Frequency-resolved N-photon correlations in the ultra-strong coupling regime

Abstract

Frequency-resolved photon emission is central to applications from quantum information encoding to high-resolution spectroscopy, and then studying their correlations is therefore essential for revealing the underlying emission pathways and multiphoton statistics. Here, we investigate frequency-resolved N-photon correlations in an ultrastrongly coupled cavity QED system where a qubit interacts with a single-mode cavity. Owing to counter-rotating interactions, the eigenstates and energy spectrum are strongly modified, giving rise to rich spectral and statistical properties in the emitted frequency-resolved photons. Through frequency-selective detection, we reveal pronounced multiphoton antibunching, as well as multiphoton bunching originating from cascade transitions among dressed eigenstates. In particular, we show that parity symmetry plays a decisive role in shaping these correlations. The symmetry-breaking opens additional transition channels and dramatically enhances the generation of correlated photon pairs and even photon triplets of different frequencies. Our work extends frequency-resolved correlations to the ultra-strong coupling regime and demonstrates their potential as a sensitive probe of symmetry in light-matter interaction systems.

Figures (4)

• Figure 1: (a) Schematic setup of the cavity QED system: a system qubit ultrastrongly interacts with a cavity mode with strength $g$, and a sensor qubit is weakly couples to the cavity with a vanishing coupling strength $\varepsilon$. The symbols $\kappa$ and $\gamma$ ($\gamma_s$) represent the decay rates of the cavity and the system qubit (sensor qubit), respectively. (b),(c) Energy Spectrum of $\widetilde{H}_{\text{QR}}$ as a function of the coupling strength $g$ for (b) $\theta=\pi/2$ and (c) $\theta=\pi/6$. In panel (b), the solid and dashed lines indicate energy levels corresponding to the eigenstates with even and odd parity, respectively. In panel (c), the lines simply indicate the energy levels and do not correspond to parity. The arrows illustrate the radiative decay transitions between eigenstates discussed later. Especially, the magenta arrows denote the symmetry-breaking-induced transitions which are forbidden in the symmetry-preserving case. In panels (b) and (c), the parameters are choose as $\omega_q = \omega_c$.
• Figure 2: Power spectra of emission $S(\omega_1)$ under weak incoherent pumping. (a) Power spectrum versus the angle $\theta$ and the sensor scanning frequency $\omega_1$. (b),(c) Line cuts of $S(\omega_1)$ for (b) $\theta=\pi/2$ and (c) $\theta=\pi/6$. The labeled peaks correspond to transitions between different eigenstates, summarized in Table \ref{['tab:tab1']}. The labels are color-coded to distinguish the different types of transitions: deep purple denotes conventional transitions between eigenstates with opposite parity, whereas blue denotes transitions induced by symmetry breaking. The inset in panel (b) shows an enlarged view of the region around peaks $\text{D}$ and $\text{E}$, highlighting the subtle peak $\text{E}$. Parameters are $\omega_q/\omega_c=1$, $g/\omega_c=0.3$, $\varepsilon/\omega_c=10^{-4}$, $\kappa/\omega_c=5\times10^{-3}$, $\gamma=\kappa$, and $\Gamma=\kappa$, $P_{\text{inc}}=0.1\kappa$.
• Figure 3: Second-order photon correlation functions $g_{\Gamma}^{(2)}(\omega_1, \omega_{10})$ vs sensor resonance frequency $\omega_1$ for (a) $\theta=\pi/2$ and (b) $\theta=\pi/6$, when one sensor is fixed at the fundamental transition frequency $\omega_{10}$. The light-blue background represents the antibunching regime ($g_{\Gamma}^{(2)}(\omega_1, \omega_{10})<1$), whereas the peaks (shaded in yellow and pink) indicate photon bunching ($g_{\Gamma}^{(2)}(\omega_1, \omega_{10})>1$). Several key dips are marked by blue dotted arrows. A key feature is the emergence of additional bunching peaks (pink) in panel (b), which are absent in panel (a). The parameters are the same as in Fig. \ref{['fig:spectrum']}.
• Figure 4: Third-order photon correlation functions $g_{\Gamma}^{(3)}(\omega_1, \omega_{2}, \omega_{3})$ vs sensor resonance frequency $\omega_1$. (a) $\theta=\pi/2$, with two sensors fixed at $\omega_2=\omega_{31}$ and $\omega_3=\omega_{10}$. (b) $\theta=\pi/6$, with two sensors fixed at $\omega_2=\omega_{21}$ and $\omega_3=\omega_{10}$. The light-blue background represents the antibunching regime ($g_{\Gamma}^{(3)}(\omega_1, \omega_{2}, \omega_{3})<1$), whereas the peaks (shaded in yellow and pink) indicate strong photon bunching ($g_{\Gamma}^{(3)}(\omega_1, \omega_{2}, \omega_{3})>1$). Several key dips are marked by blue dotted arrows. The parameters are the same as in Fig. \ref{['fig:spectrum']}.