Collective Nuclear Polaritons with Coherent and Tunable Excitation Dynamics

Abstract

We propose collective nuclear polaritons formed by hybridizing a 229Th nuclear ensemble with a vacuum-ultraviolet cavity mode generated via four-wave mixing, achieving a collective light-matter coupling that scales as $\sqrt{N}$. In the strong-coupling regime the system displays vacuum Rabi oscillations, indicating the hybridization between cavity photons and nuclear excitations. In the superradiant regime, the stored excitation is released in a cooperative burst with peak intensity scaling as $N^2$. The emission lifetime shrinks from thousands of seconds to the millisecond scale and remains tunable. Detuning sweeps across the polariton avoided crossing allow adiabatic conversion of the photonic excitation into a collective nuclear excitation, enabling reversible quantum storage. Our results demonstrate that cavity-mediated nuclear polaritons enable deterministic lifetime engineering and coherent quantum storage in nuclear systems.

Figures (4)

• Figure 1: Schematic of collective nuclear polariton excitation. A pump field ($\omega_1$) enters a nonlinear medium and generates a VUV field via FWM ($2\omega_1 = \omega_2 + \omega_{\mathrm{VUV}}$, where $\omega_2$ is the idler field), which in turn drives a $^{229}\text{Th}$ ensemble to form hybrid nuclear polaritons. The system releases energy through a directional cavity-mediated collective emission.
• Figure 2: Dynamical and spectral signatures of collective nuclear polaritons. Time evolution of (a) the intracavity photon number $|\alpha|^2$ and (b) the nuclear excitation probability $\rho_{ee}$ for varying ensemble sizes $N$, illustrating vacuum Rabi oscillations. (c) Dependence of the Rabi frequency $\Omega_R/2\pi$ on $\sqrt{N}$. Red circles denote simulations; the dashed line represents the theoretical linear scaling $g\sqrt{N}$, giving a single-particle coupling strength of $g \approx 106.8$ Hz. The simulations assume a cavity decay $\kappa_{\mathrm{VUV}} = 1000$ Hz, fulfilling the strong-coupling criterion, with the corresponding working points marked in the phase diagram (Fig. \ref{['fig3']}). (d) Eigenenergy spectrum versus normalized detuning $\Delta/g\sqrt N$. The avoided crossing between the upper (blue) and lower (red) branches shows a vacuum Rabi splitting of $2g\sqrt {N}$. Dashed lines denote the bare cavity and nuclear states. (e) Photonic and nuclear fractions of the lower polariton. At resonance ($\Delta=0$), the photonic ($|C|^2$, solid blue) and nuclear ($|X|^2$, dashed red) components intersect at 0.5, indicating maximal light-matter hybridization.
• Figure 3: Collective phase diagram and critical dynamics of the cavity-nuclear ensemble. (a) Phase diagram as a function of the cavity decay rate $\kappa_\mathrm{VUV}$ (log scale) and the collective enhancement $\sqrt{N}$ (linear scale). The red dashed line denotes the strong-coupling threshold $4 g \sqrt{N} = (\kappa_{\mathrm{VUV}} + \gamma_-)$, separating underdamped vacuum Rabi dynamics from overdamped behavior, while the green dashed line marks the cooperativity boundary $C=1$. Blue, green, and orange regions denote weak coupling, collective emission (superradiance), and strong coupling, respectively. Magenta pentagons and blue squares indicate the working points used in the superradiance and Rabi-oscillation simulations, while open circles mark the critical transition points. (b) Intracavity photon number $|\alpha|^2$ and (c) the nuclear excitation probability $\rho_{ee}$ dynamics for fixed ensemble sizes $N=400$ (blue curves) and $N=800$ (red curves). Solid (dashed) curves correspond to evolution toward (away from) the superradiant regime across the strong-coupling boundary ($(\kappa_{\mathrm{VUV}}+\gamma_-) \leq 4g\sqrt{N}$).
• Figure 4: Coherent sweep dynamics of collective nuclear polaritons for an ensemble of $N=100$. (a) Instantaneous eigenenergies of the upper (UP) and lower (LP) polariton branches under the detuning sweep $\Delta(t)=\Delta_{0}\tanh(kt)$. The dashed curve denotes the bare photonic energy $\Delta(t)$. An avoided crossing with minimum gap $2\Omega$ appears at resonance. (b) Adiabatic regime ($k=300~\mathrm{s}^{-1}$). The system follows the LP branch, achieving near-complete photonic-to-nuclear conversion. (c) Nonadiabatic regime ($k=3.0\times10^{4}~\mathrm{s}^{-1}$). The fast sweep induces a diabatic transition to the UP branch, and the bare photonic population remains dominant after resonance. (d) Transition duration $\tau_{\mathrm{jump}}$ as a function of sweep rate $k$. The dashed line indicates the $k^{-1}$ scaling.