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

Abstract

We propose an array of the Ramsey-type interferometers using $N$ superposition states, $(|0\rangle+ |1\rangle)^{\otimes N}$, 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 $\sqrt{N} α$, where $α$ is the coupling of dark matter to the qubits, and thus the sensitivity to the coupling scales as $δα\sim 1 / \sqrt{N}$. For comparison, in the detection scheme based on the Rabi-type transition, $|0\rangle \to |1\rangle$, 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.