Fig. 3: CEP-enhanced quantum coherence.

a, b SE spectrum versus QE-cavity detuning of hybrid CEP cavity for \(\phi =3\pi /4\) and the usual hybrid cavity without CEP, respectively. The white dashed lines trace the eigenenergies of \({M}_{0}\)[Eq. (6)]. c, d SE spectrum and the corresponding temporal dynamics, respectively. The circles in (c) plot the numerical results of SE spectrum calculated by the quantum master equation [Eqs. (1)–(5)] using QuTip⁸³, while the lines represent the analytical results of emission spectrum based on the quantum regression theorem using Eq. (6). The parameters are \({\gamma }_{0}=3\mu {{{{{\rm{eV}}}}}}\), \({g}_{1}=-24{{{{{\rm{meV}}}}}}\) and \({Q}_{c}={10}^{3}\). e SE spectrum in the strong-coupling regime with (solid line) and without CEP (dashed line). The pink solid line indicates the SE spectrum with \(\phi ={\phi }^{{{{{{\rm{opt}}}}}}}\) corresponding to the maximal LDOS, while the blue dashed line shows the SE spectrum of usual hybrid cavity without CEP. The inset shows the normalized LDOS of hybrid CEP cavity as the function of frequency and \(\phi\), where the horizontal dashed line indicates \({\phi }^{{{{{{\rm{opt}}}}}}}\). The parameters are \({g}_{1}=-20{{{{{\rm{meV}}}}}}\), \({g}_{a}=40{{{{{\rm{meV}}}}}}\) and \({Q}_{c}={10}^{4}\). f Shows the corresponding temporal dynamics of QE. In (d) and (f), the circles represent the results obtained by numerically calculating the quantum master equation using QuTip⁸³ while the lines show the results of Fourier transforming the SE spectrum based on the analytical spectral density [Eqs. (9)–(11)]. Parameters not mentioned are the same as Fig. 1c.