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

Abstract

We propose an array of Ramsey-type interferometers using $N$ superposition states, $(|0⟩+|1⟩{)}^{\otimes N}$, as a sensor to detect wave-like dark matter. After exposure to the dark matter wave, which induces coherent qubit transitions, the signal is the imbalance between the numbers of 0 and 1 outcomes. The signal-to-noise ratio in this scheme is proportional to $N\hat{I}{\pm }^2$, where $\hat{I}\pm$ is the coupling of dark matter to the qubits, and thus the sensitivity to the coupling scales as $\hat{I}´\hat{I}\pm \sim 1/\sqrt{N}$. For comparison, in the detection scheme based on the Rabi-type transition, $|0⟩\to |1⟩$, this scaling is achieved only when $N$ highly entangled 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 linear Paul traps as the sensor, the projected sensitivity to the coupling matches or surpasses existing laboratory, astrophysical, and cosmological bounds for $N\gtrsim 10^6$-$10^8$. We also evaluate its sensitivity to high-frequency gravitational waves. Our general framework should, in principle, be useful for other quantum sensing platforms.

21 pages, 3 figures