Observation of superfluidity in two- and one-dimensions

Even though there is no long-range-ordered state of a superfluid in dimensions lower than the three-dimension (3D) such as bulk ⁴He liquid, superfluidity has been observed for flat ⁴He films in 2D and recently for nanotubes of ⁴He in 1D by the torsional oscillator method. In the 2D state, in addition to the superfluid below the 2D Kosterlitz–Thouless transition temperature T_KT, superfluidity is also observed in a normal fluid state above T_KT, which depends strongly on the measurement frequency and the system size. In the 1D state of the nanotubes, superfluidity is directly observed as a frequency shift in the torsional oscillator experiment. Some calculations suggest a superfluidity of a 1D Bose fluid with a finite length, where thermal excitations of 2π–phase winding play the main role for superfluid onset of each tube. Dynamics of the 1D superfluidity is also suggested by observing the dissipation in the torsional oscillator experiment.