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Landau phonon-roton theory revisited for superfluid helium 4 and Fermi gases

Yvan Castin, Alice Sinatra, Hadrien Kurkjian

Published Dec 26, 2017• 0 citations
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Abstract

Liquid helium and spin-1/2 cold-atom Fermi gases both exhibit in their superfluid phase two distinct types of excitations, gapless phonons and gapped rotons or fermionic pair-breaking excitations. In the long wavelength limit, revising and extending Landau and Khalatnikov's theory initially developed for helium [ZhETF 19, 637 (1949)], we obtain universal expressions for three- and four-body couplings among these two types of excitations. We calculate the corresponding phonon damping rates at low temperature and compare them to those of a pure phononic origin in high-pressure liquid helium and in strongly interacting Fermi gases, paving the way to experimental observations.

Related papers

Landau Phonon-Roton Theory Revisited for Superfluid He4 and Fermi Gases

Yvan Castin, Alice Sinatra, Hadrien Kurkjian

Liquid helium and spin-1/2 cold-atom Fermi gases both exhibit in their superfluid phase two distinct types of excitations, gapless phonons and gapped rotons or fermionic pair-breaking excitations. In the long wavelength limit, revising and extending the theory of Landau and Khalatnikov initially developed for helium [Zh. Exp. Teor. Fiz. 19, 637 (1949)], we obtain universal expressions for three- and four-body couplings among these two types of excitations. We calculate the corresponding phonon damping rates at low temperature and compare them to those of a pure phononic origin in high-pressure liquid helium and in strongly interacting Fermi gases, paving the way to experimental observations.

arXiv:1707.09774•Physical Review Letters•Dec 26, 2017•25 citations

Landau-Khalatnikov phonon damping in strongly interacting Fermi gases

Hadrien Kurkjian, Yvan Castin, Alice Sinatra

We derive the phonon damping rate due to the four-phonon Landau-Khalatnikov process in low-temperature strongly interacting Fermi gases using quantum hydrodynamics, correcting and extending the original calculation of Landau and Khalatnikov ( Zh. Eksp. Teor. Fiz. , 19 (1949) 637). Our predictions can be tested in state-of-the-art experiments with cold atomic gases in the collisionless regime.

arXiv:1608.00402•Europhysics Letters (EPL)•Nov 1, 2016•11 citations

Phonon damping in a 2D superfluid: insufficiency of Fermi's golden rule at low temperature

Yvan Castin, Alan Serafin, Alice Sinatra

It is generally accepted that the phonon gas of a superfluid always enters a weak coupling regime at sufficiently low temperatures, whatever the strength of the interactions between the underlying particles (constitutive of the superfluid). Thus, in this limit, we should always be able to calculate the damping rate of thermal phonons by applying Fermi's golden rule to the Hamiltonian $H_3$ of cubic phonon-phonon coupling taken from quantum hydrodynamics, at least in the case of a convex acoustic branch and in the collisionless regime (where the eigenfrequency of the considered phonons remains much greater than the gas thermalization rate). Using the many-body Green's function method, we predict that, unexpectedly, this is not true in two dimensions, contrary to the three-dimensional case. We confirm this prediction with classical phonon-field simulations and a non-perturbative theory in $H_3$, where the fourth order is regularized by hand, giving a complex energy to the virtual phonons of the four-phonon collisional processes. For a weakly interacting fluid and a phonon mode in the long-wavelength limit, we predict a damping rate about three times lower than that of the golden rule.

arXiv:2307.12705•Jul 24, 2023•0 citations

Phononic collective excitations in superfluid Fermi gases at nonzero temperatures

