We have studied the ground state properties of two-dimensional 3 He -4 He mixtures at zero temperature. 3 He atoms with opposite spins form loosely bound dimers in free space and in low concentration mixtures with 4 He . The binding energy of the dimer ranges from milli-Kelvins near the saturation density to micro-Kelvins at the solidification density. The radius of such a weakly bound dimer is tens of Ångstöms. We also calculate the phase diagram of the mixture. The maximum solubility of 3 He ≈7% is determined by comparing chemical potentials in the pure and mixed fluids. The upper stability limit of the super-saturated mixture is obtained from the second derivative of the enthalpy. It becomes negative at the concentration 10-15% depending of the pressure, indicating a softening of the concentration-fluctuation mode. We also find an indication of the phase transition from the dimerized to atomic mixture.
We have studied the ground state properties of two-dimensional 3 He -4 He mixtures at zero temperature. 3 He atoms with opposite spins form loosely bound dimers in free space and in low concentration mixtures with 4 He . The binding energy of the dimer ranges from milli-Kelvins near the saturation density to micro-Kelvins at the solidification density. The radius of such a weakly bound dimer is tens of Ångstöms. We also calculate the phase diagram of the mixture. The maximum solubility of 3 He ≈7% is determined by comparing chemical potentials in the pure and mixed fluids. The upper stability limit of the super-saturated mixture is obtained from the second derivative of the enthalpy. It becomes negative at the concentration 10-15% depending of the pressure, indicating a softening of the concentration-fluctuation mode. We also find an indication of the phase transition from the dimerized to atomic mixture.
Ground-state properties of two-dimensional ${}^{3}\mathrm{He}\ensuremath{-}{}^{4}\mathrm{He}$ mixtures are studied at zero temperature. A general argument based on the long-ranged attraction of the phonon exchange is given for the existence of 3He dimers in low-concentration mixtures with 4He. The binding energy of dimers ranges from milli- to microkelvins with increasing 4He density. By comparing the 3He impurity chemical potential in 4He with the one in pure 3He we conclude that at finite pressures 3He dimers form a mixture with 4He with a maximum solubility of $\ensuremath{\approx}3%$.
In this paper a theoretical study of a possible phase transition in dilute 3 He-He(II) mixtures is presented using the Galitskii-Migdal-Feynman formalism.The effective scattering length is calculated from the Galitskii-Migdal-Feynman T -matrix, which is essentially the effective scattering amplitude dependent on the medium.It is found that at very low 3 He concentrations the s-wave effective scattering length for 3 He-He(II) varies discontinuously from positive to negative values at some critical concentration.This indicates a crossover from a regime with dimers to another with the Cooper pairs.The binding energy of the weakly-bound dimers 3 He2 is computed.The effective p-wave scattering lengths are calculated and compared to the effective s-wave scattering lengths at low and high concentrations.It is found that p-scattering has an important effect on the instability of these mixtures at concentrations x > 1%.Finally, the transport coefficients are computed and compared to the theoretical predictions of Fu and Pethick and the experimental results of König and Pobell.
When cooled to almost zero temperature, helium offers a very versatile subject for the experimental study of quantum matter. The two stable isotopes of helium, He-3, and He-4, and their mixtures, are the only macroscopic condensed matter systems that do not solidify at normal pressure even upon cooling to the absolute zero temperature. The cause for this is the large zero point energy compared to the interatomic bonds of the light noble gas. At extremely low temperatures the properties of the chemically identical isotopes differ considerably due to differences in quantum statistics. An especially interesting system is the dilute phase of the mixture of the isotopes, in which He-3 atoms form a rarefied fermi gas, whose properties can be continuously adjusted by varying the pressure and concentration, while the bosonic He-4 component remains in the background in the superfluid state. Also the He-3 component of the dilute mixture has been theoretically predicted to undergo a superfluid transition at very low temperature. \nThis thesis presents new methods for the experimental study of helium mixtures at very low temperatures, as well as results on measurements on the properties of helium fluids at previously unstudied temperature and pressure range. Adiabatic melting is a cooling method in which the cooling, based on the mixing of helium isotopes, is utilized in conditions where the heat capacity of the refrigerated system is falling fast, permitting a very low final temperature. In the first millikelvin-range trial of the new method, the mixture was cooled to 300 microkelvin temperature. This is not a particularly outstanding result compared to the traditional cooling methods, but the experiment was still encouraging as the limitations were found to be technical and no fundamental obstacles for improvements were discovered. The properties of the helium sample were studied by a sensitive pressure gauge, and by small immersed mechanical oscillators. Using these, the saturation solubility of the mixture was determined over the widest possible pressure range from zero to the melting pressure of the mixture. In addition the osmotic pressure of the mixture for several concentrations at the melting pressure was measured at millikelvin-range temperatures. Traditional vibrating wires and quartz tuning forks were used as the oscillators. Quartz tuning forks were found to be feasible sensors, though acoustic phenomena related to the high resonance frequency complicated the response.
