a Schematic of optogenetic strategy to increase frequency-specific functional interactions between the BLA and mPFC. b Example images showing ChR2-mCherry expression, with optical fiber and electrode placement in mPFC and BLA. Targeting was similarly confirmed by histological analysis in all 11 mice; see Methods section for detail. Scale bar: 300 µm. c, d Representative cross-power spectrograms illustrating differential effects of 4 Hz in- and anti-phase optical stimulation in the conditioned context (c; fear+ext memory state) and unconditioned novel context (d; no-memory state). e Averaged cross-power spectra comparing effects of in-phase and anti-phase 4 Hz stimulation to no-stimulation baseline during fear+extinction memory and no-memory states (n = 8 mice). f Quantification of the cross-power spectra from e. 4 Hz in-phase stimulation increases the 4:8 Hz cross-power ratio compared to the no-stimulation baseline, whereas 4 Hz anti-phase stimulation does not. This effect is absent in a context where the mouse has no fear memory (two-way RM ANOVA: trial F(1,7) = 34.12, P = 0.0006, stimulation F(2,14) = 7.80, P = 0.0053, trial × stimulation F(2,14) = 7.46, P = 0.0062, n = 8 mice. Holm-Sidak’s multiple comparisons test; fear+ext memory state: no light vs. 4 Hz anti-phase: t(14) = 2.01, P = 0.064; no light vs. 4 Hz in-phase t(14) = 3.39, P = 0.0087. No memory state: no light vs. 4 Hz anti-phase: t(14) = 0.33, P = 0.94; no light vs. 4 Hz in-phase t(14) = 0.29, P = 0.94). g 4 Hz in-phase stimulation increases the conditioned freezing response compared to the no-stimulation baseline, whereas 4 Hz anti-phase stimulation does not. This effect is absent in a context where the mouse has no fear memory (two-way repeated measures ANOVA: trial F(1,10) = 15.43, P = 0.0028, stimulation F(2,20) = 10.18, P = 0.0009, trial × stimulation F(2,20) = 5.28, P = 0.014, n = 11 mice. Holm-Sidak’s multiple comparisons test; fear+ext memory state: no light vs. 4 Hz anti-phase: t(20) = 0.55, P = 0.59; no light vs. 4 Hz in-phase t(20) = 5.20, P < 0.0001. No memory state: no light vs. 4 Hz anti-phase: t(20) = 0.0088, P = 0.99; no light vs. 4 Hz in-phase t(20) = 0.97, P = 0.71). All error bars and shaded area: mean ± SEM.