Serghei N. Klimin, Jacques Tempere, Hadrien Kurkjian

We study the phononic collective modes of the pairing field and their corresponding signature in both the order-parameter and density response functions for a superfluid Fermi gas at all temperatures below ${T}_{c}$ in the collisionless regime. The spectra of collective modes are calculated within the Gaussian pair fluctuation approximation. We deal with the coupling of these modes to the fermionic continuum of quasiparticle-quasihole excitations by performing a nonperturbative analytic continuation of the pairing field propagator. At low temperature, we recover the known exponential temperature dependence of the damping rate and velocity shift of the Anderson-Bogoliubov branch. In the vicinity of ${T}_{c}$, we find analytically a weakly damped collective mode whose velocity vanishes with a critical exponent of $1/2$, and whose quality factor diverges logarithmically with ${T}_{c}\ensuremath{-}T$, thereby clarifying an existing debate in the literature [Andrianov and Popov, Theor. Math. Phys. 28, 829 (1976); Ohashi and Takada, J. Phys. Soc. Jpn. 66, 2437 (1997)]. A transition between these two phononic branches is visible at intermediary temperatures, particularly in the BCS limit where the phase-phase response function displays two maxima.

arXiv:1811.07796•Physical Review A•Dec 23, 2019•22 citations

The role of pair correlations in the formation of the ground state and the elementary excitation spectrum in a superfluid Bose liquid (A Review)

Ernst A. Pashitskii

The paradoxes and disparities in the contemporary microscopic theory of superfluid helium (He–II) are discussed along with possible ways of resolving them by taking pair correlations of He4 atoms into consideration. It is shown that most paradoxes are associated with the commonly accepted initial assumption concerning the dominating role of single-particle Bose condensate (SPBC) in the quantum microstructure of the superfluid component ρs. The existence of intensive SPBC leads to a strong hybridization of the elementary excitation branches and to a common dispersion law for all boson branches, which is identified with the quasiparticle spectrum E(p) observed experimentally from slow neutron scattering in liquid helium. However, the stability of this spectrum during a transition through the λ-point and the large value of the gap in the vicinity of the “rotonic” minimum contradict both the Landau theoretical criterion of superfluidity and the small value of experimentally measured critical velocity. At the same time, a strong interaction between particles in the Bose liquid He4 strongly suppresses the SPBC which amounts to less than 1% of all He4 atoms and hence cannot be the main constituent of the superfluid component, unlike the case of a weakly nonideal Bose gas. Moreover, for a quite strong attraction between particles in a certain region of the momentum space, bound pairs of bosons can be formed in the superfluid Bose liquid, and a coherent pair condensate (CPC) analogous to the Cooper pair condensate in superconductors may appear. Such a strong CPC may completely suppress the weak SPBC. In this case, the one-particle spectrum ε(p) of elementary excitations does not hybridize with the collective (two-particle) spectrum and does not appear in the structure of the dynamic form factor S(p,ε), i.e., does not coincide with the spectrum measured from neutron scattering. The dispersion of one-particle spectrum is defined by the momentum dependence of the pair order parameter Ψ̃(p) and may have a minimum or a point of inflection at p≠0. This peculiarity in the one-particle spectrum of a Bose liquid with CPC but without SPBC vanishes together with Ψ̃(p) at the temperature Tc=Tλ of the phase transition from the superfluid to the normal state (unlike the rotonic minimum in the collective spectrum), while the corresponding critical velocity vc=min[ε(p)/p] vanishes at the λ-point in accordance with the Landau criterion and the experimental data. The assumption that the strong “Cooper-like” CPC is responsible for the quantum structure of the superfluid component ρs is confirmed indirectly by the successful application of the Justrow approximation (based on strong pair correlations) for describing the properties of liquid He4 and quantum liquid mixtures He3–4He on one hand, and by an anomalously large effective mass of He3 impurity atoms in He4, which is approximately equal to total mass of He3 and He4 atoms, thus pointing to the existence of helium atoms in superfluid liquid He–II. The value of the superfluid velocity circulation quantum in the Onsager–Feynman vortices in a Bose liquid with CPC but without SPBC is discussed as well as the critical velocities of superfluid He4 in ultrathin films and channels in which the creation and motion of quantum vortices are ruled out, and the quasiparticle spectrum undergoes dimensional quantization.

