Phasic potentials (PSPs) occur at preferred phases of cerebellar δ and hippocampal theta oscillations during REM. A, We observed PSPs in the cerebellar LFP recordings during REM (indicated by purple dots), which occurred preferentially during up phase of the δ oscillations. Moreover, hippocampal theta frequency was transiently accelerated during the up phase of the cerebellar δ oscillations. B, PSPs were found in all cerebellar recording sites and all mice. Averaged waveforms across animals (Lob II/III, n = 11; Lob VI, n = 15; Crus I, n = 11). C, Cross-correlograms between the PSPs detected at a given cerebellar region and those recorded in the others. All cross-correlograms show a peak with ≤50 ms lag, suggesting that most of the PSPs co-occurred at the three cerebellar regions near simultaneously. D, PSPs were observed during non-REM and REM sleep; however, the density of these events was significantly higher during REM (non-REM density = 0.1152 ± 0.012 PSPs/s; REM density = 0.4973 ± 0.050 PSPs/s; Wilcoxon test, p < 0.0001). E, The distributions of the interevent intervals (IEIs) were significantly different between non-REM and REM epochs (two-sample Kolmogorov–Smirnov test, p < 0.0001). During REM, PSPs were preferentially concentrated as clusters (IEIs < 1 s). F, PSPs recorded at all cerebellar regions were phase-locked to the local δ oscillations during REM. Top panels, The individual vectors of the phase-locking for each mouse (gray arrows) and the average vector across all mice (color-coded; resultant vector angle: Crus I = 342.97°, Lob II = 343.05°, Lob VI = 338.67°; resultant vector length: Crus I = 0.34, Lob II = 0.28, Lob VI = 0.41). Bottom panels, The normalized count of PSPs recorded at the different phases of δ oscillations in all mice for each cerebellar region. G, Fraction of mice with significant phase-locking (significant phase-locking was found in Crus I, 10/11 mice; Lob II/III, 11/11 mice; Lob VI 15/15 mice). H, The level of the phase-locking did not differ across cerebellar regions (one-way ANOVA, p = 0.0932). I-K, Same as for F-H, but here calculating phase-locking of PSPs detected in the cerebellum to ongoing hippocampal theta oscillations. I, Top row, Lob II/III Rayleigh's test, p < 0.001; Lob VI Rayleigh's test, p < 0.001; Crus I Rayleigh's test, p < 0.001. J, Fraction of mice with significant phase-locking of PSPS to hippocampal theta (significant phase-locking was found in Crus I, 8/11 mice; Lob II/III, 7/11 mice; Lob VI 13/15 mice). K, The level of the phase-locking to hippocampal theta did not differ across cerebellar regions. For detailed statistical comparisons, see Extended Data Figure 2-1. ***p < 0.001.