Figure 1

(a) $\Delta f(T)$ in the film states for various coverages, from $n=20.4$ to $33.0\mu \mathrm{m}\mathrm{o}\mathrm{l}/{\mathrm{m}}^2$. (b) $f(T)$ in the pressurized states. To clarify the superfluid transitions, the frequencies are shifted so as to collapse onto a single curve between one and 1.5 K. The ordinate is valid for the data of 0.074 MPa. Arrows indicate $T_c$’s. (c) $\Delta f(T)$ for various pressures above $P_f$. The “$n$-shape” anomalies are caused by resonant couplings to superfluid fourth sound.Reuse & Permissions

Figure 2

Estimation of the cell pressure above $P_f$. Solid circles: $f$ at 2.2 K. Open circles: extrapolation of $f(T>T_c)$ to 10 mK. Assuming a parallelism at $P>P_f$, $f(P)$ is obtained as the dashed line. Here, ${}^4\mathrm{H}\mathrm{e}$ is an imaginarily normal liquid in the pores, while the interspace is empty, as shown in the upper cross-sectional illustration. Adding the contribution of the bulk solid (the lower illustration), the $f(P)$ for the background frequency at ten mK is obtained as the red line. The inset shows $f(T)$ for various $P_{\mathrm{i}\mathrm{n}\mathrm{i}}$’s. Arrows: $T_c$. Dashed curves: the empty-cell backgrounds. Colored circles in the main panel and inset show the corresponding frequencies.Reuse & Permissions

Figure 3

(a) $P\mathrm{\text{−}}T$ phase diagram. The yellow area shows the superfluid phase in Gelsil. Phase boundaries of bulk ${}^4\mathrm{H}\mathrm{e}$ and ${}^4\mathrm{H}\mathrm{e}$ in a porous Vycor glass [8] are also shown. (b) Phase diagram for the film states.Reuse & Permissions

Figure 4

Estimated $\Delta f$ at 0 K and $T_c$ as a function of $P$.Reuse & Permissions