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

a Numerically simulated wave transfer efficiencies \({\left|{S}_{{AC}}\right|}^{2}\) and \({\left|{S}_{{CB}}\right|}^{2}\) as a function of \(\varDelta t\) and \({\widetilde{\kappa }}_{0}\). The black dashed line denotes the parameter space used in (b). b Simulated (curves) and measured (circles) transfer efficiencies \({\left|{S}_{{BC}}\right|}^{2}\) and \({\left|{S}_{{AB}}\right|}^{2}\) with \({\widetilde{\kappa }}_{0}=6.1{{{{{\rm{Hz}}}}}}\). The inset shows the sound circulations with \(\Delta t=90{{{{{\rm{ms}}}}}}\), 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 \(t \, > \, 0.45{{{{{\rm{s}}}}}}\), 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.