T ), the collective oscillation frequencies in a d -dimensional isotropic potential are found to be the eigenvalues of an ordinary differential operator. We suggest a method of numerical solution and discuss the zero-temperature limit. Exact results are provided for harmonic traps and certain special forms of the equation of state. We also present a phenomenological treatment of dissipation effects and discuss the possibility of exciting the different eigenmodes individually.
Crossover of the pair excitation spectrum in the ground state of a dilute two-dimensional Fermi gas is studied as a function of the attraction strength $\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}$, where ${\ensuremath{\varepsilon}}_{0}$ is the two-fermion binding energy and ${\ensuremath{\varepsilon}}_{F}$ is the Fermi energy. It is shown that at $\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}\ensuremath{\simeq}\frac{1}{4}$ the spectrum changes its character from the continuous one in the strong-coupling, or "Bose-gas," limit ($\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}\ensuremath{\gg}1$) to that which consists of two different types of excitations in the weak-coupling ($\frac{{\ensuremath{\varepsilon}}_{0}}{{\ensuremath{\varepsilon}}_{F}}\ensuremath{\ll}1$) regime: (i) long-wavelength soundlike mode with the cutoff at momentum ${q}_{c}\ensuremath{\sim}\frac{1}{{\ensuremath{\xi}}_{0}}$, and (ii) pair excitations with $q\ensuremath{\ge}\sqrt{8m\ensuremath{\mu}}$.
The spectrum of collective (pair) excitations in the ground state of a dilute twodimensional (2D) attractive Fermi-gas is studied within the functional integral formalism. The linearized equations for the fluctuations about the non-trivial saddle point are analyzed for all coupling regimes, which are characterized by the ratio ε 0 /ε F , where ε 0 is the two-fermion binding energy and ε F is the Fermi energy. The approximation takes into account propagation of the fluctuations and their interaction with the condensate. In the strong-coupling, or ‘;Bosegas’, regime (ε 0 /ε F > 1) the spectrum is continuous and has the Bogolubov form, but in the weak-coupling limit (ε 0 /ε F «1) there are two types of excitations (different from the two-fermion scattering states): (i) long-wavelength sound-like excitations with the cut-off at momentum q c ≃ l/ξ 0 (where ξ 0 is the Cooper pair size), and (ii) pair excitations with q ≃ (8 m μ) ½ , where μ is the chemical potential and m is the fermion mass. The crossover between weakand strong-coupling behavior of the excitation spectrum is found to occur at the value of the coupling parameter ε 0 /ε F ≃¼. Introduction Since the discovery of high- T c superconductivity there has been growing interest in studying 2D Fermi gases with attractive interaction, especially in the crossover regime, when the pair size ξ 0 is of the order of the interparticle distance. The importance of such a model, which can be regarded as a semiphenomenological model of a 2D superconductor, is highlighted by experimental evidence that the high- T c superconductors, most of which have a layered structure, have a short coherence length, so that k F ξ 0 ≃1, where k F is the Fermi momentum.