We consider dimerization of 3 He in a dilute solution of 3 He in superfluid 4 He filling narrow channels of a kind typically found in nanoscale porous media. Dimer formation is facilitated by the one dimensional geometry and occurs despite the fact that the interparticle interaction is too weak to lead to a bound state in bulk fluid. At sufficiently low temperatures, dimerization results in the effective "bosonization" of the system: a Bose quantum fluid of (3 He )2 arises in place of the 3 He Fermi component. At sufficiently high temperatures, for which the 3 He impurity quasiparticles form a Maxwell–Boltzmann gas, the thermodynamics is significantly affected by the presence of dimers. In particular, the specific heat and magnetic susceptibility of the 3 He component show a marked deviation from behaviour expected if dimers were absent. Solution of the Schrödinger equation for a smooth cylindrical pore indicates that the binding energy in straight nanoscale channels ought to be of sufficiently high magnitude to make experimental observation feasible. The presence of (3 He )2 dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid 4 He , due to resonant absorption and decay of dimers in the acoustic field. We have calculated the absorption coefficient. Several experiments suggest themselves, utilizing, perhaps, K-L zeolites or carbon nanotubes. If the dimers themselves turn out to be attractive, then quadrumers may appear: it may even be the case that a single 3 He polymer will form over the entire length of the channel.
We consider dimerization of 3 He in a dilute solution of 3 He in superfluid 4 He filling narrow channels of a kind typically found in nanoscale porous media. Dimer formation is facilitated by the one dimensional geometry and occurs despite the fact that the interparticle interaction is too weak to lead to a bound state in bulk fluid. At sufficiently low temperatures, dimerization results in the effective "bosonization" of the system: a Bose quantum fluid of (3 He )2 arises in place of the 3 He Fermi component. At sufficiently high temperatures, for which the 3 He impurity quasiparticles form a Maxwell–Boltzmann gas, the thermodynamics is significantly affected by the presence of dimers. In particular, the specific heat and magnetic susceptibility of the 3 He component show a marked deviation from behaviour expected if dimers were absent. Solution of the Schrödinger equation for a smooth cylindrical pore indicates that the binding energy in straight nanoscale channels ought to be of sufficiently high magnitude to make experimental observation feasible. The presence of (3 He )2 dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid 4 He , due to resonant absorption and decay of dimers in the acoustic field. We have calculated the absorption coefficient. Several experiments suggest themselves, utilizing, perhaps, K-L zeolites or carbon nanotubes. If the dimers themselves turn out to be attractive, then quadrumers may appear: it may even be the case that a single 3 He polymer will form over the entire length of the channel.
We consider dimerization of 3He in a dilute solution of 3He in superfluid 4He filling straight narrow channels that can be found in nanoscale porous media. Dimer formation is facilitated by the restricted geometry and occurs despite the fact that in bulk fluid the interparticle interaction is too weak to lead to a bound state. Dimerization results in the effective ``bosonization'' of the system: a Bose quantum fluid of (3He)2 arises in place of the 3He Fermi component. At high temperatures, when the 3He impurity quasiparticles form a Maxwell-Boltzmann gas, a drastic change in the thermodynamics occurs due to the presence of dimers. The specific heat and magnetic susceptibility of the 3He component, which we calculate at arbitrary degrees of dimerization, show a marked deviation from behavior expected of an undimerized 3He component. We show that the binding energy---which depends on the channel width---is expected to be sufficiently high to make experimental observation feasible. The presence of (3He)2 dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid 4He, due to resonant absorption and decay of dimers in the acoustic field. We have calculated the absorption coefficient. Several experiments suggest themselves, utilizing, perhaps, K-L zeolites or carbon nanotubes. If the dimers themselves turn out to be attractive, then quadrumers may appear: it may even be the case that a single 3He polymer will form over the entire length of the channel.
Low temperature structural and superfluid properties of 4He confined in cylindrical nanopores are theoretically investigated by means of first-principle quantum Monte Carlo (QMC) simulations. We vary the density of 4He inside the pore, as well as the pore diameter and the potential describing the interaction of each 4He atom with the pore surface. Accordingly, the 4He fluid inside the pore forms either a single channel along the axis, or a series of concentric cylindrical shells, with varying degrees of shell overlap. In the limit of pore length greatly exceeding its radius, the 4He fluid always displays markedly one-dimensional behavior, with no ``dimensional crossover'' above some specific pore radius and/or as multiple concentric shells form, in contrast to what was recently claimed by other authors [Phys. Rev. B 101, 104505 (2020)]. Indeed, the predicted robustness of one-dimensional physics suggests that this system may offer a broadly viable pathway to the experimental observation of exotic behavior of, e.g., junctions of interacting Tomonaga-Luttinger liquids, in an appropriately designed network of nanopores.
