Mean-field theory for interacting rotons in superfluid helium

It is shown within the framework of mean-field theory that the gas of roton excitations in superfluid helium becomes unstable at a critical temperatureT _c if the roton-roton interaction is attractive. The instability is characterized by a singularity of the specific heat and signals the transition into the normal fluid state. The roton energy gap remains finite atT _c .     

Short-wave excitations in non-local Gross-Pitaevskii model

We show that a non-local form of the Gross-Pitaevskii equation describes not only long-wave excitations, but also the short-wave ones in Bose-condensate systems. At certain parameter values, the excitation spectrum mimics the Landau spectrum of quasi-particle excitations in superfluid helium with roton minimum. The excitation wavelength, at which the roton minimum exists, is close to the inter-particle interaction range. We determine how the roton gap and the effective roton mass depend on the interaction potential parameters, and show that the existence domain of the spectrum with a roton minimum is reduced if one accounts for an inter-particle attraction.     

Coexistence of superfluid and solid helium in aerogel

The results of recent neutron scattering studies of solid helium in silica aerogel are discussed. Previously I.V. Kalinin et al., Pis’ma Zh. éksp. Teor. Fiz. 87 (1), 743 (2008) [JETP Lett. 87 (1), 645 (2008)], we detected the existence of a superfluid phase in solid helium at a temperature below 0.6 K and a pressure of 51 bar, although, according to the phase diagram, helium should be in the solid state under these conditions. This work is a continuation of the above studies whose main goal was to examine the detected phenomenon and to establish basic parameters of the existence of a superfluid phase. We have determined the temperature of the superfluid transition from solid to superfluid helium, T _C = 1.3 K, by analyzing experimental data. The superfluid phase excitation parameters (lifetime, intensity, and energy) have a temperature dependence similar to that of bulk helium. The superfluid phase coexists with the solid phase in the entire measured temperature range from T = 0.05 K to T _C and is a nonequilibrium one and disappears at T _C.     

On the mechanism of electromagnetic microwave absorption in superfluid helium

In experiments on electromagnetic (EM) wave absorption in the microwave range in superfluid (SF) helium [1?C3], a narrow EM field absorption line with a width on the order of (20?C200) kHz was observed against the background of a wide absorption band with a width of 30?C40 GHz at frequencies f ₀ ?? 110?C180 GHz corresponding to the roton gap energy ?? _r (T) in the temperature range 1.4?C2.2 K. Using the so-called flexoelectric mechanism of polarization of helium atoms (⁴He) in the presence of density gradients in SF helium (HeII), we show that nonresonance microwave absorption in the frequency range 170?C200 GHz can be due to the existence of time-varying local density gradients produced by roton excitations in the bulk HeII. The absorption bandwidth is determined by the roton-roton scattering time in an equilibrium Boltzmann gas of rotons, which is t _r-r ?? 3.4 × 10^?11 s at T = 1.4 K and decreases upon heating. We propose that the anomalously narrow microwave resonance absorption line in HeII at the roton frequency f ₀(T) = ??r(T)/2??? appears due to the following two factors: (i) the discrete structure of the spectrum of the surface EM resonator modes in the form of a periodic sequence of narrow peaks and (ii) the presence of a stationary dipole layer in HeII near the resonator surface, which forms due to polarization of ⁴He atoms under the action of the density gradient associated with the vanishing of the density of the SF component at the solid wall. For this reason, the relaxation of nonequilibrium rotons generated in such a surface dipole layer is strongly suppressed, and the shape and width of the microwave resonance absorption line are determined by the roton density of states, which has a sharp peak at the edge of the roton gap in the case of weak dissipation. The effective dipole moments of rotons in the dipole layer can be directed either along or across the normal to the resonator surface, which explains the experimentally observed symmetric doublet splitting of the resonance absorption line in an external dc electric field perpendicular to the resonator surface. We show that negative absorption (induced emission) of EM field quanta observed after triggering a Kapitza ??heat gun?? occurs when the occupation numbers for roton states due to ??pumping?? of rotons exceed the occupation numbers of EM field photons in the resonator.     

