Superfluid Fraction Research Articles

Path integral Monte Carlo simulation of global and local superfluidity in liquidHe4reservoirs separated by nanoscale apertures

We present a path integral Monte Carlo study of the global superfluid fraction and local superfluid density in cylindrically-symmetric reservoirs of liquid $^{4}$He separated by nanoaperture arrays. The superfluid response to both translations along the axis of symmetry (longitudinal response) and rotations about the cylinder axis (transverse response) are computed, together with radial and axial density distributions that reveal the microscopic inhomogeneity arising from the combined effects of the confining external potential and the $^4$He-$^4$He interatomic potentials. We make a microscopic determination of the length-scale of decay of superfluidity at the radial boundaries of the system by analyzing the local superfluid density distribution to extract a displacement length that quantifies the superfluid mass displacement away from the boundary. We find that the longitudinal superfluid response is reduced in reservoirs separated by a septum containing sufficiently small apertures compared to a cylinder with no intervening aperture array, for all temperatures below $T_{\lambda}$. For a single aperture in the septum, a significant drop in the longitudinal superfluid response is seen when the aperture diameter is made smaller than twice the empirical temperature-dependent $^4$He healing length, consistent with the formation of a weak link between the reservoirs. Increasing the diameter of a single aperture or the number of apertures in the array results in an increase of the superfluid density toward the expected bulk value.

Observation of a new superfluid phase for 3He embedded in nematically ordered aerogel.

In bulk superfluid 3He at zero magnetic field, two phases emerge with the B-phase stable everywhere except at high pressures and temperatures, where the A-phase is favoured. Aerogels with nanostructure smaller than the superfluid coherence length are the only means to introduce disorder into the superfluid. Here we use a torsion pendulum to study 3He confined in an extremely anisotropic, nematically ordered aerogel consisting of ∼10 nm-thick alumina strands, spaced by ∼100 nm, and aligned parallel to the pendulum axis. Kinks in the development of the superfluid fraction (at various pressures) as the temperature is varied correspond to phase transitions. Two such transitions are seen in the superfluid state, and we identify the superfluid phase closest to Tc at low pressure as the polar state, a phase that is not seen in bulk 3He.

Long-distance correlation-length effects and hydrodynamics ofHe4films in a Corbino geometry

Previous measurements of the superfluid density ${\ensuremath{\rho}}_{s}$ and specific heat for $^{4}\mathrm{He}$ have identified effects that are manifest at distances much larger than the correlation length ${\ensuremath{\xi}}_{3\text{D}}$ [Perron et al., Nat. Phys. 6, 499 (2010); Perron and Gasparini, Phys. Rev. Lett. 109, 035302 (2012); Perron et al., Phys. Rev. B 87, 094507 (2013)]. We report here measurements of the superfluid density which are designed to explore this phenomenon further. We determine the superfluid fraction ${\ensuremath{\rho}}_{s}/\ensuremath{\rho}$ from the resonance of 34-nm films of varying widths $4\ensuremath{\le}W\ensuremath{\le}100\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\text{m}$. The films are formed across a Corbino ring separating two chambers where a thicker 268-nm film is formed. This arrangement is realized using lithography and direct Si-wafer bonding. We identify two effects in the behavior of ${\ensuremath{\rho}}_{s}/\ensuremath{\rho}$: one is hydrodynamic, for which we present an analysis, and the other is a correlation-length effect which manifests as a shift in the transition temperature ${T}_{c}$ relative to that of a uniform 34-nm film uninfluenced by proximity effects. We find that one can collapse both ${\ensuremath{\rho}}_{s}/\ensuremath{\rho}$ and the quality factor of the resonance onto universal curves by shifting ${T}_{c}$ as $\mathrm{\ensuremath{\Delta}}{T}_{c}\ensuremath{\sim}{W}^{\ensuremath{-}\ensuremath{\nu}}$. This scaling is a surprising result on two counts: it involves a very large length scale $W$ relative to the magnitude of ${\ensuremath{\xi}}_{3\text{D}}$ and the dependence on $W$ is not what is expected from correlation-length finite-size scaling which would predict $\mathrm{\ensuremath{\Delta}}{T}_{c}\ensuremath{\sim}{W}^{\ensuremath{-}1/\ensuremath{\nu}}$.

