Measurements of superfluid $^3$He in 98% aerogel demonstrate the existence of a metastable \emph{A}-like phase and a stable \emph{B}-like phase. It has been suggested that the relative stability of these two phases is controlled by anisotropic quasiparticle scattering in the aerogel. Anisotropic scattering produced by axial compression of the aerogel has been predicted to stabilize the axial state of superfluid $^3$He. To explore this possiblity, we used transverse acoustic impedance to map out the phase diagram of superfluid $^3$He in a $\sim 98$% porous silica aerogel subjected to 17% axial compression. We have previously shown that axial anisotropy in aerogel leads to optical birefringence and that optical cross-polarization studies can be used to characterize such anisotropy. Consequently, we have performed optical cross-polarization experiments to verify the presence and uniformity of the axial anisotropy in our aerogel sample. We find that uniform axial anisotropy introduced by 17% compression does not stabilize the \emph{A}-like phase. We also find an increase in the supercooling of the \emph{A}-like phase at lower pressure, indicating a modification to \emph{B}-like phase nucleation in \emph{globally} anisotropic aerogels.
We have designed an experiment to study the role of global anisotropic quasiparticle scattering on the dirty aerogel superfluid 3He system. We observe significant regions of two stable phases at temperatures below the superfluid transition at a pressure of 25 bar for a 98% aerogel.
NMR spectra in superfluid A-like phases confined in axially deformed aerogel in presence of a magnetic field inclined with respect to deformation axis is considered. The characteristic features of dipole frequency shift in axially compressed and axially stretched cases are compared. In particular, it is shown that in axially stretched aerogel environment the stability region of coherently spin precessing mode is rather narrow due to the U(1)LIM effect.
Superfluid 3He confined to high porosity silica aerogel is the paradigm system for understanding impurity effects in unconventional superconductors. However, a crucial first step has been elusive; exact identification of the microscopic states of the superfluid in the presence of quenched disorder. Using a new class of highly uniform aerogel materials, we report pulsed nuclear magnetic resonance experiments that demonstrate definitively that the two observed superfluid states in aerogel are impure versions of the isotropic and axial p-wave states. The theoretically predicted destruction of lon…
We have performed Small Angle X-ray Scattering (SAXS) on uniaxially strained aerogels and measured the strain-induced structural anisotropy. We use a model to connect our SAXS results to anisotropy of the 3He quasiparticle mean free path in aerogel.
It may be possible to stabilize new superfluid phases of $^{3}$He with anisotropic silica aerogels. We discuss two methods that introduce anisotropy in the aerogel on length scales relevant to superfluid $^{3}$He. First, anisotropy can be induced with uniaxial strain. A second method generates anisotropy during the growth and drying stages. We have grown cylindrical $\sim$98% aerogels with anisotropy indicated by preferential radial shrinkage after supercritical drying and find that this shrinkage correlates with small angle x-ray scattering (SAXS). The growth-induced anisotropy was found to b…
Core structures of a single vortex in A-like and B-like phases of superfluid 3He in uniaxially compressed and stretched aerogels are studied by numerically solving Ginzburg-Landau equations derived microscopically. It is found that, although the A-like phase with axial pairing is extended by any uniaxial deformation, the vortex core states in the two phases depend highly on the type of deformation in aerogel: In a compressed aerogel, the first order vortex core transition (VCT) previously seen in the bulk B phase appears at any pressure in B-like phase, while no strange vortex core is expected…
Recently, one analog of the Anderson's Theorem for the $s$-wave superconductor has attracted much interest in the context of the $p$-wave polar pairing state of superfluid $^3$He in a model aerogel in the limit of strong uniaxial anisotropy. We discuss to what extent the theorem is satisfied in the polar phase in real aerogels by examining the normal to polar transition temperature $T_c$ and the low temperature behavior of the superfluid energy gap under an anisotropy of a moderate strength and comparing the obtained results with experimental data. The situation in which the Anderson's theorem…
We present results of high magnetic field experiments in pure $^3$He (in the absence of $^4$He coverage) in nematic aerogel. In this case the aerogel strands are covered with few atomic layers of solid paramagnetic $^3$He, which enables the spin-exchange mechanism for $^3$He quasiparticles scattering. Our earlier NMR experiments showed that in low fields, instead of the polar phase, the A phase is expected to emerge in nematic aerogel. We use a vibrating wire resonator with the sample of aerogel attached to it and measure temperature dependencies of resonance properties of the resonator at dif…
The polar phase of superfluid $^3$He is stable in "nematically ordered" densed aerogel. A rotating vessel with the polar superfluid can be filled either by an array of the single quantum vortices or by an array of the half-quantum vortices. It is shown that the inhomogeneous distribution of the spin part of the order parameter arising in an array of half-quantum vortices in strong enough magnetic field tilted to the average direction of aerogel strands leads to the appearance of a satellite in the NMR signal shifted in the negative direction with respect to the Larmor frequency. The satellite …
