Excitations In Superfluid 4He Research Articles

Colloquium: Spontaneous magnon decays

A theoretical overview of the phenomenon of spontaneous magnon decays in quantum antiferromagnets is presented. The intrinsic zero-temperature damping of magnons in quantum spin systems is a fascinating many-body effect, which has recently attracted significant attention in view of its possible observation in neutron-scattering experiments. An introduction to the theory of magnon interactions and a discussion of necessary symmetry and kinematic conditions for spontaneous decays are provided. Various parallels with the decays of anharmonic phonons and excitations in superfluid 4He are extensively used. Three principal cases of spontaneous magnon decays are considered: field-induced decays in Heisenberg antiferromagnets, zero-field decays in spiral antiferromagnets, and triplon decays in quantum-disordered magnets. Analytical results are compared with available numerical data and prospective materials for experimental observation of the decay-related effects are briefly discussed.

Quasiparticle breakdown in a quantum spin liquid

Much of modern condensed matter physics is understood in terms of elementary excitations, or quasiparticles--fundamental quanta of energy and momentum. Various strongly interacting atomic systems are successfully treated as a collection of quasiparticles with weak or no interactions. However, there are interesting limitations to this description: in some systems the very existence of quasiparticles cannot be taken for granted. Like unstable elementary particles, quasiparticles cannot survive beyond a threshold where certain decay channels become allowed by conservation laws; their spectrum terminates at this threshold. Such quasiparticle breakdown was first predicted for an exotic state of matter--super-fluid 4He at temperatures close to absolute zero, a quantum Bose liquid where zero-point atomic motion precludes crystallization. Here we show, using neutron scattering, that quasiparticle breakdown can also occur in a quantum magnet and, by implication, in other systems with Bose quasiparticles. We have measured spin excitations in a two-dimensional quantum magnet, piperazinium hexachlorodicuprate (PHCC), in which spin-1/2 copper ions form a non-magnetic quantum spin liquid, and find remarkable similarities with excitations in superfluid 4He. We observe a threshold momentum beyond which the quasiparticle peak merges with the two-quasiparticle continuum. It then acquires a finite energy width and becomes indistinguishable from a leading-edge singularity, so that excited states are no longer quasiparticles but occupy a wide band of energy. Our findings have important ramifications for understanding excitations with gapped spectra in many condensed matter systems, ranging from band insulators to high-transition-temperature superconductors.

Generation of intrinsic excitations in superfluid 4He by using gas jet approach

A radio frequency discharged helium gas jet was used to generate intrinsic excitations in bulk superfluid 4He. The present experimental results and our previous estimates show that metastable triplet state He atoms and excimers cannot enter directly the liquid but rather concentrate on the liquid surface. High concentration of metastable species promotes reactions, which then lead to formation of He ions. Upon electron - ion recombination, population of highly excited atomic and diatomic excimer electronic states occurs. Effect of molecular hydrogen on quenching of the helium emissions is demonstrated. Excitations are efficiently transferred from He to H2.

On the Structure of the Superfluid State and Quasiparticle Spectrum in a Bose Liquid with a Suppressed Bose–Einstein Condensate

A self-consistent model of the superfluid (SF) state of a Bose liquid with strong interaction between bosons and a weak single-particle Bose–Einstein condensate (BEC) is considered. The ratio of the BEC density n 0 to the total particle density n of the Bose liquid is used as a small parameter of the model, n 0/n≪1, unlike in the Bogolyubov theory of a quasi-ideal Bose gas, in which the small parameter is the ratio of the number of supracondensate excitations to the number of particles in an intensive BEC, (n−n 0)/n 0≪1. A closed system of nonlinear integral equations for the normal ~Σ11(p, ω) and anomalous ~Σ12(p, ω) self-energy parts is obtained with account for terms of first order in the BEC density. A renormalized perturbation theory is used, which is built on combined hydrodynamic (at p→0) and field (at p≠0) variables with analytic functions ~Σ ij (p, e) at pe0 and e→0 and a nonzero SF order parameter ~Σ12(0, 0)≠0, proportional to the density ρ s of the SF component. Various pair interaction potentials U(r) with inflection points in the radial dependence and with an oscillating sign-changing momentum dependence of the Fourier component V(p) are considered. Collective many-body effects of renormalization (“screening”) of the initial interaction, which are described by the bosonic polarization operator Π(p, ω), lead to a suppression of the repulsion [V(p)<0] and an enhancement of the effective attraction [V(p)<0] in the respective domains of nonzero momentum transfer, due to the negative sign of the real part of Π(p, ω) on the “mass shell” ω=E(p). In the framework of the “soft spheres” model with the single fitting parameter—the value of the repulsion potential at r=0—the quasiparticle spectrum E(p) is calculated, which is in good accordance with the experimental spectrum E exp(p) of elementary excitations in superfluid 4He. It is shown that the roton minimum in the quasiparticle spectrum is directly associated with the first negative minimum of the Fourier component of the renormalized (“screened”) potential of pair interaction between bosons.