Low dimensional quantum fluids, where one can probe the effects of enhanced thermal and quantum fluctuations on macroscopic quantum wavefunctions, can be experimentally realized through transverse physical confinement of superfluid helium on scales smaller than the coherence length. Reaching this scale is difficult, requiring confinement in single or multiple pores with nanometer radii. Porous silicates such as MCM-41 have a pore radius larger than the coherence length of 4He, and in this work we systematically explore the possibility of pre-plating pores with different elements to reduce the pore size without localizing the confined superfluid. Through a direct solution of the few-body Schrodinger equation combined with quantum Monte Carlo simulations, we explore the behavior of helium confined inside cylindrical nanopores for a range of pre-plating elements, including rare gases and alkali metals. For rare gases, we find that helium remains strongly attracted to the pore walls and any atoms in the core form an incompressible liquid. For alkali metals such as Cs, weak interactions between helium and the pre-plating material prevent localization near the walls and enable delocalization in the pore center. Our results extend previous results for helium wetting on flat two dimensional coated substrates to the curved geometry inside nanopores, and demonstrate that alkali pre-plated nanopores may enable a tunable one-dimensional confined quantum liquid of helium.
We study the system of a dilute gas of fermions in 3-dimensions, with attractive interactions tuned to the unitarity point, using the non-perturbative Restricted Path Integral Monte Carlo (R-PIMC) method. The pairing and superfluid properties of this system are calculated at finite temperature. The total energy at very low temperature from our results agrees closely with that of previous ground-state Quantum Monte Carlo calculations. We identify the temperature T � � 0.70ǫF below which pairing correlations develop, and estimate the critical temperature for the superfluid transition Tc � 0.25ǫF from a finite size scaling analysis of the superfluid density. PACS numbers: The recent experiments, starting with generating a degenerate gas of cold atoms[3], the use of Feshbach resonance to tune the effective interaction between the fermions[4, 5], the measurements of the gap to identify a pairing scale[6] and the measurements of vortices[7] to identify the superfluid state, have all given an impetus to the study of superfluidity in the BCS-BEC crossover regime. The nature of superconductivity or superfluidity in a many-particle system with an increasing pairing attraction was shown [1, 2] to interpolate smoothly between the BCS regime for weak attraction between the fermions, and the Bose-Einstein condensation (BEC) regime for strong coupling. In the weak coupling regime, the Cooper pair size is much larger than the interparticle spacing, and the simultaneous pairing and condensation of fermions is well described by the BCS theory. In the strong coupling regime, fermions form strongly bound bosonic molecules at a pairing temperature scale T ∗ that is considerably higher than the BEC temperature Tc. In a two species system of fermions with an attractive interaction between them, the unitary point is defined by the divergence of the zero energy s-channel scattering length, as, for two particles in free space. The unitary point is interesting since it describes a strongly correlated system with universal properties[8]. In general, there are two length scales that define the system: the interparticle spacing ∝ n −1/3 , and the scattering length as which contains information about the interaction potential. At the unitary point however, since as diverges, all the properties of the system are described by a single length scale k −1
This work studies zero-temperature Fermi gases with short-ranged and attractive interactions with focus on the dimensionality aspects by confining the system from three to two dimensions. Interacting Fermi gases are superfluids characterized as being strongly correlated if the scattering length is much larger than the other scales present. In the many-body context, this category of systems requires a careful treatment since mean-field approaches are not expected to hold under the conditions which define the strong pairing. For this reason, we employ quantum Monte Carlo methods to study the dimensionality effects in two-component Fermi gases in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensate (BCS-BEC) crossover. To be able to investigate such aspects, we consider a three-dimensional gas with periodic boundary conditions in the xy plane and a confining potential in the z direction capable of reducing the dimensionality of the system, which defines a dimensional BCS-BEC crossover. We calculate the equation of state as the energy per particle as a function of the dimensionality and as a function of the interaction parameter, which are characterized by the oscillator length in the z direction and the scattering length respectively. The greater confinement in the system lowers the interparticle distances, which increases the effects of the attractive interactions between antiparallel-spin fermions.We also calculate the density profile in the z direction over the crossover for different confinements and different interaction parameters to quantify their influence on the spatial distribution of the particles. This study connects the perspectives between theoretical and experimental works in low-dimensional ultracold Fermi gases by utilizing an approach that is similar to what it is realized in modern experiments.