Quartz Tuning Fork Pressure Gauge for High-Pressure Liquid Helium

We have measured the quality factor Q and the frequency f of a 32-kHz quartz tuning fork immersed in liquid $$^4$$ He between 0.9 and 3.0 K, over pressures ranging from the saturated vapor pressure to $$\approx $$ 25 atm. At constant pressure, as a function of temperature, the quality factor and frequency have strong features related to the temperature dependence of the superfluid fraction. At constant temperature, Q depends on the superfluid fraction, while the frequency is a smooth function of pressure. The behavior is explained using a simple hydrodynamic model. The liquid helium viscosity is obtained from measured values of Q, and together with tabulated values of the helium density as a function of pressure and temperature, the frequency shift can be parameterized as a function of temperature and pressure. The observed sensitivity is $$\approx $$ 7.8 Hz/atm. The quartz tuning fork provides a compact low power method of measuring the pressure in the bulk liquid.

Correlation effects and collective excitations in bosonic bilayers: Role of quantum statistics, superfluidity, and the dimerization transition

A two-component two-dimensional (2D) dipolar bosonic system in the bilayer geometry is considered. By performing quantum Monte Carlo simulations in a wide range of layer spacings we analyze in detail the pair correlation functions, the static response function, the kinetic and interaction energies. By reducing the layer spacing we observe a transition from weakly to strongly bound dimer states. The transition is accompanied by the onset of short-range correlations, suppression of the superfluid response, and rotonization of the excitation spectrum. A dispersion law and a dynamic structure factor for the {\em in-phase} (symmetric) and {\em out-of-phase} (antisymmetric) collective modes, during the dimerization, is studied in detail with the stochastic reconstruction method and the method of moments. The antisymmetric mode spectrum is most strongly influenced by suppression of the inlayer superfluidity (specified by the superfluid fraction $\gamma_s=\rho_s/\rho$). In a pure superfluid/normal phase only an acoustic/optical(gapped) mode is recovered. In a partially superfluid phase, both are present simultaneously, and the dispersion splits into two branches corresponding to a normal and a superfluid component. The spectral weight of the acoustic mode scales linearly with $\gamma_s$. This weight transfers to the optical branch when $\gamma_s$ is reduced due to formation of dimer states. In summary, we demonstrate how the interlayer dimerization in dipolar bilayers can be uniquely identified by static and dynamic properties.

From quantum to thermal topological-sector fluctuations of strongly interacting Bosons in a ring lattice

Inspired by recent experiments on Bose–Einstein condensates in ring traps, we investigate the topological properties of the phase of a one-dimensional Bose field in the presence of both thermal and quantum fluctuations—the latter ones being tuned by the depth of an optical lattice applied along the ring. In the regime of large filling of the lattice, quantum Monte Carlo simulations give direct access to the full statistics of fluctuations of the Bose-field phase, and of its winding number W along the ring. At zero temperature the winding-number (or topological-sector) fluctuations are driven by quantum phase slips localized around a Josephson link between two lattice wells, and their susceptibility is found to jump at the superfluid-Mott insulator transition. At finite (but low) temperature, on the other hand, the winding number fluctuations are driven by thermal activation of nearly uniform phase twists, whose activation rate is governed by the superfluid fraction. A quantum-to-thermal crossover in winding-number fluctuations is therefore exhibited by the system, and it is characterized by a conformational change in the topologically non-trivial configurations, from localized to uniform phase twists, which can be experimentally observed in ultracold Bose gases via matter–wave interference.

