Proposal for gravitational direct detection of dark matter

The only coupling dark matter is guaranteed to have with the standard model is through gravity. Here we propose a concept for direct dark matter detection using only this gravitational coupling. We suggest that an array of quantum-limited mechanical impulse sensors may be capable of detecting the correlated gravitational force created by a passing dark matter particle. We consider the effects of irreducible noise from couplings of the sensors to the environment and noise due to the quantum measurement process. We show that the signal from Planck-scale dark matter is in principle detectable using a large number of gram-scale sensors in a meter-scale array with sufficiently low quantum noise and discuss some experimental challenges en route to achieving this target.

Figure 1

Broad classification of viable dark matter models according to mass. In this work, we focus on dark matter candidates around $m_{pl}\sim {10}^{19}\mathrm{GeV}$ and above.

Figure 2

Left: kinematics of the DM-sensor scattering event, viewed from above the scattering plane. Center left: schematic of (a cross section of) the detector array, with suspended pendula used as mechanical resonators. As the DM passes through the array, it produces a correlated impulse on the sensors nearest its track. This diagram suppresses the readout mechanism (see Fig. 4), for which there are many potential implementations. Center right: simulation of an event on a $50\times 50$ plane of sensors. The colors represent impulses; blue are impulses to the left while red are to the right. The track of yellow red corresponds to the signal. Right: cartoon of single-sensor data stream, with an event.

Figure 3

Detectable DM event rates, with a variety of detector configurations. Thick lines correspond to number of events per year, assuming all DM particles have mass $m_{\chi }$. The $1/m_{\chi }$ falloff in the rate is due purely to number flux [see Eq. (8)]; by construction, all DM candidates passing through the detector are detected with $5\sigma$ confidence. Solid lines are labeled by the array lattice spacing (mm, cm, or 10 cm) of the detector and individual sensor masses (milligram in blue or gram in red). Dashed lines labeled by temperature (4 K or 10 mK) demonstrate the increased sensitivity of our scheme with improved environmental isolation. Here we are assuming background gas-limited environmental noise with the same fiducial parameters as in (7).

Figure 4

Top: circuit diagram depicting a backaction-evading velocity measurement. A pulse ${\gamma }_1$ imprints the mechanical position $x$ onto the light (described by its amplitude and phase quadratures $X$, $Y$). This is done twice, with opposite phase and a time delay $t_d$, leading to a velocity measurement. A second pulse ${\gamma }_2$ then enables a measurement of the impulse $\mathrm{\Delta }I$. Inset: concrete realization of a single velocity measurement, using a pair of optical ring cavities with a suspended mirror as the detector [14, 18, 51]. The output light is read out via interferometry. Since the photon imprints a momentum $+p$ in the first cavity and $-p$ in the second, there is no net forcing of the mechanics: the measurement produces no quantum backaction.