Fig. 4. A frequency-converting circulator based on temporal adiabatic passage.

a Numerically simulated wave transfer efficiencies ${∣S_{AC}∣}^2$ and ${∣S_{CB}∣}^2$ as a function of $\Delta t$ and ${\tilde{\kappa }}_0$. The black dashed line denotes the parameter space used in (b). b Simulated (curves) and measured (circles) transfer efficiencies ${∣S_{BC}∣}^2$ and ${∣S_{AB}∣}^2$ with ${\tilde{\kappa }}_0=6.1\mathrm{Hz}$. The inset shows the sound circulations with $\mathrm{\Delta }t=90\mathrm{ms}$, which are given in the following c–f together with c-d in Fig. 3. The gradient colors denote the one-way frequency conversions. c Recorded sound waves in three cavities. Cavity C is initially excited at $f_C$ for $t<0$, as denoted by the white arrow. d Fourier spectra of the transient pressures in (c) with $t>0.45\mathrm{s}$, showing the frequency conversion effect from $f_C$ to $f_B$. e and f are similar as (c) and (d) but with cavity B being initially excited at $f_B$, showing the wave transfer from cavity B to A with frequency conversion from $f_B$ to $f_A$. Source data are provided as a Source Data file.