Kohn-Sham approach to Fermi gas superfluidity: The bilayer of fermionic polar molecules

By using a well-established ``ab initio'' theoretical approach developed in the past to quantitatively study the superconductivity of condensed matter systems, based on the Kohn-Sham density functional theory, I study the superfluid properties and the BCS-BEC crossover of two parallel bi-dimensional layers of fermionic dipolar molecules, where the pairing mechanism leading to superfluidity is provided by the interlayer coupling between dipoles. The finite temperature superfluid properties of both the homogeneous system and one where the fermions in each layer are confined by a square optical lattice are studied at half filling conditions, and for different values of the strength of the confining optical potential. The T = 0 results for the homogeneous system are found to be in excellent agreement with diffusion Monte Carlo results. The superfluid transition temperature in the BCS region is found to increase, for a given interlayer coupling, with the strength of the confining optical potential. A transition occurs at sufficiently small interlayer distances, where the fermions becomes localized within the optical lattice sites in a square geometry with an increased effective lattice constant, forming a system of localized composite bosons. This transition should be signaled by a sudden drop in the superfluid fraction of the system.

Thermodynamics of a two-dimensional dipolar Bose gas with correlated disorder in the roton regime

We study the impact of a weak random potential with a Gaussian correlation function on the thermodynamics of a two-dimensional dipolar bosonic gas. Analytical expressions for the quantum depletion, anomalous density, the ground state energy, the equation of state and the sound velocity are derived in the roton regime within the framework of the Bogoliubov theory. Surprisingly, we find that the condensate depletion and the anomalous density are comparable. The structure factor and the superfluid fraction are also obtained analytically and numerically. We show that these quantities acquire dramatically modified profiles when the roton is close to zero yielding the transition to an unusual quantum state.

Normal and superfluid fractions of inhomogeneous nonequilibrium quantum fluids

We present a theoretical analysis of the normal and superfluid fractions of quantum fluids described by a nonequilibrium extension of the Gross-Pitaevskii equation in the presence of an external potential. Both disordered and regular potentials are considered. The normal and superfluid fractions are defined by the response of the nonequilibrium quantum fluid to a vector potential, in analogy with the equilibrium case. We find that the physical meaning of these definitions breaks down out of equilibrium. The normal and superfluid fractions no longer add up to one and for some types of external potentials, they can even become negative.

Superglass Phase of Interaction-Blockaded Gases on a Triangular Lattice.

We investigate the quantum phases of monodispersed bosonic gases confined to a triangular lattice and interacting via a class of soft-shoulder potentials. The latter correspond to soft-core potentials with an additional hard-core onsite interaction. Using exact quantum MonteCarlo simulations, we show that the low temperature phases for weak and strong interactions following a temperature quench are a homogeneous superfluid and a glass, respectively. The latter is an insulating phase characterized by inhomogeneity in the density distribution and structural disorder. Remarkably, we find that for intermediate interaction strengths a superglass occurs in an extended region of the phase diagram, where glassy behavior coexists with a sizable finite superfluid fraction. This glass phase is obtained in the absence of geometrical frustration or external disorder and is a result of the competition of quantum fluctuations and cluster formation in the corresponding classical ground state. For high enough temperature, the glass and superglass turn into a floating stripe solid and a supersolid, respectively. Given the simplicity and generality of the model, these phases should be directly relevant for state-of-the-art experiments with Rydberg-dressed atoms in optical lattices.

Superfluid-Mott transitions and vortices in the Jaynes-Cummings-Hubbard lattices with time-reversal-symmetry breaking

We investigate the groundstate behaviour of Jaynes-Cummings-Hubbard lattices in the presence of a synthetic magnetic field, via a Gutzwiller ansatz. Specifically, we study the Mott-Superfluid transition, and the formation of vortex lattices in the superfluid regime. We find a suppression of the superfluid fraction due to the frustration induced by the incommensurate magnetic and spacial lattice lengths. We also predict the formation of regime.