A computer investigation of a superfluid Bose liquid with pair interaction and with a coherent condensate of boson pairs as a model of 4He quantum liquid

One considers a superfluid (SF) state of a Bose liquid with repulsion between bosons, in which at T = 0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC), analogous to the Cooper condensate in a Fermi liquid with attraction between fermions. By iterations, one obtains a numerical solution of a closed system of nonlinear integral equations for the normal ∼ϵ 11 ( p , ω) and anomalous ∼ϵ 12( p, ω) self-energy parts in the framework of the model of “semi-transparent spheres”. A quasiparticle spectrum is then obtained, which is in good agreement with the experimental spectrum of elementary excitations in superfluid 4He.

Measurement and simulation of the inelastic resolution function of a time-of-flight spectrometer

The deconvolution of inelastic neutron scattering data requires the knowledge of the inelastic resolution function. The inelastic resolution function of the time-of-flight spectrometer IN5/ILL has been measured by exploiting the sharp resonances of the roton and maxon excitations in superfluid 4He for the two respective (q,ω) values. The calculated inelastic resolution function for three different instrumental setups is compared to the experimentally determined resolution function. The agreement between simulation and experimental data is excellent, allowing us in principle to extrapolate the simulations and thus to determine the resolution function in the whole accessible dynamic range of IN5 or any other time-of-flight spectrometer.

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.

One-dimensional excitations in superfluid 4He and 3He-4He mixture films adsorbed in porous materials

A normal-fluid component varying as T$^{2}$ is observed at very low temperatures in superfluid $^4$He and $^3$He-$^4$He mixture films adsorbed in alumina powder. The normal fluid appears to arise from thermally excited third sound that has one-dimensional propagation characteristics. A Landau model of third sound excitations in an infinite cylindrical pore by Saam and Cole provides good agreement with the experimental measurements over a wide range of $^4$He and $^3$He coverages. However, it is unclear why the powder substrate can be modeled as having cylindrical pores.

High-resolution measurements of excitations in superfluid4He beyond the roton

High-resolution neutron inelastic scattering studies of thewavevector and temperature dependence of the excitation spectrum of4He in the superfluid and normal-fluid phases have been made inthe wavevector region `beyond the roton', 2.0<Q<3.6 Å-1, at a pressure of 20 bar. The scattering in this regionexhibits two separate components: a sharp peak at low energies anda broader continuum at higher energies. The relative intensity ofthese two peaks is Q-dependent. We find that the two-rotonenergy, 2Δ, is never exceeded by the sharp peak at thispressure. The data are compared with the density-quasiparticle modelof Glyde and Griffin and a tentative analysis of the temperaturedependence of the condensate fraction n0 is made.

High Resolution Measurements of the Temperature Dependence of the Roton Energy of Superfluid 4He

New measurements of the roton excitations in superfluid 4He have been made using the IRIS spectrometer (energy resolution ∼20 μeV at the roton energy) at the ISIS spallation neutron source. The roton energy was determined over a temperature range of 0.56 to 1.61 K. High resolution (energy resolution <1 μeV) neutron inelastic scattering measurements by Andersen et al.2 of the dependence of the 4He roton energy on temperature have shown significant deviations from the expected behaviour; the temperature variation was found to be discontinuous and slower than predicted by the established roton-roton interaction theory due to Bedell, Pines and Zawadowski (BPZ). 3 We find that our results can be described well by the BPZ theory over this temperature range and we do not observe the anomalous behaviour reported by Andersen et al. We offer some explanations as to the origin of this apparent disagreement.

Dynamics of liquid 4He in vycor

Using inelastic neutron scattering, we have observed well-defined phonon-roton ( p-r) excitations in superfluid 4He in Vycor over a wide wave-vector range, 0.3</=Q</=2.15 A(-1). The p-r energies and lifetimes at all temperatures are the same as in bulk liquid 4He. However, the weight of the single p-r component does not scale with the superfluid fraction rho(S)(T)/rho as it does in the bulk. In particular, we observe a p-r excitation above T(c) = 1.952 K, where rho(s)(T) = 0 in Vycor. This suggests, if the p-r excitation intensity scales with the Bose condensate, that there is a separation of the Bose-Einstein condensation temperature and the superfluid transition temperature T(c) of 4He in Vycor.

Pressure Dependence of the Multiphonon Excitations of Superfluid 4He

The pressure dependence of the multiphonon excitations in superfluid 4He has been studied, using neutron inelastic scattering. High-resolution measurements have been made at 0,5 K over a wavevector range 0.6<Q<2.2 A−1, at various pressures between 0 and 20 bars. The experimental data are presented and existing theoretical calculations are discussed.

Roton wave–packets in 3–Dimensional and 2–Dimensional 4 He

We have obtained new information on the elementary excitations in superfluid 4 He by studying local observables relative to roton wave–packets built from accurate variational representations of the excited states. The same technique has been applied also to study a pure 2–Dimensional system, where the spectrum, computed through a variational Monte Carlo simulation, still shows a modified phonon–maxon–roton dispersion relation. In the roton region, collective quantum effects are present, but when the average momentum of the wave–packet matches with the wave–vector of the roton minimum the interference effects between neighboring atoms disappear and the local density and momentum essentially coincide with those of a single particle excitation. A roton, as well as a single particle excitation, has a velocity vector field which is very similar to that of a smoke–ring scaled down to atomic size.

