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. B, Condensed matter

Third sound in layered superfluids: H↓ on He4

Robert Alan Guyer, Michael David Miller

Published May 1, 1982• 58 citations
Publisher

Abstract

In order to minimize the possibility of spin flips due to interactions with and on the walls of a sample cell, spin-polarized hydrogen (H\ensuremath{\downarrow}) is studied in a $^{4}\mathrm{He}$ sample cell, i.e., a sample cell which has been coated with a film of superfluid $^{4}\mathrm{He}$. At low temperatures it is expected that the most dense H\ensuremath{\downarrow} sample will first form in the physisorbed state on the $^{4}\mathrm{He}$ film. In this paper we examine in detail the hydrodynamic consequences of this layered film configuration. We derive the expression for third sound in the general case that the films are compressible and both films have undergone superfluid transitions. In this case two propagating modes will be seen which will provide an uneqivocal demonstration of a superfluid transition in the H\ensuremath{\downarrow} film. We specialize to various limiting cases: incompressible films, saturated and unsaturated films, and the normal fluid H\ensuremath{\downarrow} blanket. In our discussion we stress the point that even if the H\ensuremath{\downarrow} has not gone superfluid it will still shift the $^{4}\mathrm{He}$ third-sound speed, that this shift is a direct measure of the H\ensuremath{\downarrow} film areal density, and that the magnitude of this shift is expected to be well within the precision of present-day third-sound experimental techniques. Thus third sound is expected to be a primary diagnostic tool in the study of H\ensuremath{\downarrow} films.

DOI
10.1103/physrevb.25.5749

Related papers

Structure and Modes of a Superfluid Atmosphere

Robert Alan Guyer, Wayne M. Saslow

A theory of the structure, energetics, and modes of a film formed from a non-self-bound fluid is developed and applied to spin-polarized hydrogen at zero temperature. A hydrogen film is found to saturate at areal density ${{n}_{s}}^{\mathrm{sat}}=1.1\ifmmode\times\else\texttimes\fi{}{10}^{14}$ ${\mathrm{cm}}^{\ensuremath{-}2}$ and to support a third-sound mode with velocity that varies strongly with areal density.

Physical Review Letters•Nov 7, 1983•6 citations

THE MODE OF SOUND IN GASEOUS SUPERFLUID FILM OF SPIN POLARIZED HYDROGEN ATOMS (H↓) ABSORBED ON HELIUM FILM

NI WAN-SUN, 南京大学物理系及声学研究所

The mode of sound in gaseous superfluid film of spin polarized hydrogen atoms (H↓) absorbed on helium film is discussed. Principally, it ia the fourth sound in two dimensions resulting from compressibility of the gaseous film and different from the usual third sound resulting from the variances of thickness of helium film.

Acta Physica Sinica•Jan 1, 1983•0 citations

Spin-polarized hydrogen-helium film system: A surface "polaron"

Robert Alan Guyer, Michael David Miller, J. Yaple

Experimental investigations of spin-polarized hydrogen H\ensuremath{\downarrow} are carried out in a sample cell lined with a helium film whose purpose is to shield the H\ensuremath{\downarrow} atoms from magnetic impurities in the walls. The purpose of the He buffer is to minimize spin flips which cause recombination into the ${\mathrm{H}}_{2}$ molecular ground state and degradation of the sample. In this paper, we focus our attention on the H\ensuremath{\downarrow}-$^{4}\mathrm{He}$ film system and investigate the consequences of allowing the adsorbed H\ensuremath{\downarrow} atom to interact with a dynamic He surface. The coupling between the H\ensuremath{\downarrow} atom and the modes of the film raises the possibility that the atom will find it energetically favorable to be localized in the plane parallel to the surface of the film, i.e., to form a H\ensuremath{\downarrow} polaron. Using a simple model for the atom-film interaction, we show that polaron production can be important. We estimate the order of magnitude for the parallel binding energy and find that it can be comparable to the experimentally measured binding energy. We call attention to the important characteristics of the particle-film system that influence the size and nature of the polaron; e.g., the effect of evolution of the film from $^{4}\mathrm{He}$ to $^{3}\mathrm{He}$ and the consequences of the mobility of the surface modes. Where polaron effects are important the parallel binding problem and the perpendicular binding problem are strongly interdependent and cannot be factored. We then use a simple perturbation theory argument to calculate the polaron effective mass. We finally calculate the ripplon-mediated H\ensuremath{\downarrow}-H\ensuremath{\downarrow} interaction and show that it is short ranged and attractive.

