Searching for Dark Particles with Quantum Optics

We propose a way to use optical tools from quantum imaging and quantum communication to search for physics beyond the standard model. Spontaneous parametric down-conversion (SPDC) is a commonly used source of entangled photons in which pump photons convert to a signal-idler pair. We propose to search for “dark-SPDC” (dSPDC) events in which a new dark-sector particle replaces the idler. Though it does not interact, the presence of a dark particle can be inferred by the properties of the signal photon. Examples of dark states include axionlike particles and dark photons. We show that the presence of an optical medium opens the phase space of the down-conversion process, or decay, which would be forbidden in a vacuum. Search schemes are proposed that employ optical imaging and/or spectroscopy of the signal photons. The signal rates in our proposal scales with the second power of the small coupling to new physics, as opposed to light-shining-through-wall experiments, the signal of which scales with coupling to the fourth power. We analyze the characteristics of the optical media needed to enhance dSPDC and estimate the rate.

Popular Summary

Some of the well-motivated extensions of the standard model of particle physics include new light particles that interact with photons, such as dark photons or axionlike particles. This paper proposes a way to search for such new particles using the tools of quantum optics. The process is inspired by spontaneous parametric down-conversion (SPDC), in which a pump photon converts in a nonlinear optical medium to two photons, a signal and an idler.

In this technique, “dark SPDC” (dSPDC), the idler is replaced by a dark photon or axion, which is invisible and not detected. Still, its presence may be deduced by the presence and properties of the signal photon that is produced in the same process. dSPDC may have an advantage over other techniques in which a dark particle is both produced and detected. It opens up a new direction of research at the interface of particle physics and quantum optics.

Figure 1

A pictorial representation of the dSPDC process. A dark particle $\phi$ is emitted in association with a signal photon. The presence of $\phi$ can be inferred from the distribution of the signal photon in angle and/or frequency. We consider both the collinear (${\theta }_s=0$) and noncollinear (${\theta }_s\ne 0$) cases.

Figure 2

Left: the allowed phase space for SPDC (black), dSPDC with $m=0$ (red), and dSPDC with $m=0.1{\omega }_p$ (blue), shown as in the plane of signal emission angle as a function of frequency ratio ${\alpha }_{\omega }$. The indices of refraction here are $n_p=1.658$ and $n_s=1.486$ as an example, inspired by calcite. The inset shows an enlargement of the dSPDC phase space. Right: sketches depicting the momentum phase-matching condition $\mathrm{\Delta }\mathbf{k}=0$ for SPDC and dSPDC, with massless $\phi$. In both cases, we take the same ${\omega }_p$ and ${\omega }_s$. Due to the index of refraction for $\phi$ being essentially one and that for the idler photon being larger (say, approximately $1.5$), phase matching in dSPDC has a smaller signal emission angle than that of SPDC.

Figure 3

Solutions to the phase-matching conditions for the collinear dark-SPDC process for the signal-photon energy as a function of the mass of a dark particle $\phi$. This phase space is relevant for waveguide-based experiments. Both axes are normalized to the pump frequency. The two branches correspond to configurations in which $\phi$ is emitted forward (bottom) and backward (top).

Figure 4

The phase-space distribution $d^2\hat{\mathrm{\Gamma }}/d(\cos {\theta }_s)d{\alpha }_{\omega }$ for SPDC in arbitrary units. The distribution is strongly peaked along the region of phase space in which phase matching is achieved. We use $L=1$, ${\lambda }_p=L/10$, $n_p=2$ and $n_s=n_i=4$. These parameters are unrealistic in practice but allow for clear visualization of the distribution. The dashed lines show slices of fixed signal angle or energy.

Figure 5

The phase-space distribution $d^2\hat{\mathrm{\Gamma }}/d(\cos {\theta }_s)d{\alpha }_{\omega }$ in arbitrary units for the dSPDC process for $m=0$ (left) and $m=0.5{\omega }_p$ (right). The distributions are strongly peaked where the respective phase-matching conditions are satisfied. The other parameters are as in Fig. 4, with somewhat exaggerated indices of refraction to allow us to see the features in the distribution.

Figure 6

Slices of the phase-space distributions for SPDC and for dSPDC with different choices of the $\phi$ mass. On the left, we show angle distributions with fixed signal frequency, and on the right, we show frequency distributions for fixed signal angle. These distributions allow us to separate SPDC backgrounds from the dSPDC signal, as well as the dSPDC signal for different values of $m_{\phi }$. The distributions become narrower for thicker crystals, enhancing the signal to background separation power. For these distributions, we use $L=1\mathrm{ cm}$, ${\lambda }_p=400\mathrm{ nm}$ and for the refractive indices $n_p=1.49$ and $n_s=n_i=1.66$, inspired by calcite.

Figure 7

The regions in which the refractive indices $n_p$ and $n_s$ allow the phase matching with ${\alpha }_{\omega }\equiv {\omega }_s/{\omega }_p=\frac{1}{2}$ for the SPDC process (in this case, assuming that $n_i=n_s$) and dSPDC (in this case, assuming that $m/({\omega }_p)\ll 1$).

Figure 8

A sketch showing the overlap of the pump, signal, and dark particle (or idler) beams with the crystal. In general, it is desirable to maximize the integration length, which is defined by the overlap of the three beams and the crystal.