Careful measurements down to very low temperatures (1 mK) of the quantum Hall plateau-to-plateau transition have been carried out for long-range Columbic disordered two-dimensional electron systems embedded in Al_xGa_1-xAs-Al_0.32Ga_0.68 As heterostructures with x=0 and 0.21%. A cross-over behavior is observed form the high temperature (1.2k) non-universal scaling regime to a low temperature, universal scaling regime, with the temperature exponent k ranging from 0.58 to 0.42 respectively. The crossover temperature increases with increasing x from 120 mK for x=0% to 250 mK for x=0.21%.

Temperature dependence of the dR_xy/dB for the transverse Hall resistance R_xy for  applied magnetic fields B. k is the fitted exponent.

NMR studies have been carried out from 1.2 to 0.010 K of ³He impurities in solid ⁴He for ³He concentrations ranging from 20 to 2000 ppm . Sharp changes in both the spin-spin relaxation times (T₂) and the signal amplitudes are observed at low temperatures (from ~0.08 to 0.2 K) corresponding to phase separation with the formation of liquid nanodroplets of ³He at low temperatures. A novel low noise preamplifier was developed that could operate at low temperatures and in high magnetic fields and thus deployed near the NMR cell in order to observe the weak signals at very low concentrations.

AC magnetic susceptibility measurements at very low temperatures (to 1 mK) of the organic compound NiCl₂-4SC(NH₂)₂ have been used to determine the lower and upper critical fields, H_c1 and H_c2, respectively, for the field- induced Bose-Einstein condensation. The transitions were determined from measurements of the for temperatures down to 1 mK and for fields from 1 to 13 T. The key parameter is the exponent for the temperature dependence of H_c1 given by H_c1(T)-H_c1(0) =aT^ which is predicted to be 3/2 for a 3D BEC condensation.

We investigate the influence of strong magnetic fields on superfluid ³He in high porosity aerogel. As in the pure bulk, it is expected that strong magnetic fields will split the superfluid transition into two transitions, namely the normal Fermi liquid to the superfluid A₁-phase and the A₁-phase to the A₂-phase. We will investigate the field dependence of the A₁-A₂ splitting for the full pressure range and magnetic fields up to 15 Tesla. The A₁-phase is unique in nature since it is a fully spin polarized superfluid. The existence of such a polarized superfluid is expected on the basis of particle-hole asymmetry but has not yet been observed in the presence of strong quasiparticle scattering. We propose to determine this splitting and its dependence on pressure. The measurements at low pressures near the critical pressure have a potential to reveal astounding phenomena related to the quantum phase transition. Since the splitting is expected to be smaller than for bulk liquid (where it is ~60 mK/Tesla at melting pressure) and due to the low superfluid transition temperatures (< 2mK), this project requires the ability to produce magnetic fields larger than 10 Tesla with a nuclear demagnetization stage. The High B/T Facility, equipped with a 15 Tesla superconducting magnet and a PrNi5 nuclear demagnetization stage is a perfect platform and is the only place for this proposed research in this country. Simultaneous measurements of high frequency shear impedance of the pure and dirty superfluids will be performed. This research will provide important and urgent information on the superfluid phases in aerogel and make a significant contribution in completing the phase diagram of this system. Technically, the high frequency shear impedance measurement will prove as a valuable tool to study quantum fluids in high magnetic fields since it does not require field dependent tuning and is sensitive to all the transition features including the first order A-B transition. This research also promotes the development of dielectric constant thermometers for use at high magnetic fields and low temperatures.

An important effect predicted by Fermi-liquid theory is the field-induced relaxation of transverse spin currents. Unlike all other transport coefficients, the transverse spin diffusion should tend to a finite limit at low temperatures in high magnetic fields. The NMR spin echoes technique was used to measure the transverse diffusion to test for the predicted field dependence in dilute ³He-⁴He mixtures under extremely high B/T conditions, B = 14.75 T and T ≥ 1.73 mK. The ³He concentration x₃ was adjusted close to 3.8% at which the spin-rotation parameter μM₀ vanishes. In this way the transverse diffusion coefficient D_┴ and longitudinal spin coefficient D_║ were measured while keeping μM₀ < 1. It is found that the temperature dependence of D_┴ deviates strongly from 1/T², with anisotropy temperature T = 4.26 mK. This value is close to the theoretical prediction for dilute solution and suggests that spin current relaxation remains finite as temperature tends to zero. This is the first practice of NMR at such low temperatures and high magnetic fields.