Quantized Vortex State in hcp Solid 4He

The quantized vortex state appearing in the recently discovered new states in hcp ⁴He since their discovery (Kim and Chan, Nature, 427:225–227, 2004; Science, 305:1941, 2004) is discussed. Special attention is given to evidence for the vortex state as the vortex fluid (VF) state (Anderson, Nat. Phys., 3:160–162, 2007; Phys. Rev. Lett., 100:215301, 2008; Penzev et al., Phys. Rev. Lett., 101:065301, 2008; Nemirovskii et al., arXiv:0907.0330, 2009) and its transition into the supersolid (SS) state (Shimizu et al., arXiv:0903.1326, 2009; Kubota et al., J. Low Temp. Phys., 158:572–577, 2010; J. Low Temp. Phys., 162:483–491, 2011). Its features are described. The historical explanations (Reatto and Chester, Phys. Rev., 155(1):88–100, 1967; Chester, Phys. Rev. A, 2(1):256–258, 1970; Andreev and Lifshitz, JETP Lett., 29:1107–1113, 1969; Leggett, Phys. Rev. Lett., 25(22), 1543–1546, 1970; Matsuda and Tsuneto, Prog. Theor. Phys., 46:411–436, 1970) for the SS state in quantum solids such as solid ⁴He were based on the idea of Bose Einstein Condensation (BEC) of the imperfections such as vacancies, interstitials and other possible excitations in the quantum solids which are expected because of the large zero-point motions. The SS state was proposed as a new state of matter in which real space ordering of the lattice structure of the solid coexists with the momentum space ordering of superfluidity. A new type of superconductors, since the discovery of the cuprate high T _c superconductors, HTSCs (Bednorz and Mueller, Z. Phys., 64:189, 1986), has been shown to share a feature with the vortex state, involving the VF and vortex solid states. The high T _c s of these materials are being discussed in connection to the large fluctuations associated with some other phase transitions like the antiferromagnetic transition in addition to that of the low dimensionality. The supersolidity in the hcp solid ⁴He, in contrast to the new superconductors which have multiple degrees of freedom of the Cooper pairs with spin as well as angular momentum freedom, has a unique feature of possessing possibly only the momentum fluctuations and vortex ring excitations associated with the possible low dimensional fluctuations of the subsystem(s). The high onset temperature of the VF state can be understood by considering thermally excited low D quantized vortices and it may be necessary to seek low dimensional sub-systems in hcp He which are hosts for vortices.     

Time-of-Flight Measurements on Quantized Vortex Lines in Rotating 3He-B

Vortex loops are injected into a long cylindrical sample of rotating vortex-free superfluid ³He-B. Using non-invasive NMR techniques, we measure the time required for them to expand along the sample axis to form rectilinear vortex lines. From the axial flight time we deduce the dissipative mutual friction parameter a which is found to agree with previously reported measurements. The flight time displays no anomaly at 0.6T _c, where the character of the vortex dynamics abruptly changes from regular over-damped flow to turbulence.     

Vortex Dynamics in hcp Solid 4He

The peculiar features noted in (Penzev et al. in Phys. Rev. Lett. 101: 065301, 2008) we conjecture are evidence of a vortex fluid state in solid He. We suggest to analyze this state by means of the dynamics of quantized vortices, as used for the tangle of vortices in superfluid turbulence. We introduce parameters of the vortex tangle dynamics, e.g., relaxation time for the drift of lines in parallel to the torsional oscillation axis. We briefly discuss the transition from the supposed vortex fluid state into the supposed supersolid state (Shimizu et al. in Phys. Rev. Lett., arXiv:0903.1326).     