On the dispersion of the “roton” second sound in the superfluid helium

At sufficiently high frequencies of the sound when the energy equilibrium between the phonon and roton gases is not established in the superfluid helium there may propagate the second sound through the gas of rotons (“roton” second sound). In the systems of rotons the equilibrium with respect to the number of rotons can be not complete (the chemical potential is not exactly equal to zero). The dispersion of the roton second sound in these conditions is investigated.     

Creation evidence of the second non-dispersive Zakharenko wave by helium atomic beams in superfluid helium-II at low temperatures

In this work, the experimental results of the creation of the second non-dispersive Zakharenko wave (C _ph = C _g ≠ 0) in the negative roton branch (the so-called second sound) of the bulk elementary excitations (BEEs) energy spectra are introduced. Several BEE signals detected by a bolometer situated in the isotopically pure liquid helium-II at low temperatures ∼100 mK are shown, which give evidence of negative roton creation in the liquid by helium atomic beams striking the liquid surface. The negative roton signals were clearly distinguished by the following ways: the negative roton signal created by helium atomic beams appeared earlier than the positive roton signal created by the beams, and presence of both positive and negative roton signals together. It is natural that the negative roton creation by the beams requires the ⁴He-atom energies ∼12 K, while the positive roton creation by the atomic beams requires energies ∼35 K. Therefore, successive increase in the heater power resulting in an increase in the ⁴He-atom energies gives solid evidence that the negative rotons are first created in the liquid by the helium atomic beams.      

Emission and absorption of phonons by rotons in superfluid helium

The roton spectrum of superfluid helium apparently has a threshold for phonon emission and absorption processes. We calculate the roton spectral function near the threshold for phonon emission in order to determine the effect of the phonon emission process on the roton line width. The spectral function develops a line shape anomaly due to a strong energy dependence of the roton self-energy. The line width is generally smaller than the sum of the phonon emission rate and the roton-roton collision rate. We also derive the ultrasonic attenuation due to the absorption of phonons by thermal rotons above the threshold.     

Excitations in correlated superfluids near a continuous transition into a supersolid

We study a superfluid on a lattice close to a transition into a supersolid phase and show that a uniform superflow in the homogeneous superfluid can drive the roton gap to zero. This leads to supersolid order around the vortex core in the superfluid, with the size of the modulated pattern around the core being related to the bulk superfluid density and roton gap. We also study the electronic tunneling density of states for a uniform superconductor near a phase transition into a supersolid phase. Implications are considered for strongly correlated superconductors.     

Dynamical effects in superfluid helium 4

The close structural similarity between the commutation relations of harmonic oscillator operators and the operators for Bose fields is exploited to study the excitation spectrum in superfluid helium 4. By applying ‘broken symmetry’ condition it is shown how the creation of phonon gives rise to superfluid behaviour of liquid He 4. The energy gap needed for roton excitation is derived.     

Nonclassical rotational inertia in helium crystals

It has been proposed that the observed nonclassical rotational inertia (NCRI) in solid helium results from the superflow of thin liquid films along interconnected grain boundaries within the sample. We have observed NCRI in large (4)He crystals grown at constant temperature and pressure, demonstrating that the superfluid grain boundary model cannot explain the phenomenon.     

Acoustic modes in 2D atomic hydrogen on the surface of superfluid <Superscript>4</Superscript>He

Possible acoustic modes in a superfluid 2D gas of hydrogen atoms adsorbed on the surface of liquid helium at T ? 0.1 K are considered depending on the oscillation frequency and times of energy and momentum transfers both between 2D subsystems of hydrogen atoms and ripplons and into the bulk liquid or substrate. Analogues of the usual and second sounds are realized in 2D hydrogen at high frequencies. In the case of weak coupling with the bulk liquid and substrate, ripplons provide an addition to the normal hydrogen component, which leads to a change in the speed of the second sound. In the most interesting range of low frequencies, an analogue of the fourth sound is realized, when ripplons and the normal hydrogen component are immobile and only the superfluid hydrogen component moves. In this case, when the rate of heat transfer into the bulk liquid is much lower than the sound frequency, oscillations of the temperature of hydrogen can be observed in phase with density oscillations. Methods for exciting acoustic modes are discussed.     