Low Temperature Physics•Feb 1, 1999•14 citations

Open questions for strongly interacting Fermi gases with zero-range interactions

Yvan Castin

We review some unresolved theoretical issues in three-dimensional two-component Fermi gases, drawing on recent experiments on cold atoms in immaterial traps close to a magnetic Feshbach resonance. We distinguish successively (i) the open questions arising in the few-body problem with Wigner-Bethe-Peierls contact interactions - essentially the stability of the gas with respect to the Efimov effect and the calculation of the cluster (or virial) coefficients, (ii) those arising in the effective low-energy theory of Landau and Khalatnikov quantum hydrodynamics - essentially the damping of phonon modes and the coherence time of the condensate of pairs, and finally (iii) questions requiring a complete, microscopic solution of the many-body problem, such as the specific properties of the acoustic excitation branch (Goldstone) of the condensate of pairs, or its collective excitation branch (Higgs) in the broken-pair continuum.

arXiv:2410.20866•Oct 28, 2024•0 citations
Liquid helium and spin-1/2 cold-atom Fermi gases both exhibit in their superfluid phase two distinct types of excitations, gapless phonons and gapped rotons or fermionic pair-breaking excitations. In the long wavelength limit, revising and extending Landau and Khalatnikov's theory initially developed for helium [ZhETF 19, 637 (1949)], we obtain universal expressions for three- and four-body couplings among these two types of excitations. We calculate the corresponding phonon damping rates at low temperature and compare them to those of a pure phononic origin in high-pressure liquid helium and in strongly interacting Fermi gases, paving the way to experimental observations.
Liquid helium and spin-1/2 cold-atom Fermi gases both exhibit in their superfluid phase two distinct types of excitations, gapless phonons and gapped rotons or fermionic pair-breaking excitations. In the long wavelength limit, revising and extending the theory of Landau and Khalatnikov initially developed for helium [Zh. Exp. Teor. Fiz. 19, 637 (1949)], we obtain universal expressions for three- and four-body couplings among these two types of excitations. We calculate the corresponding phonon damping rates at low temperature and compare them to those of a pure phononic origin in high-pressure liquid helium and in strongly interacting Fermi gases, paving the way to experimental observations.
It is generally accepted that the phonon gas of a superfluid always enters a weak coupling regime at sufficiently low temperatures, whatever the strength of the interactions between the underlying particles (constitutive of the superfluid). Thus, in this limit, we should always be able to calculate the damping rate of thermal phonons by applying Fermi's golden rule to the Hamiltonian H3H_3H3​ of cubic phonon-phonon coupling taken from quantum hydrodynamics, at least in the case of a convex acoustic branch and in the collisionless regime (where the eigenfrequency of the considered phonons remains much greater than the gas thermalization rate). Using the many-body Green's function method, we predict that, unexpectedly, this is not true in two dimensions, contrary to the three-dimensional case. We confirm this prediction with classical phonon-field simulations and a non-perturbative theory in H3H_3H3​, where the fourth order is regularized by hand, giving a complex energy to the virtual phonons of the four-phonon collisional processes. For a weakly interacting fluid and a phonon mode in the long-wavelength limit, we predict a damping rate about three times lower than that of the golden rule.
We study the phononic collective modes of the pairing field and their corresponding signature in both the order-parameter and density response functions for a superfluid Fermi gas at all temperatures below Tc{T}_{c}Tc​ in the collisionless regime. The spectra of collective modes are calculated within the Gaussian pair fluctuation approximation. We deal with the coupling of these modes to the fermionic continuum of quasiparticle-quasihole excitations by performing a nonperturbative analytic continuation of the pairing field propagator. At low temperature, we recover the known exponential temperature dependence of the damping rate and velocity shift of the Anderson-Bogoliubov branch. In the vicinity of Tc{T}_{c}Tc​, we find analytically a weakly damped collective mode whose velocity vanishes with a critical exponent of 1/21/21/2, and whose quality factor diverges logarithmically with ${T}_{c}\ensuremath{-}T$, thereby clarifying an existing debate in the literature [Andrianov and Popov, Theor. Math. Phys. 28, 829 (1976); Ohashi and Takada, J. Phys. Soc. Jpn. 66, 2437 (1997)]. A transition between these two phononic branches is visible at intermediary temperatures, particularly in the BCS limit where the phase-phase response function displays two maxima.