Physical review. B, Condensed matter•Apr 1, 1982•17 citations

Second sound and the density response function in uniform superfluid atomic gases

Hu, H., Taylor, Edward Karim, Xia-Ji Liu +2 more

Recently there has been renewed interest in second sound in superfluid Bose and Fermi gases. By using two-fluid hydrodynamic theory, we review the density response $\chi_{nn}(\bq,\omega)$ of these systems as a tool to identify second sound in experiments based on density probes. Our work generalizes the well-known studies of the dynamic structure factor $S(\bq,\omega)$ in superfluid $^4$He in the critical region. We show that, in the unitary limit of uniform superfluid Fermi gases, the relative weight of second vs. first sound in the compressibility sum rule is given by the Landau--Placzek ratio $\lp\equiv (\bar{c}_p-\bar{c}_v)/\bar{c}_v$ for all temperatures below $T_c$. In contrast to superfluid $^4$He, $\lp$ is much larger in strongly interacting Fermi gases, being already of order unity for $T \sim 0.8 T_c$, thereby providing promising opportunities to excite second sound with density probes. The relative weights of first and second sound are quite different in $S(\bq,\omega)$ (measured in pulse propagation studies) as compared to $\mathrm{Im}\chi_{nn}(\bq,\omega)$ (measured in two-photon Bragg scattering). We show that first and second sound in $S(\bq,\omega)$ in a strongly interacting Bose-condensed gas are similar to those in a Fermi gas at unitarity. However, in a weakly interacting Bose gas, first and second sound are mainly uncoupled oscillations of the thermal cloud and condensate, respectively, and second sound has most of the spectral weight in $S(\bq,\omega)$. We also discuss the behaviour of the superfluid and normal fluid velocity fields involved in first and second sound.

•Jan 1, 2010•35 citations

Second sound and the density response function in uniform superfluid atomic gases

H Hu, E Taylor, X-J Liu +2 more

Recently, there has been renewed interest in second sound in superfluid Bose and Fermi gases. By using two-fluid hydrodynamic theory, we review the density response χ nn ( q , ω) of these systems as a tool to identify second sound in experiments based on density probes. Our work generalizes the well-known studies of the dynamic structure factor S ( q , ω) in superfluid 4 He in the critical region. We show that, in the unitary limit of uniform superfluid Fermi gases, the relative weight of second versus first sound in the compressibility sum rule is given by the Landau–Placzek ratio for all temperatures below T c . In contrast to superfluid 4 He, LP is much larger in strongly interacting Fermi gases, being already of order unity for T ∼0.8 T c , thereby providing promising opportunities to excite second sound with density probes. The relative weights of first and second sound are quite different in S ( q , ω) (measured in pulse propagation studies) as compared with Imχ nn ( q , ω) (measured in two-photon Bragg scattering). We show that first and second sound in S ( q , ω) in a strongly interacting Bose-condensed gas are similar to those in a Fermi gas at unitarity. However, in a weakly interacting Bose gas, first and second sound are mainly uncoupled oscillations of the thermal cloud and condensate, respectively, and second sound has most of the spectral weight in S ( q , ω). We also discuss the behaviour of the superfluid and normal fluid velocity fields involved in first and second sound.

arXiv:1001.0772•New Journal of Physics•Apr 22, 2010•33 citations

Second Sound in Ultracold Atomic Gases

Лев П. Питаевский, S. Stringari

We provide an overview of the recent theoretical and experimental advances in the study of second sound in ultracold atomic gases. Starting from the Landau two fluid hydrodynamic equations we develop the theory of first and second sound in various configurations characterized by different geometries and quantum statistics. These include the weakly interacting 3D Bose gas, the strongly interacting Fermi gas at unitarity in the presence of highly elongated traps and the dilute 2D Bose gas, characterized by the Berezinskii-Kosterlitz-Thouless transition. An explicit comparison with the propagation of second sound in liquid Helium is carried out to elucidate the main analogies and differences. We also make an explicit comparison with the available experimental data and point out the crucial role played by the superfluid density in determining the temperature dependence of the second sound speed.