The Superfluid Transition and Vortex Dynamics in Submonolayer Superfluid 4He Films in Porous Glass Under Rotation

A combination of a rotating dilution refrigerator and high-Q torsional oscillator technique has been used to study dynamics of vortices in thin ⁴ He films adsorbed on the porous glass (d=1m pore size). Under rotation an additional dissipation peak with the amplitude proportional to the angular velocity is seen at the middle of the superfluid transition, on the low temperature side of the stationary peak which is present even at =0. We attribute this peak to the 3D Type vortices created in multiply connected ⁴ He film by the rotation. Peak shape of the rotation-induced dissipation could be interpreted as a freezing of the 3D vortices well below T _c     

Torsional Oscillator Study of Thin He Films Under High Speed Rotation

Superfluidity is often compared with superconductivity and rotation is contrasted with magnetic field. In the case of superconductors, it is possible to destroy the superconducting state by application of a sufficiently high magnetic field. Agthough it is not yet technically feasible to destroy the superfluid state through rotation, significant modification of the superfluid can be achieved through rotation. In the experiments reported here we are studying the influence of rotation on the dissipation in superfluid films adsorbed in a porous medium. A new peak in the film dissipation is observed while under rotation at a temperature somewhat below the transition temperature. The dissipative feature we observe is related to the resugt for 2D films under rotation previously reported by Adams and Glaberson, however our observations for films in a porous medium under rotation differ considerably in detail. A theoretical discussion of these resugts has recently been given by Fukuda, et al. (to be published).     

Pinning Mechanism of the Dislocation Lines in bcc Solid 3He

The strain amplitude dependence of the energy dissipation and the shear modulus at several temperatures are measured in bcc solid ³ He and the results are compared with the model of a pinned dislocation loop of Granato and Lücke. In spite of the pure solid, the strong amplitude dependence of the dissipation is found in bcc solid ³ He by the high-Q torsional oscillator measurements, in contrast with the result of the ultrasonic and the torsional-oscillator measurements in hcp solid ⁴ He. In pure solids, the loop length of the dislocations cannot be limited by impurities. In order to clarify a pinning mechanism, the loop length and the network length are obtained from the experimental result by using the model of Granato and Lücke. Where, the loop length is determined by the pinning centers, and the network length is limited by the dislocation network nodes. It is found that the temperature dependence of the loop length is the same as that of the network length. This result shows that the pinning centers are the network nodes of the dislocation lines in ultra pure bcc solid ³ He.     

The Plastic Flow of Solid 4He Through a Porous Membrane

The flow velocity of solid ⁴He through a porous membrane frozen into a crystal has been measured in the temperature interval 0.1–1.8 K. A flat capacitor consisting of a metalized plastic porous membrane and a fixed electrode is applied and the gap in the capacitor is filled with examined helium. The flow of helium through the membrane pores is caused by a d.c. voltage applied to the capacitor plates. Above T～1 K the velocity of solid ⁴He flow decreases with lowering temperature following the Arrhenius law with the activation energy of the process close to that of vacancies. At low temperatures the flow velocity is almost independent of temperature and the absolute value of the velocity V in this region is less than 10^?11 cm/s under the voltage 400 V.     

Observation of Non-Classical Rotational Inertia in Bulk Solid 4He

In recent torsional oscillator experiments by Kim and Chan (KC), a decrease of rotational inertia has been observed in solid ⁴He in porous materials (Kim, E., Chan, M.H.W. in Nature 427:225, 2004; J. Low Temp. Phys. 138:859, 2005) and in a bulk annular channel (Kim, E., Chan, M.H.W. in Science 305:1941, 2004). This observation strongly suggests the existence of “non-classical rotational inertia” (NCRI), i.e. superflow, in solid ⁴He. In order to study such a possible “supersolid” phase, we perform torsional oscillator experiments for cylindrical solid ⁴He samples. We have observed decreases in rotational inertia below 200 mK for two solid samples (pressures P=4.1 and 3.0 MPa). The observed NCRI fraction at 70 mK is 0.14%, which is about 1/3 of the fraction observed in the annulus by KC. Our observation is the first experimental confirmation of the possible supersolid finding by KC.     

