Effective Minkowski-to-Euclidean signature change of the magnon BEC pseudo-Goldstone mode in polar <Superscript>3</Superscript>He

We discuss the effective metric experienced by the Nambu–Goldstone mode propagating in the broken symmetry spin-superfluid state of coherent precession of magnetization. This collective mode represents the phonon in the RF driven or pulsed out-of-equilibrium Bose–Einstein condensate (BEC) of optical magnons. We derive the effective BEC free energy and consider the phonon spectrum when the spin superfluid BEC is formed in the anisotropic polar phase of superfluid ³He, experimentally observed in uniaxial aerogel ³He-samples. The coherent precession of magnetization experiences an instability at a critical value of the tilting angle of external magnetic field with respect to the anisotropy axis. From the action of quadratic deviations around equilibrium, this instability is interpreted as a Minkowski-to-Euclidean signature change of the effective phonon metric. We also note the similarity between the magnon BEC in the unstable region and an effective vacuum scalar “ghost” condensate.     

Orbital glass and spin glass states of <Superscript>3</Superscript>He-A in aerogel

Glass states of superfluid A-like phase of ³He in aerogel induced by random orientations of aerogel strands are investigated theoretically and experimentally. In anisotropic aerogel with stretching deformation two glass phases are observed. Both phases represent the anisotropic glass of the orbital ferromagnetic vector Ηthe orbital glass (OG). The phases differ by the spin structure: the spin nematic vector \(\hat d\) can be either in the ordered spin nematic (SN) state or in the disordered spin-glass (SG) state. The first phase (OG-SN) is formed under conventional cooling from normal ³He. The second phase (OG-SG) is metastable, being obtained by cooling through the superfluid transition temperature, when large enough resonant continuous radio-frequency excitation is applied. NMR signature of different phases allows us to measure the parameter of the global anisotropy of the orbital glass induced by deformation.     

Magnon BEC in superfluid <Superscript>3</Superscript>He-A

The new mode of magnetization precession in superfluid ³He-A in a squeezed aerogel has been recently reported. We consider this mode in terms of the Bose-Einstein condensation (BEC) of magnons. The difference between magnon BEC states in ³He-A and in ³He-B is discussed. The article is published in the original.     

NMR on superfluid<Superscript>3</Superscript>He in aerogel

The transition to superfluidity of³He in high porosity (98.2%) acrogel has been observed by nuclear magnetic resonance techniques. The onset of the transition at all pressures above 13 bar is marked by a sharp increase in NMR frequency similar to that observed in bulk³He-A. This suggests that the aerogel/superfluid phase is highly homogeneous although both the transition temperature, T_c, and the amplitude of the order parameter are substantially suppressed. The acrogel strands are ≈ 50Å in diameter, much smaller than the superfluid coherence length. Consequently, we have attempted to interpret our observations as an impurity scattering problem. Based on our measurements of the magnetic field dependence of T_c it appears that both magnetic and potential scattering play important roles where the magnetic scattering can be associated with solid³He on the aerogel surface. This is determined by isotopic exchange with⁴He, a process which appears to stabilize a new superfluid state similar to the bulk B-phase.     

Interaction of two magnetic resonance modes in the polar phase of superfluid <Superscript>3</Superscript>He

We report results of low frequency nuclear magnetic resonance (NMR) experiments in the superfluid polar phase of ³He, which is stabilized by a new type of “nematic” aerogel—nafen. We have found that an interaction between transverse and longitudinal NMR modes may essentially influence the spin dynamics. Theoretical formulas for NMR resonant frequencies are derived and applied for interpretation of the experimental results.     

Transverse and longitudinal nuclear magnetic resonance in superfluid <Superscript>3</Superscript>He in anisotropic aerogel

It is found that the properties of nuclear magnetic resonance of both superfluid phases of ³He in an anisotropic aerogel can be described in terms of the bulk superfluid order parameters with the orbital order parameter vector fixed by anisotropy of the aerogel sample. It is also shown that, by proper squeezing, it is possible to attain a sample with isotropic NMR properties.     

Coherent precession of magnetization in the superfluid 3He A-phase

We report the first observation of coherent precession of magnetization in superfluid 3He A-like phase (CP-A) in aerogel. The coherent precession in bulk 3He A-phase is unstable due to the positive feedback of spin supercurrent to the gradient of phase of precession. It was predicted that the homogeneous precession will be stable if the orbital momentum of the 3He A-phase can be oriented along the magnetic field. We have succeeded to prepare this configuration by emerging 3He in uniaxially deformed anisotropic aerogel. The dissipation rate of coherent precession states in aerogel is much larger than that in bulk 3He B-phase. We propose a mechanism of this dissipation.     

Low-temperature instability of uniform spin precession in the <Emphasis Type="Italic">B</Emphasis> phase of pure <Superscript>3</Superscript>He and <Superscript>3</Superscript>He in an aerogel

The magnetic-field dependences of the threshold temperature of the low-temperature instability of uniform spin precession in pure ³He-B and ³He-B in an aerogel have been determined for the bulk mechanism. These dependences appear to be different. The theoretical dependence of the threshold temperature for the pure case has been compared with the experimental dependence. The threshold temperature of the instability for ³He in the aerogel has been estimated for typical experimental conditions.     

Spin dynamics of superfluid<Superscript>3</Superscript>He in non-hydrodynamic regime

We review recent results of experimental and theoretical studies of superfluid³He spin dynamics at ultra low temperature, where density of the normal component is virtually zero. We describe a number of new phenomena: catastrophic relaxation, NMR in the Landau field, surface instability of homogeneous precession, persistent NMR signal etc. We propose that superfluid³He in the ultralow temperature limit may provide a system for the experimental modelling of nonequilibrium quantum field theories.     

