Resonant Absorption of Bosonic Dark Matter in Molecules

We propose a new class of bosonic dark matter (DM) detectors based on resonant absorption onto a gas of small polyatomic molecules. Bosonic DM acts on the molecules as a narrow-band perturbation, like an intense but weakly coupled laser. The excited molecules emit the absorbed energy into fluorescence photons that are picked up by sensitive photodetectors with low dark count rates. This setup is sensitive to any DM candidate that couples to electrons, photons, and nuclei, and may improve on current searches by several orders of magnitude in coupling for DM masses between 0.2 eV and 20 eV. This type of detector has excellent intrinsic energy resolution, along with several control variables—pressure, temperature, external electromagnetic fields, and molecular species or isotopes—that allow for powerful background rejection methods as well as precision studies of a potential DM signal. The proposed experiment does not require usage of novel exotic materials or futuristic technologies, relying instead on the well-established field of molecular spectroscopy and on recent advances in single-photon detection. Cooperative radiation effects, which arise due to the large spatial coherence of the nonrelativistic DM field in certain detector geometries, can tightly focus the DM-induced radiative emission in a direction that depends on the DM’s velocity, possibly permitting a detailed reconstruction of the full 3D velocity distribution in our Galactic neighborhood, as well as further background rejection.

Popular Summary

Most of the matter in the Universe does not appear to interact with light, and has been detected only via its gravitational effects. The properties of this “dark matter” remain a mystery—its mass, spin, and nongravitational interactions are unknown. We propose an experimental detection strategy based on a process whereby dark-matter particles passing through the Earth resonantly excite a gas of molecules, stimulating them to emit light.

If the dark-matter particle has a mass in the electron-volt range or below typical molecular transition energies, it must be a boson, as dictated by the Pauli exclusion principle. The ensemble of dark matter can be thought of as a peculiar type of excitation source: one that is intense but weakly coupled; one with a large and almost isotropic spread of momenta but still in a narrow frequency band; one where the waves move slowly.

Most of the dark matter would fly through any experiment, but our two proposed experimental configurations could detect occasional resonant absorption of dark matter. The first and simplest setup looks for anomalous single-photon fluorescence in a shielded volume of some gas. The other setup uses a stack of slabs containing gases with alternating densities to pick up the cooperative radiation emitted by the molecules, which is unique to excitation by dark matter and even provides precise directional information.

A discovery of dark matter in this type of detector would be a watershed moment, allowing detailed precision studies of the dominant matter component of the cosmos and opening up a new field of dark-matter astronomy.

Figure 1

Angular dependence of the logarithmic intensity emitted by a molecular gas at large cooperation number $\overline{r}\gg 1$ in a slab-shaped container with dimensions ${\tilde{R}}_x={\tilde{R}}_y={10}^3$ and ${\tilde{R}}_z=1$, whose orientation is depicted by the blue prism. The intensity is exponentially peaked in the directions close to the normal vector of each of the faces, and it is largest, by far, along the $z$ direction, perpendicular to the two largest faces of the container. For illustrative purposes, we pick $v_0={10}^{-2}$ and $v_{\mathrm{lab}}=0$, while we also exaggerate the thickness of the slab.

Figure 2

Density plot of the logarithmic intensity as measured by a horizontal screen placed far above a thin slab in the $xy$ plane, zoomed in on the directions close to the normal vector defined by $\theta =0$, which pierces the screen at the location of the dot shown. The angular radius of the main emission region is the expected DM velocity dispersion measure $v_0\approx 0.78\times {10}^{-4}\mathrm{rad}$. The vector shows the angular offset of the cone’s center to the normal; its magnitude and direction are given by the projection ${\mathbf{v}}_{\mathrm{lab}\perp }$ of the average DM velocity ${\mathbf{v}}_{\mathrm{lab}}$ onto the $xy$ plane in the lab frame.

