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.     

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.     

Roton-roton crossover in strongly correlated dipolar Bose-Einstein condensates

We study the pair correlations and excitations of a dipolar Bose gas layer. The anisotropy of the dipole-dipole interaction allows us to tune the strength of pair correlations from strong to weak perpendicular and weak to strong parallel to the layer by increasing the perpendicular trap frequency. This change is accompanied by a roton-roton crossover in the spectrum of collective excitations, from a roton caused by the head-to-tail attraction of dipoles to a roton caused by the side-by-side repulsion, while there is no roton excitation for intermediate trap frequencies. We discuss the nature of these two kinds of rotons and the relation to instabilities of dipolar Bose gases. In both regimes of trap frequencies where rotons occur, we observe strong damping of collective excitations by decay into two rotons.     

Rotons in interacting ultracold bose gases

In three dimensions, noninteracting bosons undergo Bose-Einstein condensation at a critical temperature, T(c), which is slightly shifted by ΔT(c), if the particles interact. We calculate the excitation spectrum of interacting Bose systems, (4)He and (87)Rb, and show that a roton minimum emerges in the spectrum above a threshold value of the gas parameter. We provide a general theoretical argument for why the roton minimum and the maximal upward critical temperature shift are related. We also suggest two experimental avenues to observe rotons in condensates. These results, based upon a path-integral Monte Carlo approach, provide a microscopic explanation of the shift in the critical temperature and also show that a roton minimum does emerge in the excitation spectrum of particles with a structureless, short-range, two-body interaction.     

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.     

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.     

On the electric activity of superfluid helium at the excitation of first and second sound waves

We show that the electric activity of superfluid helium (HeII) observed in the experiments [3] during the excitation of standing second sound waves in an acoustic resonator can be described in terms of the phenomenological mechanism of the inertial polarization of atoms in a dielectric, in particular, in HeII, when the polarization field induced in the medium is proportional to the mechanical acceleration, by analogy with the Stewart-Tolman effect. The variable relative velocity w = v _n − v _s of the normal and superfluid HeII components that emerges in the second sound wave determines the mean group velocity of rotons, V _g ≈ w, with the density of the normal component related to their equilibrium number density in the temperature range 1.3 K ≤ T ≤ 2 K. Therefore, the acceleration of the 4He atoms involved in the formation of a roton excitation is proportional to the time derivative of the relative velocity.w. In this case, the linear local relations between the variable values of the electric induction, electric field strength, and polarization vector should be taken into account. As a result, the variable displacement current induced in the bulk of HeII and the corresponding potential difference do not depend on the anomalously low polarizability of liquid helium. This allows the ratio of the amplitudes of the temperature and potential oscillations in the second sound wave, which is almost independent of T in the above temperature range, consistent with experimental data to be obtained. At the same time, the absence of an electric response during the excitation of first sound waves in the linear regime is related to an insufficient power of the sound oscillations. Based on the experimental data on the excitation of first and second sounds, we have obtained estimates for the phenomenological coefficient of proportionality between the polarization vector and acceleration and for the drag coefficient of helium atoms by rotons in the second sound wave. We also show that the presence of a steady heat flow in HeII with nonzero longitudinal velocity and temperature gradients due to finite viscosity and thermal conductivity of the normal component leads to a change in the phase velocities of the first and second sound waves and to an exponential growth of their amplitudes with time, which should cause the amplitudes of the electric signals at the first and second sound frequencies to grow. This instability is analogous to the growth of the amplitude of long gravity waves on a shallow-water surface that propagate in the direction of decreasing basin depth.     

Bose condensation of particle-antiparticle systems

We discuss some important papers that have appeared in the last twenty years on the possibility of Bose condensation in particle-antiparticle systems. Electron-hole systems in some semiconductors provide the background for a non-relativistic treatment. Bose condensation and the superfluid phase of the electron-hole fluid are strongly favoured. Next, pairing and the appearance of the superfluid vacuum state in fermion-antifermion system are considered from a relativistic viewpoint. Special attention is given to the pairs in the stateJ ^P=0⁺. The pairing in the fundamental fermion-antifermion sea may provide the background subquantal level of reality of the universe.     

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.     

Semiclassical mechanics of rotons

The roton elementary excitations in superfluid liquid ⁴He have an unusual dispersion curve. The energy is an approximately quadratic function of (p - p₀), the difference between the magnitude of the momentum p and a characteristic value p₀. As a result, while for p > p₀ a roton has its (group) velocity parallel to its momentum, when p < p₀ the velocity and momentum are antiparallel. When p = p₀, the roton has non-zero momentum but zero velocity. These kinematic properties lead to unusual trajectories when rotons scatter or experience external forces. This paper examines this behaviour in the classical (ray optics) limit, where the roton wavelength is small compared with all other dimensions. Several experiments illustrate these effects. The examples are interesting in themselves, and also offer unconventional pedagogical possibilities.     