Orientation effect on superfluid <Superscript>3</Superscript>He in anisotropic aerogel

The orientation of the order parameter in the A-like and B-like phases of superfluid ³He immersed in uniaxially compressed aerogel is reported. With the use of NMR methods, it is found that the orbital momentum of the A-and B-like phases is oriented along the deformation. In the A-like phase, a relatively narrow NMR line with an anomalously large negative frequency shift is observed. The Leggett frequency in the A-like phase, which shows the same energy gap suppression as in the B-like phase, is measured. The text was submitted by the authors in English.     

Magnetic relaxation in superfluid<Superscript>3</Superscript>He-B at very low temperatures

Main properties of the spin supercurrents and coherent precession of magnetization in the superfluid³He-B in hydrodynamic regime seem to be very well understood now. But recently surprisingly new unpredicted phenomena such as, for example, “catastrophic” relaxation, persistent spin precession, very strong magnetic relaxation, etc., have been observed in³He-B at ultralow temperatures in so-called non-hydrodynamic regime using both pulse and cw-NMR techniques. This paper deals with some of these new phenomena (a “linear term” in magnetic relaxation and a reduction of magnetization of coherent precession with magnetic field gradient) observed by cw-NMR technique, compares these results with new effects found by pulse NMR and speculates about the nature of these new phenomena.     

Porosity dependence of sound propagation in liquid-<Superscript>4</Superscript>He-filled aerogel

Longitudinal sound-wave propagation has been studied in an aerogel-liquid ⁴He system for various porosities of aerogel. The superfluid transition was identified as the absorption peak, whose magnitude was suppressed by aerogel. The sound velocity was analyzed within a hydrodynamic theory in both normal and superfluid phases. The absorption peak due to phonon-roton interaction around 1 K was not observed even with the most porous aerogel. The low-temperature sound velocity and attenuation show that direct collisions of phonons with aerogel strands play an important role in the acoustic properties.     

Low-temperature stability limit of the coherent spin precession in <Superscript>3</Superscript>He-B

It has been shown that the instability of uniform spin precession in the bulk of the ³He-B superfluid phase is due to the joint action of the anisotropy of the velocities of spin waves and dipole interaction. In the leading approximation in the ratio of the Leggett frequency to the Larmor frequency, the growth increments of the amplitudes of spin waves for all of the possible decay channels have been found. The maximum increment has been determined for all of the angles of spin deviation from the equilibrium orientation. The minimum temperature to which precession is stable has been estimated.     

Linear NMR in the Polar Phase of <Superscript>3</Superscript>He in Aerogel

³He is an example of the system with non-trivial Cooper paring. A few different superfluid phases are known in this system. Recently the new one, the polar phase, have been observed in ³He confined in nematically ordered aerogel. A number of various topological defects including half-quantum vortices can exist the polar phase. In this work, we present theoretical and numerical studies of linear nuclear magnetic resonance in the polar phase both in the uniform order-parameter texture and in the presence of half-quantum vortices.     

Metastability and superfluid fraction of the A-like and B phases of <Superscript>3</Superscript>He in aerogel in zero magnetic field

We report the low-frequency sound measurements of the metastable A-like (A*) phase of superfluid ³He confined within a 98% open aerogel matrix in zero magnetic field. The second soundlike (slow) mode provides an accurate determination of the superfluid fraction of (and the transition between) the A* and B phases. The A* and B phases exhibit stable coexistence in the presence of disorder, the ratio of their superfluid fractions (ρ _a ^A* /ρ _s ^B ) is much smaller than that of the bulk A and B phases, and argues that the A* and bulk A phases are distinct.     

Nuclear magnetic relaxation of <Superscript>3</Superscript>He in contact with an aerogel above the Fermi temperature

The spin kinetics of ³He in an aerogel has been studied above the Fermi temperature. The magnetic relaxation times T ₁ and T ₂ of adsorbed, gaseous, and liquid ³He in a 95% silica aerogel at a temperature of 1.5 K have been determined as functions of frequency by means of pulse nuclear magnetic resonance. It has been found that the time T ₁ is linear in frequency in all three cases, whereas T ₂ is independent of frequency. To explain the observed behavior of the longitudinal relaxation rate, a theoretical model of relaxation in the adsorbed layer of ³He taking into account the filamentary structure of the aerogel is proposed.     

Recent results on hyperpolarized<Superscript>3</Superscript>He−<Superscript>4</Superscript>He liquid mixtures

Laser optical pumping in low magnetic field provides very high nuclear polarizations in gaseous helium mixtures, and is used to prepare polarized liquid. Wall relaxation in glass cells is effiently reduced using cesium coatings, and bulk longitudinal relaxation times are measured. In highly magnetized samples, dipolar fields control the spin dynamics in anisotropic volumes and weak external magnetic field inhomogeneities. Long lived magnetostatic modes are observed by pulsed NMR. Detailed analysis of their frequency and damping gives information on magnetization density and spin diffusion coefficient in polarized mixtures. Experiments are performed above 0.2 K on mixtures with³He concentrations of order a few percents or larger. When phase separation occurs, the³He-rich phase retains a high polarization.     

Aerogel: Impurities in superfluid<Superscript>3</Superscript>He?

We present results of torsional oscillator experiments that are in progress or completed at Cornell. Taken together, these experiments suggest that the properties of superfluid³He in aerogel are substantially different from those exhibited by bulk superfluid³He. Featured are the differences between bulk and superfluid³He in aerogel with temperature and pressure. Comparisons to proposed models of³He in aerogel are also made.