This thesis describes experimental work on dilute mixtures of ³He in 4He, mainly at millikelvin temperatures. The isotopic helium mixture has the unique property of remaining a miscible liquid down to the absolute zero temperature. In the mK regime, it consists of two very different components: perfectly superfluid 4He, and a weakly interacting degenerate Fermi liquid of ³He, predicted by theory to undergo transition to the superfluid state at an extremely low temperature. To discover that transition, new ways of cooling helium mixtures need to be developed, as it is not likely that the conventional method of nuclear demagnetization of copper can be improved to reach helium temperatures notably below the temperatures of order 0.1 mK attained so far. \n Adiabatic melting of 4He in the presence of liquid ³He is probably the most promising method of cooling helium mixtures to microkelvin temperatures. It produces helium mixture colder than the initial temperature as a direct consequence of the mixing of the isotopes. The starting configuration is attainable by pressurizing liquid helium mixture to its solidification pressure at a temperature below some tens of mK, as only 4He then enters the solid phase. This thesis describes an experiment in which the method of adiabatic melting was, for the first time, realized at sub-millikelvin temperatures, where the superfluidity of the pure ³He phase enables, in principle, a drastic decrease of temperature. In the experiments, cooling from initial temperatures between 0.3 and 0.9 mK was detected, temperature reduction remaining below a factor of two for recognized reasons of a technical rather than fundamental nature. \n A capacitive differential pressure transducer, constructed for the experiment, was used for high accuracy measurements of the temperature dependence of the melting pressure of helium mixtures with several ³He concentrations. The melting pressure is suitable for thermometry and carries information on the interactions of ³He particles in the mixture. Also, the response of a quartz tuning fork immersed in helium was studied. Its sensitivity to the properties of the surrounding fluid was utilized to determine the saturation concentration of dilute ³He across the entire accessible pressure range. The tuning fork was found to exhibit a complex pattern of anomalies attributed to resonant modes of second sound, or concentration waves, inside its cylindrical container.
It has been suggested recently that 4 He can be prepared and studied as a quasi one-dimensional quantum fluid. We calculate the static and dynamic properties of one-dimensional 4 He using variational methods based upon the Jastrow-Feenberg wavefunction and its extension to dynamic systems with time-dependent, correlated wavefunctions. The zero temperature equation of state shows that in one-dimension 4 He is just barely self-bound with a binding energy of 0.002 K at a density of 0.036 A -1 . We also calculate the excitation spectrum including corrections that contain multi-phonon processes and study the density dependence of the roton feature as well as the static response function. In addition we demonstrate the presence of strong anomalous dispersion in the phonon regime. Finally, we introduce a 3 He impurity and calculate the zero concentration chemical potential as a function of He linear density. We also compute the 3 He- 3 He effective interaction in the 4 He background and compute the energy of dimerization.
We study the finite temperature-density phase diagram of an attractive fermionic system that supports two-body (dimer) and three-body (trimer) bound states in free space. Using interactions characteristic for nuclear systems, we obtain the critical temperature Tc2 for the superfluid phase transition and the limiting temperature Tc3 for the extinction of trimers. The phase diagram features a Cooper-pair condensate in the high-density, low-temperature domain which, with decreasing density, crosses over to a Bose condensate of strongly bound dimers. The high-temperature, low-density domain is populated by trimers whose binding energy decreases toward the density-temperature domain occupied by the superfluid and vanishes at a critical temperature Tc3>Tc2.