Resonance excitation of slow rotons: Linewidth

An explanation of an anomalously narrow microwave absorption line in superfluid ⁴He has been proposed. It has been shown that the experimentally observed resonance linewidth agrees with the assumption of parametric excitation of a macroscopic coherent roton state.     

Exotic vortex structures of the dipolar Bose–Einstein condensates trapped in harmonic-like and toroidal potential

Based on the tunable intensity and waist of Gaussian laser, harmonic-like and toroidal potentials can be achieved and the ground-state properties of the dipolar Bose–Einstein condensate (BEC) trapped in such potentials are investigated. It is found that, in the harmonic-like potential, the singly and doubly quantized vortices can exist in the scale condensate and translate respectively into vortex pairs and triangular vortex lattice with increasing dipole–dipole interaction (DDI). Especially, the sandwich-like structure can be observed in the ground-state density profiles by tuning the direction and strength of DDI for some rotating frequency. In the toroidal potential, the competition between the inter-component interaction and DDI can induce the transition between immiscible and miscible states, and results in the structures of a doubly quantized vortex surrounded by a vortex ring. It is worth emphasizing that, with the increasing of DDI, the doubly quantized vortex in the harmonic-like potential becomes two singly quantized vortices, while in the toroidal potential it is no happen due to the presence of Gaussian barrier.     

Dynamics of confined quantum fluids

We examine the static and dynamic properties of liquid ⁴He in confined geometries. Confinement is modeled by placing the liquid between two rigid, attractive walls with strengths corresponding to Geltech, Vycor, or glass. The liquid arranges itself in a series of layers, with increasing areal density it undergoes a sequence of layering transitions familiar from classical fluids. We identify “bulk” excitations that propagate throughout the film, and “layer” excitations that propagate only close to the substrate. Both have the typical phonon-roton dispersion relation, but the energy of the layer-roton minimum depends sensitively on the substrate strength, thus providing a mechanism for a direct measurement of this quantity. Bulk-like roton excitations are largely independent of the interaction between the matrix and the helium atoms. While the bulk-like rotons are very similar to their true bulk counterparts, the layer modes are not in close relation to two-dimensional rotons and should be regarded as a completely independent kind of excitation.     

Ground-state properties of a one-dimensional system of dipoles

A one-dimensional (1D) Bose system with dipole-dipole repulsion is studied at zero temperature by means of a quantum Monte Carlo method. It is shown that, in the limit of small linear density, the bosonic system of dipole moments acquires many properties of a system of noninteracting fermions. At larger linear densities, a variational Monte Carlo calculation suggests a crossover from a liquidlike to a solidlike state. The system is superfluid on the liquidlike side of the crossover and is normal deep on the solidlike side. Energy and structural functions are presented for a wide range of densities. Possible realizations of the model are 1D Bose atomic systems, with permanent dipoles or dipoles induced by static field or resonance radiation; or indirect excitons in coupled quantum wires; etc. We propose parameters of a possible experiment and discuss manifestations of the zero-temperature quantum crossover.     

Superfluid bose liquid with a suppressed BEC and an intensive pair coherent condensate as a model of 4He

One introduces a model of the superfluid state of a Bose liquid with repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate, there exists an intensive pair coherent condensate, analogous to the Cooper condensate in a Fermi liquid with attraction between fermions. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is solved numerically, and a quasiparticle spectrum is obtained, which is in good agreement with the experimental spectrum of elementary excitations in superfluid 4He. It is shown that the roton minimum in the spectrum is associated with the negative minimum of the Fourier component of the pair interaction potential.     

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.     

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.      

The Roton Minimum: Is it a General Feature of Strongly Correlated Liquids?

The roton minimum is a deep minimum in the collective excitation spectrum of the liquid, forming around fairly high k ‐values. We have discovered, through MD simulations, that this appears to be a general feature of strongly coupled liquids and is ubiquitous in 2D and 3D Yukawa liquids. We suggest that the physical origin of the roton minimum has to be sought in the quasi‐localization of particles in a strongly correlated liquid and in the ensuing formation of local microcrystals whose averaged frequency dispersion would show roton minimum‐like feature (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quantum phase diagram for homogeneous Bose‐Einstein condensate

We calculate the quantum phase transition for a homogeneous Bose gas in the plane of s‐wave scattering length a_s and temperature T. This is done by improving a one‐loop result near the interaction‐free Bose‐Einstein critical temperature T_c⁽⁰⁾ with the help of recent high‐loop results on the shift of the critical temperature due to a weak atomic repulsion based on variational perturbation theory. The quantum phase diagram shows a nose above T_c⁽⁰⁾, so that we predict the existence of a reentrant transition above T_c⁽⁰⁾, where an increasing repulsion leads to the formation of a condensate.