Localization of weakly interacting Bose gas in quasiperiodic potential

We study the localization properties of weakly interacting Bose gas in a quasiperiodic potential. The Hamiltonian of the non-interacting system reduces to the well known ‘Aubry–André model’, which shows the localization transition at a critical strength of the potential. In the presence of repulsive interaction we observe multi-site localization and obtain a phase diagram of the dilute Bose gas by computing the superfluid fraction and the inverse participation ratio. We construct a low-dimensional classical Hamiltonian map and show that the onset of localization is manifested by the chaotic phase space dynamics. The level spacing statistics also identify the transition to localized states resembling a Poisson distribution that are ubiquitous for both non-interacting and interacting systems. We also study the quantum fluctuations within the Bogoliubov approximation and compute the quasiparticle energy spectrum. Enhanced quantum fluctuation and multi-site localization phenomenon of non-condensate density are observed above the critical coupling of the potential. We briefly discuss the effect of the trapping potential on the localization of matter wave.

Perturbation Theory for Superfluid in Nonuniform Potential

Perturbation theory of superfluid fraction in terms of nonuniform potential is constructed. We find that the coefficient of the leading term is determined by the dynamical structure factor or density fluctuation of the system. The results for the ideal Bose gas and the interacting Bose system with linear dispersion are consistent to implications from Landau’s criterion. We also find that the superfluidity of Tomonaga–Luttinger liquid with \(K>2\) is shown to be stable against nonuniform potential.

Superfluidity, BEC, and dimensions of liquidHe4in nanopores

We present path integral Monte Carlo (PIMC) calculations of the superfluid fraction, ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}$, and the one-body density matrix (OBDM) [Bose-Einstein condensation (BEC)] of liquid $^{4}\mathrm{He}$ confined in nanopores. Liquid $^{4}\mathrm{He}$ in nanopores represents a dense Bose liquid at reduced dimension and in disorder. The goal is to determine the effective dimensions of the liquid in the pores. It is to test whether observed properties, such as a very low onset temperature for superflow, ${T}_{c}$, can be predicted by a standard, static PIMC ${\ensuremath{\rho}}_{S}/\ensuremath{\rho}$. We simulate a cylinder of liquid of diameter ${d}_{L}$ surrounded by 5 \AA{} of inert solid $^{4}\mathrm{He}$ in a nanopore of diameter $d$; $d={d}_{L}+10\phantom{\rule{0.28em}{0ex}}\AA{}$. We find a PIMC ${\ensuremath{\rho}}_{S}(T)/\ensuremath{\rho}$ and OBDM that scales as a 1D fluid Luttinger liquid at extremely small liquid pore diameters only, ${d}_{L}=6\phantom{\rule{0.28em}{0ex}}\AA{}$. At this ${d}_{L}$, the liquid fills the pore in a 1D line at the center of the pore and there is no PIMC superflow. In the range $8\ensuremath{\le}{d}_{L}\ensuremath{\le}22\phantom{\rule{0.28em}{0ex}}\AA{}$ the PIMC ${\ensuremath{\rho}}_{S}(T)/\ensuremath{\rho}$ scales as a 2D liquid. In this ${d}_{L}$ range the liquid fills the pores in 2D-like cylindrical layers. The crossover from no superflow at $d=16\phantom{\rule{0.28em}{0ex}}\AA{}$ to superflow at $d\ensuremath{\ge}18\phantom{\rule{0.28em}{0ex}}\AA{}$ agrees with experiment. There is a crossover to 3D scaling at larger ${d}_{L}\ensuremath{\simeq}22\phantom{\rule{0.28em}{0ex}}\AA{}$. In the range $8\ensuremath{\le}{d}_{L}\ensuremath{\le}22\phantom{\rule{0.28em}{0ex}}\AA{}$, the ${T}_{c}$ predicted using the Kosterlitz-Thouless 2D scaling criterion of the OBDM agrees well with that obtained from ${\ensuremath{\rho}}_{S}(T)/\ensuremath{\rho}$. These results suggest that the superflow observed in small pore media is standard static superflow with the low ${T}_{c}$ arising from its 2D character. An operational onset temperature, ${T}_{\mathrm{BEC}}$, for BEC can be defined as the temperature at which there is a crossover from exponential to algebraic decay in the OBDM. This definition leads to a ${T}_{\mathrm{BEC}}\ensuremath{\ge}{T}_{c}$ as observed in larger pore media.

