Critical flow and dissipation in a quasi-one-dimensional superfluid

• Published in: Science advances Vol. 1; no. 4; p. e1400222
• Main Authors: Duc, Pierre-François, Savard, Michel, Petrescu, Matei, Rosenow, Bernd, Del Maestro, Adrian, Gervais, Guillaume
• Format: Journal Article
• Language: English
• Published: United States American Association for the Advancement of Science 01.05.2015
• Subjects: Quantum Mechanics; SciAdv r-articles; mass flow; strongly-correlated systems; superfluidity; dissipation; luttinger liquids; quantum fluids
• ISSN: 2375-2548; 2375-2548
• DOI: 10.1126/sciadv.1400222

In one of the most celebrated examples of the theory of universal critical phenomena, the phase transition to the superfluid state of (4)He belongs to the same three-dimensional (3D) O(2) universality class as the onset of ferromagnetism in a lattice of classical spins with XY symmetry. Below the transition, the superfluid density ρs and superfluid velocity v s increase as a power law of temperature described by a universal critical exponent that is constrained to be identical by scale invariance. As the dimensionality is reduced toward 1D, it is expected that enhanced thermal and quantum fluctuations preclude long-range order, thereby inhibiting superfluidity. We have measured the flow rate of liquid helium and deduced its superfluid velocity in a capillary flow experiment occurring in single 30-nm-long nanopores with radii ranging down from 20 to 3 nm. As the pore size is reduced toward the 1D limit, we observe the following: (i) a suppression of the pressure dependence of the superfluid velocity; (ii) a temperature dependence of v s that surprisingly can be well-fitted by a power law with a single exponent over a broad range of temperatures; and (iii) decreasing critical velocities as a function of decreasing radius for channel sizes below R ≃ 20 nm, in stark contrast with what is observed in micrometer-sized channels. We interpret these deviations from bulk behavior as signaling the crossover to a quasi-1D state, whereby the size of a critical topological defect is cut off by the channel radius.