The paradoxes and disparities in the contemporary microscopic theory of superfluid helium (He–II) are discussed along with possible ways of resolving them by taking pair correlations of He4 atoms into consideration. It is shown that most paradoxes are associated with the commonly accepted initial assumption concerning the dominating role of single-particle Bose condensate (SPBC) in the quantum microstructure of the superfluid component ρs. The existence of intensive SPBC leads to a strong hybridization of the elementary excitation branches and to a common dispersion law for all boson branches, which is identified with the quasiparticle spectrum E(p) observed experimentally from slow neutron scattering in liquid helium. However, the stability of this spectrum during a transition through the λ-point and the large value of the gap in the vicinity of the “rotonic” minimum contradict both the Landau theoretical criterion of superfluidity and the small value of experimentally measured critical velocity. At the same time, a strong interaction between particles in the Bose liquid He4 strongly suppresses the SPBC which amounts to less than 1% of all He4 atoms and hence cannot be the main constituent of the superfluid component, unlike the case of a weakly nonideal Bose gas. Moreover, for a quite strong attraction between particles in a certain region of the momentum space, bound pairs of bosons can be formed in the superfluid Bose liquid, and a coherent pair condensate (CPC) analogous to the Cooper pair condensate in superconductors may appear. Such a strong CPC may completely suppress the weak SPBC. In this case, the one-particle spectrum ε(p) of elementary excitations does not hybridize with the collective (two-particle) spectrum and does not appear in the structure of the dynamic form factor S(p,ε), i.e., does not coincide with the spectrum measured from neutron scattering. The dispersion of one-particle spectrum is defined by the momentum dependence of the pair order parameter Ψ̃(p) and may have a minimum or a point of inflection at p≠0. This peculiarity in the one-particle spectrum of a Bose liquid with CPC but without SPBC vanishes together with Ψ̃(p) at the temperature Tc=Tλ of the phase transition from the superfluid to the normal state (unlike the rotonic minimum in the collective spectrum), while the corresponding critical velocity vc=min[ε(p)/p] vanishes at the λ-point in accordance with the Landau criterion and the experimental data. The assumption that the strong “Cooper-like” CPC is responsible for the quantum structure of the superfluid component ρs is confirmed indirectly by the successful application of the Justrow approximation (based on strong pair correlations) for describing the properties of liquid He4 and quantum liquid mixtures He3–4He on one hand, and by an anomalously large effective mass of He3 impurity atoms in He4, which is approximately equal to total mass of He3 and He4 atoms, thus pointing to the existence of helium atoms in superfluid liquid He–II. The value of the superfluid velocity circulation quantum in the Onsager–Feynman vortices in a Bose liquid with CPC but without SPBC is discussed as well as the critical velocities of superfluid He4 in ultrathin films and channels in which the creation and motion of quantum vortices are ruled out, and the quasiparticle spectrum undergoes dimensional quantization.
We review some unresolved theoretical issues in three-dimensional two-component Fermi gases, drawing on recent experiments on cold atoms in immaterial traps close to a magnetic Feshbach resonance. We distinguish successively (i) the open questions arising in the few-body problem with Wigner-Bethe-Peierls contact interactions - essentially the stability of the gas with respect to the Efimov effect and the calculation of the cluster (or virial) coefficients, (ii) those arising in the effective low-energy theory of Landau and Khalatnikov quantum hydrodynamics - essentially the damping of phonon modes and the coherence time of the condensate of pairs, and finally (iii) questions requiring a complete, microscopic solution of the many-body problem, such as the specific properties of the acoustic excitation branch (Goldstone) of the condensate of pairs, or its collective excitation branch (Higgs) in the broken-pair continuum.