The Structure of a Quantized Vortex in a Bose-Einstein Condensate

The structure of a quantized vortex in a Bose-Einstein Condensate is investigated using the projection method developed by Peierls, Yoccoz, and Thouless. This method was invented to describe the collective motion of a many-body system beyond the mean-field approximation. The quantum fluctuation has been properly built into the variational wave function, and a vortex is described by a linear combination of Feynman wave functions weighted by a Gaussian distribution in their center positions. In contrast to the solution of the Gross-Pitaevskii equation, the particle density is finite at the vortex axis and the vorticity is distributed in the core region.     

Observation of Non-Classical Rotational Inertia in Solid 4He Confined in Porous Gold

No Heading Recent torsional oscillator measurements on solid ⁴He confined in Vycor glass at 62 bars show supersolid response, an abrupt drop in rotational moment of inertia, at 175 mK¹. We have investigated the pore-size dependence of the supersolid behavior by confining solid ⁴He in a different porous host, porous gold, of a considerably larger pore diameter. When solid ⁴He in porous gold is cooled below 0.2 K a sharp drop in the resonant period is found. The supersolid response exhibits a strong dependence on the amplitude of oscillation.PACS numbers: 67.80–s. 67.80 Mg., 0.5.70.Fh, 05.30.Jp     

Mass Flux Through a Cell Filled with Solid 4He Induced by the Thermo-Mechanical Effect

We have induced a mass flow through a sample cell filled with hcp solid ⁴He by the imposition of a temperature difference between two reservoirs filled with superfluid liquid helium connected to each other by porous Vycor glass rods in series with the bulk solid ⁴He. The Vycor rods allow us to perform this experiment at pressures greater than the bulk melting pressure. The imposition of a change in the temperature difference between the reservoirs results in a rate-limited flux that creates a change in the pressure difference. The equilibrium pressure and temperature differences are in accord with predictions based on the fountain effect.     

Charged Tangles of Quantized Vortices in Superfluid 4He

We show that turbulence in superfluid ⁴He at low temperatures can be generated and probed by injected ions trapped on vortex cores. The results of our recent experiments, in which negative ions were injected during short and long periods, in different quantities, and into different applied electric fields, are outlined. Three very different mechanisms of vortex-assisted transport of trapped ions were observed: one is on isolated vortex rings while two others are associated with tangles of vortex lines. It seems there are two different types of vortex tangles that can be characterized by the velocity of ion motion through them: a drifting polarized tangle in a low-dissipation state that mainly advects trapped ions, and a more isotropic tangle in a highly-dissipative state, sustained by a continuous forcing by the ion current in an applied electric field, through which trapped ions move rapidly.     

Pinning of Quantized Vortices in Mixed 3He-4He Droplets

We use density functional theory to investigate the structure of mixed ³ He _{N 3} – ⁴ He _{N 4} droplets with an embedded Xe atom that pins a quantized vortex line. While ³ He atoms are distributed along the vortex line and on the surface of the ⁴ He drop, the impurity is mostly coated by ⁴ He atoms. Results for N ₄ =500 and a number of ³ He atoms up to N ₃ =100 are presented, and the binding energy of the dopant to the vortex line is determined.     

Variational Study of a 3He Impurity Near a 4He Vortex Core

The system of kinetic equations for distribution functions of impurity excitations in solid 3He–⁴ He mixtures in the presence of phonons is solved. The results obtained allows us to calculate the spin diffusion coefficient of ³ He–⁴ He quantum crystals. The found expression differs from the results of the previous theoretical studies. A comparison of the obtained diffusion coefficient with experimental data makes it possible to determine the numerical values of the energy band width of impurity excitations.     

Isochoric Compressibility of Solid 4He

We have performed experiments in which we inject atoms into hcp, solid ⁴He contained in a cell of fixed volume at pressures greater than the bulk melting pressure. We measure the change in pressure of the solid in response to the injection, which gives a measure of the isochoric compressibility. We show that at T??700?mK the solid undergoes very little growth and is incompressible. With decreasing temperature the compressibility rises, saturates near T??400 mK and may show weak evidence of a decrease near T??250 mK. Measurements at lower temperatures are necessary to fully test the predictions.