Coherent collective response in many-qubit systems for dark matter detection

We propose an array of the Ramsey-type interferometers using $N$ superposition states, $(\mathrm{\mid }0⟩+\mathrm{\mid }1⟩{)}^{\otimes N}$, as a sensor to detect wave-like dark matter. After the exposure to the dark matter wave, which induces the coherent qubit transitions, the signal is the imbalance between the probabilities of detecting 0 and 1. The signal-to-noise ratio in this scheme is proportional to $\sqrt{N}\alpha$, where $\alpha$ is the coupling of dark matter to the qubits, and thus the sensitivity to the coupling scales as $\delta \alpha \sim 1\mathrm{/}\sqrt{N}$. For comparison, in the detection scheme based on the Rabi-type transition, $\mathrm{\mid }0⟩\to \mathrm{\mid }1⟩$, this scaling is achieved only when highly entangled $N$ qubits are used. Since the Ramsey-type measurement does not require entangled states, one can consider much larger $N$ by simply placing a large number of qubits within the de Broglie wavelength of the dark matter. We demonstrate that, using trapped-ion qubits in a linear Paul trap as the sensor, the projected sensitivity to the coupling matches or surpasses existing laboratory, astrophysical, and cosmological bounds for $N\gtrsim {10}^6$. We also evaluate its sensitivity to high-frequency gravitational waves. Our general framework should, in principle, be useful for other quantum sensing platforms.