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Dressed cavity modes are observed from the cavity transmission of a weak probe beam. Lasing occurs near the dressed cavity mode {f}_{{rm{c}}}^{{prime} } determined by fitting the transmission peak at δ pr < 0. The observed avoided crossing (dark blue) in zones I and II does not correspond to the one expected for a constant atom number (simulation shown in turquoise). For instance, in zone I, {f}_{{rm{c}}}^{{prime} } changes by <100 kHz over a range of > 3 MHz of f c , which would normally correspond to a change in the dressed cavity frequency of Δ {f}_{{rm{c}}}^{{prime} }=1.3 MHz. This pinning of the cavity frequency is achieved by a self-regulated reduction in the atom number in the cavity as f c changes. In zones III and IV, the atom number is independent of f c .
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