arXiv:1510.01306•Cambridge University Press eBooks•Oct 4, 2018•15 citations
In order to minimize the possibility of spin flips due to interactions with and on the walls of a sample cell, spin-polarized hydrogen (H\ensuremath{\downarrow}) is studied in a 4He^{4}\mathrm{He}4He sample cell, i.e., a sample cell which has been coated with a film of superfluid 4He^{4}\mathrm{He}4He. At low temperatures it is expected that the most dense H\ensuremath{\downarrow} sample will first form in the physisorbed state on the 4He^{4}\mathrm{He}4He film. In this paper we examine in detail the hydrodynamic consequences of this layered film configuration. We derive the expression for third sound in the general case that the films are compressible and both films have undergone superfluid transitions. In this case two propagating modes will be seen which will provide an uneqivocal demonstration of a superfluid transition in the H\ensuremath{\downarrow} film. We specialize to various limiting cases: incompressible films, saturated and unsaturated films, and the normal fluid H\ensuremath{\downarrow} blanket. In our discussion we stress the point that even if the H\ensuremath{\downarrow} has not gone superfluid it will still shift the 4He^{4}\mathrm{He}4He third-sound speed, that this shift is a direct measure of the H\ensuremath{\downarrow} film areal density, and that the magnitude of this shift is expected to be well within the precision of present-day third-sound experimental techniques. Thus third sound is expected to be a primary diagnostic tool in the study of H\ensuremath{\downarrow} films.
Experimental investigations of spin-polarized hydrogen H\ensuremath{\downarrow} are carried out in a sample cell lined with a helium film whose purpose is to shield the H\ensuremath{\downarrow} atoms from magnetic impurities in the walls. The purpose of the He buffer is to minimize spin flips which cause recombination into the H2{\mathrm{H}}_{2}H2​ molecular ground state and degradation of the sample. In this paper, we focus our attention on the H\ensuremath{\downarrow}-4He^{4}\mathrm{He}4He film system and investigate the consequences of allowing the adsorbed H\ensuremath{\downarrow} atom to interact with a dynamic He surface. The coupling between the H\ensuremath{\downarrow} atom and the modes of the film raises the possibility that the atom will find it energetically favorable to be localized in the plane parallel to the surface of the film, i.e., to form a H\ensuremath{\downarrow} polaron. Using a simple model for the atom-film interaction, we show that polaron production can be important. We estimate the order of magnitude for the parallel binding energy and find that it can be comparable to the experimentally measured binding energy. We call attention to the important characteristics of the particle-film system that influence the size and nature of the polaron; e.g., the effect of evolution of the film from 4He^{4}\mathrm{He}4He to 3He^{3}\mathrm{He}3He and the consequences of the mobility of the surface modes. Where polaron effects are important the parallel binding problem and the perpendicular binding problem are strongly interdependent and cannot be factored. We then use a simple perturbation theory argument to calculate the polaron effective mass. We finally calculate the ripplon-mediated H\ensuremath{\downarrow}-H\ensuremath{\downarrow} interaction and show that it is short ranged and attractive.
Recently there has been renewed interest in second sound in superfluid Bose and Fermi gases. By using two-fluid hydrodynamic theory, we review the density response $\chi_{nn}(\bq,\omega)$ of these systems as a tool to identify second sound in experiments based on density probes. Our work generalizes the well-known studies of the dynamic structure factor $S(\bq,\omega)$ in superfluid 4^44He in the critical region. We show that, in the unitary limit of uniform superfluid Fermi gases, the relative weight of second vs. first sound in the compressibility sum rule is given by the Landau--Placzek ratio $\lp\equiv (\bar{c}_p-\bar{c}_v)/\bar{c}_v$ for all temperatures below TcT_cTc​. In contrast to superfluid 4^44He, $\lp$ is much larger in strongly interacting Fermi gases, being already of order unity for T∼0.8TcT \sim 0.8 T_cT∼0.8Tc​, thereby providing promising opportunities to excite second sound with density probes. The relative weights of first and second sound are quite different in $S(\bq,\omega)$ (measured in pulse propagation studies) as compared to $\mathrm{Im}\chi_{nn}(\bq,\omega)$ (measured in two-photon Bragg scattering). We show that first and second sound in $S(\bq,\omega)$ in a strongly interacting Bose-condensed gas are similar to those in a Fermi gas at unitarity. However, in a weakly interacting Bose gas, first and second sound are mainly uncoupled oscillations of the thermal cloud and condensate, respectively, and second sound has most of the spectral weight in $S(\bq,\omega)$. We also discuss the behaviour of the superfluid and normal fluid velocity fields involved in first and second sound.
Recently, there has been renewed interest in second sound in superfluid Bose and Fermi gases. By using two-fluid hydrodynamic theory, we review the density response χ nn ( q , ω) of these systems as a tool to identify second sound in experiments based on density probes. Our work generalizes the well-known studies of the dynamic structure factor S ( q , ω) in superfluid 4 He in the critical region. We show that, in the unitary limit of uniform superfluid Fermi gases, the relative weight of second versus first sound in the compressibility sum rule is given by the Landau–Placzek ratio for all temperatures below T c . In contrast to superfluid 4 He, LP is much larger in strongly interacting Fermi gases, being already of order unity for T ∼0.8 T c , thereby providing promising opportunities to excite second sound with density probes. The relative weights of first and second sound are quite different in S ( q , ω) (measured in pulse propagation studies) as compared with Imχ nn ( q , ω) (measured in two-photon Bragg scattering). We show that first and second sound in S ( q , ω) in a strongly interacting Bose-condensed gas are similar to those in a Fermi gas at unitarity. However, in a weakly interacting Bose gas, first and second sound are mainly uncoupled oscillations of the thermal cloud and condensate, respectively, and second sound has most of the spectral weight in S ( q , ω). We also discuss the behaviour of the superfluid and normal fluid velocity fields involved in first and second sound.
We provide an overview of the recent theoretical and experimental advances in the study of second sound in ultracold atomic gases. Starting from the Landau two fluid hydrodynamic equations we develop the theory of first and second sound in various configurations characterized by different geometries and quantum statistics. These include the weakly interacting 3D Bose gas, the strongly interacting Fermi gas at unitarity in the presence of highly elongated traps and the dilute 2D Bose gas, characterized by the Berezinskii-Kosterlitz-Thouless transition. An explicit comparison with the propagation of second sound in liquid Helium is carried out to elucidate the main analogies and differences. We also make an explicit comparison with the available experimental data and point out the crucial role played by the superfluid density in determining the temperature dependence of the second sound speed.