Temperature dependence of the phonon-maxon excitations in superfluid4He at SVP and 20 bars

We report high resolution neutron inelastic scattering measurements of the dynamic structure factor S(Q, ω) of liquid4He in the phonon-maxon collective excitation regime. The temperature dependence of the excitations in the range 0.5 < Q < 1.3 A−1 at saturated vapour pressure (SVP) and an applied pressure of 20 bars has been studied. Results of this study have been compared with the novel “density-quasiparticle” description of the excitations in4He by Glyde and Griffin. The analysis is discussed with reference to previous studies.

Accurate description of excitations in superfluid4He

An accurate quantitative description of the maxon-roton excitations in superfluid4He is still an open many-body problem. We present a new variational Monte Carlo calculation of this excitation spectrum. Our calculation starts from a shadow wave function in which all the pseudopotentials are optimized with a basis set method. The phase factors of the excitation are introduced in the subsidiary variables and an explicit backflow term is also introduced. The computed excitation spectrum is in good agreement with experiment at all wave vectors, the deviations being at the level of 5%. Double roton excitations and strength of the single excitation peak are also computed.

Excitations in superfluid 4He and the condensate

Starting from an accurate representation of the wave function of the ground state and of the phonon-roton excitations based upon the shadow function we present a microscopic density matrix for superfluid 4He. The roton and maxon energy is computed both at zero and at finite temperature at different densities. The separate contributions of kinetic and potential energy of the roton excitation are computed and we find that a roton lowers the potential energy. The roton contribution to the depletion of the Bose-Einstein condensate n 0 is computed. Excitation of 5 to 10 rotons is needed for the depletion of one atom from the condensate and no simple relation is found between the T dependence of n 0 and of g( r). Other quantities we compute as function of T are the static structure factor and the strength of the ‘one-photon’ peak of the dynamical structure factor. Comparison of our results with experiment gives some evidence that additional excitations become important above about 2 K.

The role of the condensate in the existence of phonons and rotons

Interpretations of the characteristic phonon-roton excitations in superfluid4He are discussed to assess the role of the condensate. In the celebrated Landau, Feynman, Feenberg and subsequent Correlated Basic Function methods, the phonon-roton excitations are interpreted as collective density excitations. This picture, suitably modified at higher Q to take account of the correlated motion of neighbors (backflow), provides our best description of neutron scattering data at low temperature. The condensate does not play an explicit role. In the Field Theory, second quantized formulation of Bogoliubov, Hugenholtz and Pines, Gavoret and Nozieres and the subsequent Dielectric Function formulation, the condensate plays an explicit role. Because of the condensate, both regular density (particle-hole) and single particle excitations contribute to the density response. The regular density (two-particle) and single particle excitations mix as particles scatter into and out of the condensate. This Density-Quasiparticle picture provides a good description of the temperature dependence of neutron scattering data. From this description, the phonon at low Q is interpreted as a joint density/quasiparticle mode strongly coupled via the condensate. At higher Q, the sharp maxon-roton is interpreted as a quasiparticle excitation less strongly coupled into the density. The sharp maxon-roton peak is a unique feature of the condensate and could not be observed in S(Q, ω) without a condensate.

Search for Single-Particle Excitations in Super fluid 4He

From their neutron scattering measurements, Blagoveshchenskii et al. have inferred the existence of a new branch of free-particle excitations in superfluid 4He in the same wave vector region as the familiar phonon-roton excitations. We report the results of a detailed search for free-particle excitations in superfluid 4He using neutron scattering techniques. To a high level of sensitivity (≈ 0.01% of the roton intensity) we find no evidence for such excitations.

Neutron scattering as a probe of particle-like excitations in superfluid4He: A model calculation

In the microscopic theory of Bose-condensed liquids, the condensate wave function leads to a coupling of the density fluctuations and the single-particle excitations. A simple parametrized model of this based on coupling weakly damped zero-sound modes with strongly damped free-particle-like excitations similar to Q/sup 2//2m explains why the phonon-roton resonance in S(Q,w) for superfluid /sup 4/He exists above and below Tlambda but only pays the role of an elementary excitation below Tlambda. It is pointed out that this model also predicts that S(Q,w) should exhibit a weak, low-frequency peak centered at Q/sup 2//2m, with weight roughly proportional to the condensate fraction n/OMICRON/. As a stimulus to further experimental searches for this branch, some model calculations are given for S(Q,w) for Q similar to 1A/sup -1/.

Study of two-phonon excitations in superfluid 4He

We explain the second branch of excitations in superfluid 4 He observed by Cowley and Woods, by accounting for two-phonon contributions to the dynamic structure function, S( k , ω). Our theory gives a good fit with the experimental data in the high energy region for several values of momentum transfer. It is observed that the contribution to S( k , ω) due to two-phonon excitations is of the order of k 2 as against its k 4 dependence reported in earlier theories.