The Breakdown of Superfluidity in Liquid 4He VI. Macroscopic Quantum Tunnelling by Vortices in Isotopically Pure He II

Measurements are reported of the rate v at which negative ions nucleate quantized vortices in isotopically pure superfluid ⁴He for electric fields E, temperatures T and pressures P within the range 10³<= E <= 10⁶ V m^-1, 75 <= T <= 500 mK, 12 <= P <= 23 bar (= 2.3 MPa). The form of ν (E, T) differs in unexpected ways from that observed in earlier work at higher P, exhibiting: a pronounced dip in ν (T) at ca. 0.3 K whose depth and precise position depends on E and P; an exponential increase in ν (T) at higher T, with an activation energy considerably smaller than the roton energy gap; and distinct structure in ν (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 ν 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 ν (T) are ascribed to phonon damping of the tunnelling process, and the kinks observed in some of the low-temperature ν (E) curves are attributed to tunnelling of the system into the first excited state of the nascent vortex loop.