Motivated by the recent observation and argument on a large half-quantum vortex (HQV) pair connencted by a Kibble wall in superfluid 3He in nematic aerogels, we numerically study to what extent a huge HQV pair can intrinsically occur with no pinning effect due to the aerogel structure in the polar-distorted B (PdB) phase of superfluid 3He. By fully examining the impurity-scattering induced pairing vertex, the emergence of Anderson's Theorem in the p-wave superfluid is verified in the two opposite limits, the isotropic and strongly anisotropic limits. Solving numerically the resulting Ginzburg-…
We present experiments on nematic aerogel oscillating in superfluid $^3$He. This aerogel consists of nearly parallel mullite strands and is attached to a vibrating wire moving along the direction of the strands. Previous nuclear magnetic resonance experiments in $^3$He confined in similar aerogel sample have shown that the superfluid transition of $^3$He in aerogel occurs into the polar phase and the transition temperature ($T_{ca}$) is only slightly suppressed with respect to the superfluid transition temperature of bulk $^3$He. In present experiments we observed a change in resonant properti…
It was found that NMR properties of both superfluid phases of $^3$He in 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 was also shown that by a proper squeezing it is possible to get the aerogel sample with isotropic NMR properties.
Results of experiments with liquid 3He immersed in a new type of aerogel are described. This aerogel consists of Al2O3 strands which are nearly parallel to each other, so we call it as a "nematically ordered" aerogel. At all used pressures a superfluid transition was observed and a superfluid phase diagram was measured. Possible structures of the observed superfluid phases are discussed.
The superfluid state in bulk liquid $^3$He is realized in the form of A or B phases. Uniaxially anisotropic aerogel (nafen) stabilizes transition from the normal to the polar superfluid state which on further cooling transitions to the axipolar orbital glass state (Phys. Rev. Lett. {\bf 115}, 165304 (2015)). This is the case in nafen aerogel preplated by several atomic layers of $^4$He. When pure liquid $^3$He fills the same nafen aerogel a solid-like layer of $^3$He atoms coats the aerogel structure. The polar state is not formed anymore and a phase transition occurs directly to the axipolar …
Longitudinal sound attenuation measurements in superfluid 3He in 98% aerogel were conducted at pressures between 14 and 33 bar and in magnetic fields up to 4.44 kG. The temperature dependence of the ultrasound attenuation in the A-like phase was determined for the entire superfluid region exploiting the field induced meta-stable A-like phase at the highest field. In the lower field, the A-B transition in aerogel was identified by a smooth jump in attenuation on both cooling and warming. Based on the transitions observed on warming, a phase diagram as a function of pressure (P), temperature (T)…
We report the results of high frequency acoustic shear impedance measurement on superfluid helium-3 confined in 98% porosity silica aerogel. Using 8.69 MHz continuous wave excitation, we measured the acoustic shear impedance as a function of temperature for the sample pressure of 28.4 and 33.5 bar. We observed the A-B transition on warming in zero magnetic field. Our observations show that the A and B phases in aerogel coexist in a temperature range of about 100 micro-Kelvin in width. We propose that the difference in the relative stability of the A and B phases, arising from anisotropic scatt…
We present results of nuclear magnetic resonance (NMR) experiments in superfluid 3He in two samples of nematic aerogel consisting of nearly parallel mullite strands. The samples were cut from the same piece of the aerogel, but one of them was squeezed by 30% in the direction transverse to the strands. In both samples the superfluid transition of 3He occurred into the polar phase, where no qualitative difference between NMR properties of 3He in these samples was found. The difference, however, has appeared on further cooling, after the transition to the polar-distorted A phase (PdA phase) with …
We report on orientation of the order parameter in the 3He-A and 3He-B phases caused by aerogel anisotropy. In 3He-A we have observed relatively homogeneous NMR line with an anomalously large negative frequency shift. We can attribute this effect to an orientation of orbital momentum along the axis of density anisotropy. The similar orientation effect we have seen in 3He-B. We can measure the A-phase Leggett frequency, which shows the same energy gap suppression as in the B-phase. We observe a correlation of A - B transition temperature and NMR frequency shift.
Porous aerogel is a source of elastic scattering in superfluid 3He and modifies the properties of the superfluid, suppressing the transition temperature and order parameter. The specific heat jumps for the B-phase of superfluid 3He in aerogel have been measured as a function of pressure and interpreted using the homogeneous and inhomogeneous isotropic scattering models. The specific heat jumps for other p-wave states are estimated for comparison.