Intrinsic-to-extrinsic supersolid transition and fractionally modulated states in a lattice ultracold Bose gas with long-range interaction

We investigate the intrinsic-to-extrinsic supersolid (SS) transition in a lattice ultracold Bose gas with strong long-range interaction. When changing the depth of the periodic lattice potential, the transition is shown to manifest in the ground-state wave function and energy, the change of superfluid fraction ${f}_{s}$, and a roton instability. Near the transition in the extrinsic SS phase, due to the competition between the long-range interaction and the periodic potential, we show that there exist a variety of stable fractionally modulated states (FMSs) upon the change of the effective length of the long-range interaction. Consequence of the transition across different FMSs is discussed.

Two-dimensional dipolar bosons with weak disorder

We consider two-dimensional dipolar bosonic gas with dipoles oriented perpendicularly to the plane in a weak random potential. We investigate analytically and numerically the condensate depletion, the one-body density-matrix, the ground state energy, the sound velocity and the superfluid fraction. Concentrating on the regime where a roton-like excitation spectrum forms, our results show that the superfluidity disappears below a critical value of disorder strength yielding the transition to a non-trivial quantum regime.

Superfluidity and Bose–Einstein Condensation in a Dipolar Bose Gas with Weak Disorder

We investigate the properties of a three-dimensional homogeneous dipolar Bose gas in a weak random potential with a Gaussian correlation function at finite temperature. Using the Bogoliubov theory (beyond the mean field), we calculate the superfluid and the condensate fractions in terms of the interaction strength on the one hand and in terms of the width and the strength of the disorder on the other. The influence of the disordered potential on the second-order correlation function, the ground state energy, and the chemical potential is also analyzed. We find that for fixed strength and correlation length of the disorder potential, the dipole–dipole interaction leads to modify both the condensate and the superfluid fractions. We show that for a strong disorder strength the condensed fraction becomes larger than the superfluid fraction. We discuss the effect of the trapping potential on a disordered dipolar Bose in the regime of large number of particles.

Antiferromagnetic Spinor Condensates in a Two-Dimensional Optical Lattice.

We experimentally demonstrate that spin dynamics and the phase diagram of spinor condensates can be conveniently tuned by a two-dimensional optical lattice. Spin population oscillations and a lattice-tuned separatrix in phase space are observed in every lattice where a substantial superfluid fraction exists. In a sufficiently deep lattice, we observe a phase transition from a longitudinal polar phase to a broken-axisymmetry phase in steady states of lattice-confined spinor condensates. The steady states are found to depend sigmoidally on the lattice depth and exponentially on the magnetic field. We also introduce a phenomenological model that semiquantitatively describes our data without adjustable parameters.

Dipolar Bose gas in a weak isotropic speckle disorder

We investigate the properties of a homogeneous dipolar Bose gas in a weak three-dimensional (3D) isotropic speckle disorder at finite temperature. By using the Bogoliubov theory (beyond the mean field), we calculate the condensate and the superfluid fractions as a function of density and strengths of disorder and interaction. The influence of disorder on the anomalous density, the chemical potential and the ground state energy is also analyzed. We show that the peculiar interplay of the DDI and weak disorder makes the superfluid fraction and sound velocity anisotropic.

Theory of excitations of dipolar Bose–Einstein condensate at finite temperature

We present a systematic study of dilute three-dimensional dipolar Bose gas employing a finite temperature perturbation theory (beyond the mean field). We analyze in particular the behavior of the anomalous density, we find that this quantity has a finite value in the limit of weak interactions at both zero and finite temperatures. We show that the presence of the dipole–dipole interaction enhances fluctuations, the second order correlation function and thermodynamic quantities such as the chemical potential, the ground state energy, the compressibility and the superfluid fraction. We identify the validity criterion of the small parameter of the theory for Bose-condensed dipolar gases.