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_sof 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_sα |1 - T=T_c|^ζ, where T_cis 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 Tc. 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_tis larger than the pore size, the 4D XY critical phenomenon is observed. In the very vicinity of T_cat which the correlation length exceeds L_t, 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 Tc is well explained by this phase-matching process.