It is established theoretically that an ordered state with continuous symmetry is inherently unstable to arbitrarily small amounts of disorder [1, 2]. This principle is of central importance in a wide variety of condensed systems including superconducting vortices [3, 4], Ising spin models [5] and their dynamics [6], and liquid crystals in porous media [7, 8], where some degree of disorder is ubiquitous, although its experimental observation has been elusive. Based on these ideas it was predicted [9] that 3He in high porosity aerogel would become a superfluid glass. We report here our nuclear …
We report the first observation of coherent quantum precession of magnetization (CQP) in superfluid 3He-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 3He-A could 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 then one i…
We have found a new stable spin state in the A-like phase of superfluid 3He confined to intrinsically anisotropic aerogel. The state can be formed by radiofrequency excitation applied while cooling through the superfluid transition temperature and its NMR properties are different from the standard A-like phase obtained in the limit of very small excitation. It is possible that this new state is formed by textural domain walls pinned by aerogel.
It is shown that in the polar phase of superfluid 3 He, stabilized by nematic aerogel, at the condition of specular reflection of quasi-particles from the strands of aerogel the temperature dependence of the gap in the spectrum of quasi-particles coincides with that in the bulk polar phase without impurities. The analogy with the Anderson theorem for conventional superconductors is discussed.
We report the first observation of superfluid $β$ phase of $^3$He. This phase is realized in $^3$He in nematic aerogel in presence of high magnetic field right below the superfluid transition temperature. We use a vibrating aerogel resonator to detect the transition to the $β$ phase and measure the region of existence of this phase.
$^3$He 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 $^3$He 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 NMR in the polar phase both in the uniform order-parameter texture and in the presence of half-quantum vortices.
Motivated by the recent prediction that uniaxially compressed aerogel can stabilize the anisotropic A phase over the isotropic B phase, we measure the pressure dependent superfluid fraction of 3He entrained in 10% axially compressed, 98% porous aerogel. We observe that a broad region of the temperature-pressure phase diagram is occupied by the metastable A phase. The reappearance of the A phase on warming from the B phase, before superfluidity is extinguished at Tc, is in contrast to its absence in uncompressed aerogel. The phase diagram is modified from that of pure 3He, with the disappearanc…
Motivated by the disparity between the experimentally observed properties of superfluid 3He in aerogel and predictions of the Abrikosov and Gorkov theory of superconducting alloys we consider effect of correlated pair-breaking impurities on the temperature dependence of the square of magnitude of the average order parameter and related thermodynamic properties of a Fermi superfluid. We show that the correlations, increasing the spectral density of the fluctuations with small wave vectors increase the transition temperature and enhance a temperature region below Tc where fluctuations of the ord…
One of the most spectacular discoveries made in superfluid $^3$He confined in a nanostructured material like aerogel or nafen was the observation of the destruction of the long-range orientational order by a weak random anisotropy. The quenched random anisotropy provided by the confining material strands produces several different glass states resolved in NMR experiments in the chiral superfluid $^3$He-A and in the time-reversal-invariant polar phase. The smooth textures of spin and orbital order parameters in these glasses can be characterized in terms of the randomly distributed topological …
The magnetic dipole-dipole interaction does not prevent existence of half-quantum vortices in the polar phase of superfluid He-3 which can be stable in uniaxial anisotropic aerogel. Here we discus this exotic possibility. After developing a phenomenological theory of phase transition from the normal to polar superfluid state and then to axipolar superfluid state we calculate the NMR properties of such type superfluids at the rest or under rotation filled by an array either single quantum or half quantum vortices.
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.
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.
The phenomenon of the spontaneous phase-coherent precession of magnetization in superfluid 3He and the related effects of spin superfluidity are based on the true Bose-Einstein condensation of magnons. Several different magnon BEC states have been observed: homogeneously precessing domain (HPD); BEC condensation in the spin-orbit potential trap (Q-balls); coherent precession with fractional magnetization; and two modes of the coherent precession in squeezed aerogel. The spin superfluidity effects, like spin Josephson phenomena, spin current vortices, spin phase slippage, long distance magnetiz…
We predict a dynamical classical superfluid-insulator transition in a Bose-Einstein condensate (BEC) trapped in a combined optical and axially-symmetric harmonic potentials initiated by a periodic modulation of the radial trapping potential. The transition is marked by a loss of phase coherence in the BEC and a subsequent destruction of the interference pattern upon free expansion. For a weak modulation of the radial potential the phase coherence is maintained. For a stronger modulation and a longer time of holding in the modulated trap, the phase coherence is destroyed signaling a classical s…
