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Physical review. B, Condensed matter

Dimerization of 3He in 3He-4He dilute mixtures filling narrow channels

Eugene P. Bashkin, John Wojdylo

Published Sep 1, 2000• 3 citations
Publisher

Abstract

We consider dimerization of ${}^{3}\mathrm{He}$ in a dilute solution of ${}^{3}\mathrm{He}$ in superfluid ${}^{4}\mathrm{He}$ 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 ${(}^{3}\mathrm{He}{)}_{2}$ arises in place of the ${}^{3}\mathrm{He}$ Fermi component. At high temperatures, when the ${}^{3}\mathrm{He}$ 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 ${}^{3}\mathrm{He}$ component, which we calculate at arbitrary degrees of dimerization, show a marked deviation from behavior expected of an undimerized ${}^{3}\mathrm{He}$ 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 ${(}^{3}\mathrm{He}{)}_{2}$ dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid ${}^{4}\mathrm{He},$ 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 ${}^{3}\mathrm{He}$ polymer will form over the entire length of the channel.

DOI
10.1103/physrevb.62.6614

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We consider dimerization of 3He{}^{3}\mathrm{He}3He in a dilute solution of 3He{}^{3}\mathrm{He}3He in superfluid 4He{}^{4}\mathrm{He}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{(}^{3}\mathrm{He}{)}_{2}(3He)2​ arises in place of the 3He{}^{3}\mathrm{He}3He Fermi component. At high temperatures, when the 3He{}^{3}\mathrm{He}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{}^{3}\mathrm{He}3He component, which we calculate at arbitrary degrees of dimerization, show a marked deviation from behavior expected of an undimerized 3He{}^{3}\mathrm{He}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{(}^{3}\mathrm{He}{)}_{2}(3He)2​ dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid 4He,{}^{4}\mathrm{He},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{}^{3}\mathrm{He}3He 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 examine the thermodynamics of a two-dimensional Fermi gas model describing adsorbed 3{}^{3}3Hein a thin superfluid 4{}^{4}4Hefilm. The 3{}^{3}3Hesystem is characterized by both a hydrodynamic effective mass and a set of discrete transverse single-particle states that model the effects of the interaction with the substrate that supports the film. We show that the magnetization steps seen in experiment are a simple manifestation of the T=0KT=0\mathrm{K}T=0K equation of state. We prove that perfectly horizontal magnetization steps rigorously disappear at any finite temperature. We show that the thermal stability of the steps is determined by the larger of $\ensuremath{\Delta}\ensuremath{\epsilon}/2,$ one-half of the level spacing, and ${\ensuremath{\mu}}_{m}{\mathcal{H}}_{0},$ the magnetic energy. We derive the conditions under which there exist points in the phase space (termed invariant points) through which all low-temperature isotherms pass exponentially close. The invariant points appear for magnetization versus 3{}^{3}3Hecoverage, chemical potential versus magnetization, magnetic susceptibility versus coverage, and speed of sound squared versus coverage. We compare our calculated invariant points for the magnetization versus coverage with experiment and find good agreement. We show that there exist small regions of thermodynamic phase space in which the temperature derivative of the pressure is negative. We explain these anomalous regions as the result of 3{}^{3}3Heatoms ``spilling over'' from a full Fermi sea to an empty Fermi sea upon the application of a small increase in temperature. Through a Maxwell relation, this behavior can also be seen as in the appearance of a local peak in low-temperature entropy isotherms versus coverage. In the limit of a two state model, we calculate the specific heat and show that a Schottky peak develops in the low 3{}^{3}3Hecoverage limit. We calculate the magnetic susceptibility and predict that it should exhibit a steplike structure versus 3{}^{3}3Hecoverage similar to that of the magnetization. We calculate the speed of sound and show that it should exhibit zero-temperature discontinuities at the points where new Fermi seas begin to be occupied. Both the steplike structure in the magnetic susceptibility and the discontinuity-type structure in the speed of sound persist to temperatures on the order of 100 mK, and are analyzed in terms of invariant points in their respective phase diagrams. We show explicitly that, in the Fermi gas limit, the zero-field magnetic susceptibility is simply proportional to the isothermal compressibility.
The last five years have seen a burst of activity leading to the current view that 3He atoms dissolved in superfluid liquid 4He show remarkable resemblance to a weakly-interacting Fermi gas. This is because the solvent 4He, having vanishingly small entropy, specific heat, viscosity and magnetic susceptibility, behaves almost as if it were a massive vacuum, in which 3He atoms float. So at last a real Fermi ‘gas’ is available and can readily be cooled to temperatures well below its Fermi degeneracy temperature. This model of solute 3He, with its weaknesses and strengths, is the basis of this article.
Mixture of the two stable helium isotopes, 3He and 4He, is a versatile system to study at low temperatures. It is a mixture of two fundamentally different quantum mechanical particles: fermions and bosons. Bosonic 4He component of the dilute mixture is known to become superfluid at about 2 K, while superfluidity of the dilute fermionic 3He component has not yet been observed. The transition is anticipated to occur at temperatures below 0.0001 K (i.e. 100 uK). To reach such ultra-low temperatures, new cooling methods need to be developed, one of which is the main subject of this thesis. Current, well-established, cooling methods rely on external cooling, where a metallic coolant is used to decrease temperature in a liquid helium sample. Their performance is limited by rapidly increasing thermal boundary resistance. Our novel adiabatic melting method relies on internal cooling process, where both the coolant and the sample are same helium. First, we create a phase-separation in the mixture by increasing its pressure to about 25 times the atmospheric pressure. This solidifies the 4He component, and we ideally end up with a system of pure solid 4He and pure liquid 3He. The phase-separated system is then precooled by conventional methods, after which the solid is melted. This allows 4He to mix with 3He again in heat absorbing process, resulting in a saturated mixture with about 8% molar 3He concentration. In theory, the mixing can reduce temperature by more than a factor 1000, but external heat leaks and imperfect phase-separation reduced this to the factor 5-7 in this work. We study the performance of the melting method under various conditions, such as different melting rates, various total amount of 3He, and alternate configurations of the setup. We also developed a computational model of the system, which was needed to evaluate the lowest achieved temperatures, as the mechanical oscillators used for thermometry had already become insensitive. For it, we studied the thermal coupling parameters of our system, including thermal boundary resistances and 3He thermal conductivity. The lowest resolved temperature was (90 +- 20) uK, still above the superfluid transition of the 3He component of the mixture. We also present suggestions for future improvements for the setup.
The ground-state properties of two-component bosonic mixtures in a one-dimensional optical lattice are studied both from few- and many-body perspectives. We rely directly on a microscopic Hamiltonian with attractive intercomponent and repulsive intracomponent interactions to demonstrate the formation of a quantum liquid. We reveal that its formation and stability can be interpreted in terms of finite-range interactions between dimers. We derive an effective model of composite bosons (dimers) which correctly captures both the few- and many-body properties and validate it against exact results obtained by the density matrix renormalization group method for the full Hamiltonian. The threshold for the formation of the liquid coincides with the appearance of a bound state in the dimer-dimer problem and possesses a universality in terms of the two-body parameters of the dimer-dimer interaction, namely, scattering length and effective range. For sufficiently strong effective dimer-dimer repulsion we observe fermionization of the dimers which form an effective Tonks-Girardeau state and identify conditions for the formation of a solitonic solution. Our predictions are relevant to experiments with dipolar atoms and two-component mixtures.