4D-XY superfluid transition and dissipation in ⁴He confined in nanoporous media

⁴He confined in nanoporous Gelsil glass is a unique, strongly correlated Bose system exhibiting quantum phase transition (QPT) by controlling pressure. Previous studies revealed that the QPT occurs with four-dimensional (4D) XY criticality, which appears in the zero-temperature limit of the superfluid density. However, the P-T phase diagram also suggested that the 4D XY nature appears at finite temperatures. Here, we have determined the critical exponent of the superfluid density ρ_s of ⁴He in two Gelsil samples that have pore diameter to be about 3 nm, using a newly developed mechanical resonator technique. The critical exponent ζ in the powerlaw fitting ρ_s ∝ |1 − T/T_c|^ζ, where T_c is the superfluid transition temperature, was found to be 1.0 ± 0.1 for all pressures realized in this experiment, 0.1 < P < 2.4 MPa. This value of ζ gives decisive evidence that the finite-temperature superfluid transition belongs to the 4D XY universality class. The emergence of the 4D XY criticality is explained by the existence of many nanoscale superfluid droplets, the so-called localized Bose-Einstein condensates (LBECs), above T_c. Due to the large energy cost for ⁴He atoms to move between the LBECs, the phase of the LBEC order parameters fluctuates not only in spatial (3D) but imaginary time (+1D) dimensions, resulting in the 4D XY criticality by a temperature near T_c. Since the finite size of the system in the imaginary time dimension L_τ is larger than the pore size, the 4D XY critical phenomenon is observed. In the very vicinity of T_c at which the correlation length exceeds L_τ, there may be a crossover from 4D to 3D XY criticality. Below T_c, macroscopic superfluidity grows in the nanopores of Gelsil by the alignment of the phases of the LBEC order parameters. An excess dissipation peak observed below T_c is well explained by this phase-matching process. (author)