The breakdown of superfluidity in liquid 4 HE VI. Macroscopic quantum tunnelling by vortices in isotopically pure He II

Abstract

Measurements are reported of the rate v at which negative ions nucleate quantized vortices in isotopically pure superfluid ⁴ He for electric fields E , temperatures T and pressures P within the range 10 ³ ⩽ E ⩽ 10 ⁶ V m ^-1 , 75 ⩽ T ⩽ 500 mK, 12 ⩽ P ⩽ 23 bar (= 2.3 MPa). The form of v ( E, T ) differs in unexpected ways from that observed in earlier work at higher P , exhibiting: a pronounced dip in v ( T ) at ca . 0.3 K whose depth and precise position depends on E and P ; an exponential increase in v ( T ) at higher T , with an activation energy considerably smaller than the roton energy gap; and distinct structure in v ( E ). The experimental data are discussed and analysed in terms of the macroscopic quantum tunnelling model proposed by Muirhead et al . ( Phil. Trans. R. Soc. Lond . A 311, 433 (1984)). The relatively small barrier heights of ca . 2—3 K deduced from the data on this basis are construed as confirmation that the initial vortex is a loop rather than an encircling ring. The temperature dependence of v at low pressures is interpreted in terms of a phonon-driven vortex nucleation mechanism, and values for its cross section are extracted from the data. The minima in v ( T ) are ascribed to phonon damping of the tunnelling process, and the kinks observed in some of the low-temperature v ( E ) curves are attributed to tunnelling of the system into the first excited state of the nascent vortex loop.