title: Critical flow and dissipation in a quasi-one-dimensional superfluid.
abstract: 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.
authors.affiliation: Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada.
authors.forename: Pierre-François
authors.initials: PF
authors.lastname: Duc
authors.affiliation: Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada.
authors.forename: Michel
authors.initials: M
authors.lastname: Savard
authors.affiliation: Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada.
authors.forename: Matei
authors.initials: M
authors.lastname: Petrescu
authors.affiliation: Institut für Theoretische Physik, Universität Leipzig, D-04103 Leipzig, Germany.
authors.forename: Bernd
authors.initials: B
authors.lastname: Rosenow
authors.affiliation: Department of Physics, University of Vermont, Burlington, VT 05405, USA.
authors.forename: Adrian
authors.initials: A
authors.lastname: Del Maestro
authors.affiliation: Department of Physics, McGill University, Montreal, Quebec H3A 2T8, Canada. ; Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada.
authors.forename: Guillaume
authors.initials: G
authors.lastname: Gervais
keywords: dissipation; luttinger liquids; mass flow; quantum fluids; strongly-correlated systems; superfluidity