Quantum Enhanced Dark-Matter Search with Entangled Fock States in High-Quality Cavities

TL;DR

The paper introduces a quantum-enhanced dark-matter search that uses a network of N entangled, high-Q superconducting cavities prepared in an $m$-photon Fock state. By distributing and reconcentrating the excitation with an entanglement-distribution gate, and leveraging stimulated emission from the Fock state, the protocol achieves a scan-rate improvement that scales as $\mathcal{R}_\text{scan} \propto N^2(m+1)$ under realistic noise. The approach combines coherent dark-matter-induced displacements with photon counting to surpass the standard quantum limit, while remaining robust to decoherence, beam-splitter infidelity, and thermal backgrounds. The authors provide analytical and numerical analyses of signal, background, and SNR, and argue that current circuit-QED technology already supports the required components, offering a practical path toward faster, scalable searches for wave-like dark matter such as dark photons. The work suggests that large networks of entangled cavities, controlled with high-fidelity beamsplitters and qubit-enabled state preparation, could dramatically accelerate DM exploration across wide mass ranges.

Abstract

We present a quantum-enhanced protocol for detecting wave-like dark matter using an array of $N$ entangled superconducting cavities initialized in an $m$-photon Fock state. By distributing and recollecting the quantum state with an entanglement-distribution operation, the scan rate scales as $N^2(m+1)$ while thermal excitation is the dominant background, significantly outperforming classical single-cavity methods under matched conditions. We evaluate the robustness of our scheme against additional noise sources, including decoherence and beamsplitter infidelity, through theoretical analysis and numerical simulations. In practice, the key requirements, namely high-Q superconducting radio-frequency cavities that support long integration times, high-fidelity microwave beamsplitters, and universal cavity control, are already available on current experimental platforms, making the protocol experimentally feasible.

Figures (11)

• Figure 1: A sketch of our proposed system. An array of $N$ cavities is networked by high-fidelity beamsplitter operations. The first cavity in the array is also coupled to a qubit for the intial Fock state preparation, and readout.
• Figure 2: Quantum circuit for detecting DM with entangled Fock states. A prepared $m$-photon Fock state in the primary cavity is distributed across $N$ cavities by the entanglement-distribution gate $U_{\mathrm{ED}}$. During the integration time $\tau_{\text{int}}$, the dark-photon field displaces each mode by $D_i(\alpha)$. Applying $U_{\mathrm{ED}}^{\dagger}$ coherently maps the uniform displacement to the primary cavity, $D_1(\sqrt{N}\alpha)$, which is measured via the ancilla qubit, followed by reset.
• Figure 3: Effective circuit relations for the dark matter signal (left) and cavity heating during integration time (right), which is the dominant source of noise. The signal is coherent across the cavity network and thus scales with the number of cavities $N$, whereas the background is incoherent and does not scale. The non-heating effects can arise from photon loss $\gamma_{\downarrow}$, dephasing $\gamma_{\phi}$, and beamsplitter infidelity, which reduce sensing efficiency but do not introduce $N$-scaling of the background.
• Figure 4: The dependence of the signal-to-noise ratio on the single-shot integration time $\tau_\mathrm{int}$, for different choices of the initial Fock state $|m\rangle$, in a two-cavity setup. The cavities are at 7GHz, with decay time $T_\downarrow = 2.27ms$ (about 100 times $\tau_\textrm{DM}$), dephasing time $T_\phi = 22.7ms$, and a heating time of $T_\uparrow = 1.9ms$ (corresponding to an equilibrium temperature of 50mK). The SNR is evaluated for a total integration time of $\tau_\textrm{tot}= 1s$, assuming an DM-cavity coupling of $g= 73.6Hz$. Stars mark the optimal $\tau_{\text{int}}$ that maximizes the SNR, which shifts to shorter values as $m$ increases.
• Figure 5: Scan rate at 90% CL exclusion versus the number of cavities $N$ for several initial Fock numbers $m$, normalized to the single-cavity rate. Solid lines show the ideal prediction from Eq. \ref{['eq:scan_rate']} without loss. Dots represent Lindblad master equation simulations at optimally chosen $\tau_\text{int}$, with beamsplitter fidelity $\mathcal{F}_\textrm{BS}=99$% and other parameters the same as Fig. \ref{['fig:SNR_vs_m_main']}.