Figure 3

Electronic potential energy $U(R)$ curves for a (hypothetical) homonuclear diatomic molecule as a function of internuclear separation $R$ for five different electronic states, labeled by their quantum numbers, $X\text{−}{}^1{\mathrm{\Sigma }}_g^{+}$, $A\text{−}{}^1{\mathrm{\Sigma }}_u^{+}$, $a\text{−}{}^1{\mathrm{\Sigma }}_g^{+}$, $b\text{−}{}^3{\mathrm{\Sigma }}_u^{+}$, and $B\text{−}{}^1{\mathrm{\Pi }}_u$, respectively. Ticks in the potential well of each curve indicate vibrational energy levels, e.g., labeled from $v=0,\dots ,6$ in the fourth excited electronic state $B\text{−}{}^1{\mathrm{\Pi }}_u$. Exemplary vibrational wave functions ${\psi }_v(R)$ are plotted in gray (with arbitrary vertical units) for a few vibrational states, including the lowest three of the ground electronic state. Rotational energy splittings are not shown. The ground state $X\text{−}{}^1{\mathrm{\Sigma }}_g^{+}$ can be excited to the first excited state $a\text{−}{}^1{\mathrm{\Sigma }}_g^{+}$ by a monopole operator, and to $A\text{−}{}^1{\mathrm{\Sigma }}_u^{+}$ and $B\text{−}{}^1{\mathrm{\Pi }}_u$ by a dipole operator. A spin-dipole operator can also cause transitions to the spin-triplet state $b\text{−}{}^3{\mathrm{\Sigma }}_u^{+}$, in addition to those caused by a regular dipole operator.

Figure 4

Experimental setup: Bulk (top diagram) and stack (bottom diagram) configurations. Molecular gas (depicted by light blue volumes) is pumped into containers capable of supporting pressures up to 10 bar. In the bulk configuration, DM absorption events yield isotropic, single fluorescence photons, whose paths are indicated by thick red lines. Reflective coatings (shown as silver colored sheets) lining the container boundary retain the signal photons until they impinge onto a large-area photodetector, displayed as yellow tiles at the top. The stack configuration features a pattern of alternating molecular density in the form of multiple slabs. This container geometry and the spatial coherence of DM can produce cooperatively emitted photons nearly perpendicular to the slabs, making it possible to focus them onto a tiny photodetector by a lens. The photon direction is sensitive to the DM velocity vector projected onto the plane defined by the slabs. For illustrative purposes, we do not show shielding, cooling, or electromagnetic field and pressure control systems in either setup. We also left out the reflective coatings on the front and top faces of the bulk setup.

Figure 5

Figures of Stark frequency scanning that show how electric fields of order $B_e/{\mu }_e$ can shift rotational transition energy splittings in a ${}^1\mathrm{\Sigma }$ molecule by an $\mathcal{O}(1)$ amount, providing continuous coverage. Top panel: Rotational energy levels $E^{\mathrm{rot}}$ with quantum numbers $(J,M)$ as a function of electric field $E=|\mathbf{E}|$ for a diatomic molecule with rotational energy constant $B_e$ and permanent electric dipole moment ${\mu }_e$. Bottom panel: Rotational energy splittings ${\omega }_0^{\mathrm{rot}}$ for transitions with selection rules $\mathrm{\Delta }J=\pm 1$ and $\mathrm{\Delta }M=0$, $\pm 1$ (which includes E1-allowed transitions), as a function of electric field $E$. Color coding and the dashed pattern indicate the initial state and are consistent with the top panel. Only levels with $J\le 3$ are shown; Stark shifts become less dramatic with increasing $J$.

Figure 6

Dynamic rates of the two-level subsystem $|v=0,J=1⟩\leftrightarrow |v=1,J=0⟩$ in carbon monoxide (CO), as a function of pressure $P$. We plot the collisional broadening rate ${\gamma }_{\mathrm{col}}$ (green line), the coherent emission rate in the absence or presence of decoherence—$(\overline{r}-1){\gamma }_0$ as the dashed red lines and ${\eta }_{\mathrm{coh}}(\overline{r}-1){\gamma }_0$ as solid red—for two temperatures $T=100\mathrm{K}$ (thick line) and $T=77\mathrm{K}$ (thin line). Also shown are the incoherent radiative rate ${\gamma }_0$ (blue line), a benchmark natural radioactive decay rate ${\mathrm{\Gamma }}_{\mathrm{RD}}$ (dashed purple line) before an active veto, and the nonradiative quenching rate ${\gamma }_{\text{quench}}^{\mathrm{vib}}$ (orange line). The collisional width ${\gamma }_{\mathrm{col}}$ comes within a factor of 3 (30) from the rotational energy $B_e$ (dashed black line) at the boiling point pressure of 5.5 bar (0.6 bar) at $T=100\mathrm{K}$ ($T=77\mathrm{K}$). This shows that collisional broadening is an effective mechanism for frequency scanning. Notice that because the collisional rate dominates every other dynamical timescale, it reduces the coherent emission rate so that only 1 out of every $\mathcal{O}(1000)$ DM particles absorbed will produce a photon.