Neutron scattering study of the excitation spectrum of solid helium at ultra-low temperatures

There has been a resurgence of interest in the properties of solid helium due to the recent discovery of non-classical rotational inertia (NCRI) in solid ⁴He by Chan and coworkers below 200 mK which they have interpreted as a transition to a ‘supersolid’ phase. We have carried out a series of elastic and inelastic neutron scattering measurements on single crystals of hcp ⁴He at temperatures down to 60 mK. While we have found no direct evidence of any change in the excitation spectrum at low temperatures, we have found that the excitation spectrum of solid ⁴He shows several interesting features, including extra branches in addition to the phonon branches. We interpret these extra branches as single particle excitations due to propagating vacancy waves, which map on to the famous ‘roton minimum’ long known in the excitation spectrum of superfluid liquid ⁴He. The results show that in fact solid ⁴He shares several features in common with the superfluid.      

Josephson effect in coherent roton aggregates

A localized microwave electromagnetic field in liquid helium behaves as a laser of rotons: it produces a coherent roton aggregate. We show that the whispering gallery mode of the dielectric resonator excites multiple coherent aggregates simultaneously and predict a Josephson effect between them. The superfluid velocity around the resonator acts as a “voltage across the weak link” in superconducting Josephson junctions. Josephson frequency-velocity relation agrees with existing experimental data.     

Observation of a superfluid phase in solid helium

Evidence of a superfluid liquid phase present in polycrystalline helium at a temperature of 0.2 K and a pressure of 51 bar has been obtained by means of inelastic neutron scattering. The superfluid component is absent at a temperature of 0.6 K and the same pressure. Thus, a “solid helium-superfluid helium” phase transition has been discovered. The sample of solid helium in a porous medium (silica aerogel) has been prepared with the use of a capillary blocking technique. The shape of the structure factor of the superfluid phase indicates the presence of clusters or the effects of a restricted geometry. The results may be used to explain the nonclassical rotational inertia phenomenon in solid helium (often referred to as supersolidity, Nature, 2004).     

Helium impurity nanocluster gels in superfluid helium

Rapid cooling of a helium impurity gas mixture to the superfluid helium temperatures allows us to prepare an impurity-helium condensate with jelly-like structure (impurity gel) in superfluid He-II. It is clear that the properties of these gels should be substantially different from those of a bulk impurity substance, constituting a new class of soft matter — quantum gel, where superfluid He-II filling the nanopores between the randomly connected impurity nanoclusters serves as the dispersion medium of the gel.     

Neutron diffraction study of polycrystalline 4He in a porous medium

The elastic (diffraction) component of the neutron scattering cross section, which carries information on the atomic structure of solid helium confined in silica aerogel, has been studied. Analysis of the crystalline structure of solid helium in a porous medium, which is determined from the existing neutron diffraction data, indicates that the superfluid phase is localized inside a hexagonal close-packed phase and is not present in a body-centered cubic crystal. It has also been revealed that the addition of the ³He isotope changes the structure of solid helium and hardly affects the formation of a superfluid phase.     

Phonons, rotons, and layer modes of liquid 4He in aerogel

We report the first observation of two-dimensional layer modes in both fully filled and partially filled aerogel. Using complementary high-energy resolution and high statistical precision neutron scattering instruments, and two different 87% porous aerogel samples, we show that the three-dimensional (3D) phonon-roton excitation energies and lifetimes of liquid 4He in aerogel are the same as in bulk 4He within current precision. The layer modes are the excitations that distinguish aerogel from the bulk rather than a difference in the 3D roton energy.     

Roton dipole moment

The roton excitation in the superfluid ⁴He does not possess a stationary dipole moment. However, a roton has an instantaneous dipole moment, such that at any given moment one can find it in the state either with positive or with negative dipole moment projection on its momentum direction. The instantaneous value of electric dipole moment of roton excitation is evaluated. The result is in reasonable agreement with recent experimental observation of the splitting of microwave resonance absorption line at roton frequency under external electric field.     

On the energy spectrum of helium II

It is shown that the spectrum of the bulk excitations in helium II, which ends at the Pitaevskii point, should be recovered at a certain critical point with the coordinates of about several roton energies and momenta in the form of the spectrum of vortex rings. As the momentum increases, the spectrum of surface capillary waves should be transformed to the spectrum of surface vortex half-rings.     

Roton dipole moment

JETP Letters - The roton excitation in the superfluid 4He does not possess a stationary dipole moment. However, a roton has an instantaneous dipole moment, such that at any given moment one can...