Figure 7

Rate of absorption ${\mathrm{\Gamma }}_{\mathrm{abs}}$ (solid green line) and rate of focused, coherent emission ${\mathrm{\Gamma }}_{\mathrm{rad}}^{\mathrm{S}}$ (solid red line) as a function of DM energy $\omega \simeq m$, in the phase I version of the stack configuration, filled with carbon monoxide (the ${}^{12}\mathrm{C}{}^{16}\mathrm{O}$ isotopologue) at a pressure of 5 bar, temperature of 100 K, and “stack enhancement parameter” $\overline{S}/m{R}_z\sim 10$ [cf. Eq. (7)]. The case study shown assumes a kinetically mixed photon with $\epsilon ={10}^{-12}$, zoomed in on the energy range around CO’s first vibrational absorption line $|v=0⟩\to |v=1⟩$ at ${\omega }_e=0.27\mathrm{eV}$, with rotational fine structure of splitting $2B_e$ clearly visible. This plot shows that the thermally occupied rotational levels of the ground state allow us to expand the frequency coverage of vibrational and electronic transitions. The dashed green line shows the absorption rate for ${}^{12}\mathrm{C}{}^{18}\mathrm{O}$, displaying the isotope shift on the rovibrational structure.

Figure 8

Reach for the kinetic mixing parameter $\epsilon$ of a hidden photon with mass $m_{{\gamma }^{\prime }}$. The $\mathrm{SNR}=1$ sensitivity estimates for the bulk configurations (BI and BII) are shown as thick blue bands, and those of the stack configurations (SI and SII) as thin red bands. Sensitivity curves are also shown for a single molecular species with the following assumptions: ${\mathrm{I}}_2$ (blue) in BI, HCl (blue) in BII, CO (red) in SI, and ${\mathrm{H}}_2$ (red) in SII. Solar emission constraints and DM-induced ionization limits in Xenon10 are shown as gray regions. Above the black line in the top right, hidden photon DM runs afoul of constraints on $N_{\mathrm{eff}}$.

Figure 9

Reach for the gauge coupling $g$ of a $B-L$ vector with mass $m_{{\gamma }^{\prime }}$. Gross sensitivity projections and exclusion regions are as in Fig. 8, with the addition of an exclusion region coming from searches for short-range fifth forces. We also indicate with the dashed green line the $B-L$ gauge coupling that would yield a Coulomb force between nucleons with a strength equal to that of gravity, and with the dotted black line the gauge coupling below which the $B-L$ vector is cosmologically stable against decays into three massless neutrino species.

Figure 10

Reach for the scalar dark matter coupling $d_{m_e}$ to electrons as a function of scalar mass $m_{\varphi }$. Sensitivity projections for the bulk (BI, BII) and stack (SI, SII) configurations are shown with assumptions as listed in Table 4. Gray exclusion regions depict constraints from stellar cooling processes in red giants (RG) and from short-range fifth-force searches. Parameter space below the upper green band is technically natural (i.e., not fine-tuned) for a 10-TeV cutoff, while the $H$ portal model [see Eqs. (134) and (135)] populates the region below the lower green band.

Figure 11

Reach for scalar dark matter couplings to photons ($d_e$), light quarks ($d_{{\widehat{m}}_q}$), and gluons ($d_g$) as a function of scalar mass. Labels are as in Fig. 10, except the cooling bound on $d_e$ comes from cooling processes in the Sun rather than red giants, and we also show constraints from telescope searches for scalar decays into two photons in the same plot. In addition, we indicate the experimentally allowed region for the scalar coupling $d_{\widehat{m_q}}$ of the QCD axion.

Figure 12

Reach for the pseudoscalar coupling $G_{aNN}$ to nucleons as a function of pseudoscalar mass $m_a$, for the configurations BII (thick blue band), SI, and SII (thin red bands). The green band indicates the typical mass-coupling relation between $m_a$ and $G_{aNN}\sim 1/f_a$ for the QCD axion. The gray exclusion region is a “robust” bound set by a combination of the neutrino burst duration of SN1987a and null observations of axion scattering events in water Čerenkov detectors after the same supernova.

Figure 13

Reach for the pseudoscalar coupling $G_{aee}$ to electrons as a function of pseudoscalar mass $m_a$ for the BI and BII configurations (thick blue bands) and the SI and II configurations (thin red bands). The green bands indicate the predicted coupling in two benchmark QCD axion models, namely, DFSZ (top) and KSVZ (bottom). The gray exclusion region is excluded by indirect determinations of white dwarf cooling rates.